Models for Predictive Railway Traffic Management

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Pavle K

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Summary

The potential growth in transport demand in the next decade and

beyond requires a change from reactive to proactive traffic control

to maintain and improve the reliability of railway traffic. In order to

enable an anticipative approach to traffic management, it is necessary

to develop the tools for monitoring, prediction and optimisation of the

traffic operations. This thesis presents the models that can be used

as components for a decision support system for predictive traffic

management.

About the Author

Pavle Kecman received his M.Sc. degree from the University of Belgrade

in 2008. In June 2010 he joined the Department of Transport and Planning,

Delft University of Technology, as a Ph.D. candidate. He currently works as

a postdoctoral researcher at the Department of Science and Technology,

Linköping University in Sweden.

TRAIL Research School ISBN 978-90-5584-175-2

Pavle Kecman

Models for Predictive RailwayTraffic Management

Propositions

Pertaining to the dissertationModels for Predictive Railway Traffic Management

Pavle Kecman20 October 2014

1. Extracting and processing information from a real-time data streamrequires all typical steps for offline data analysis to be performedsimultaneously. (Chapter 3)

2. Having in mind the observed variability of running and dwell times,accurate modelling of the latter requires more attention in order tocreate valid railway planning and control models. (Chapter 4)

3. A data-driven approach outperforms microscopic simulation tools forreal-time prediction in terms of prediction quality, requirements forimplementation and computation speed. (Chapter 5)

4. A macroscopic rescheduling model that takes into account minimumheadway times in stations and overtaking constraints on open trackprovides fast solutions of good quality. Thus it is applicable to serve as adecision support system for traffic controllers. (Chapter 6)

5. In order to ensure sustainable mobility, the transport market should bestrictly regulated based on the proven (dis)advantages of certain modesfor certain trips.

6. The number of citations does not say much about the paper quality justlike the number of sold copies or tickets is not a quality indicator of amusic record or a movie.

7. George Orwell’s dystopian principle: “Who controls the past, controls thefuture” is turning out to be correct with the increasing impact of historicaldata on decision making processes in economy, finance, trade and retail.

8. Rational people push the world forward but it’s the irrational people thatmake it worth living in.

9. Copyright infringement has a better effect on arts and popular culturethan the restrictive intellectual property laws.

10. Everything looks bad if you think about it long enough.

These propositions are considered opposable and defendable and have beenapproved as such by the promotor Prof. Dr.- Ing. I.A. Hansen.

Models for Predictive Railway TrafficManagement

Pavle Kecman

Delft University of Technology, 2014

This research is supported by the Dutch Technology Foundation STW, which is partof the Netherlands Organisation for Scientific Research (NWO), and which is partly

funded by the Ministry of Economic Affairs.

Cover illustration: Aleksandar Martic

Models for Predictive Railway TrafficManagement

Proefschrift

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.Ch.A.M. Luyben,

voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 20 oktober 2014 om 10:00 uur

door

Pavle Kecman

Master of Science in Traffic & Transport Engineering

University of Belgrade

geboren te Belgrado, Servie

Dit proefschrift is goedgekeurd door de promotor:Prof. Dr.- Ing. I.A. Hansen

Toegevoegd promotor: Dr. R.M.P. Goverde

Samenstelling promotiecommissie:

Rector Magnificus voorzitterProf. Dr.- Ing. I.A. Hansen Technische Universiteit Delft, promotorDr. R.M.P. Goverde Technische Universiteit Delft, toegevoegd promotorProf. dr. ir. R.P.B.J. Dollevoet Technische Universiteit DelftProf. dr. L.G. Kroon Erasmus Universiteit RotterdamProf. Dr.-Ing. J. Pachl Technische Universitat BraunschweigProf. dr. C. Roberts University of BirminghamProf. dr. D. Mandic University of BelgradeProf. dr. ir. S.P. Hoogendoorn Technische Universiteit Delft, reserve

This thesis is the result of a Ph.D. study carried out from 2010 to 2014 at Delft Uni-versity of Technology, Faculty of Civil Engineering and Geosciences, Department ofTransport and Planning.

TRAIL Thesis Series no. T2014/5, the Netherlands TRAIL Research School

TRAILP.O. Box 50172600 GA DelftThe NetherlandsPhone: +31 (0) 15 278 6046Fax: +31 (0) 15 278 4333E-mail: [email protected]

ISBN 978-90-5584-175-2

Copyright cbe 2014 by Pavle Kecman.

This work is licensed under the Creative Commons Attribution-NonCommercial 3.0Unported License. It may be freely shared, copied and redistributed in any medium orformat. Transformation and building upon the material is permitted for non-commercialpurposes under the condition that the work is properly cited.

Printed in the Netherlands

”Nigdar ni tak bilo da ni nekak bilo, pak ni vezda ne bu da nam nekak ne bu.”- Miroslav Krleza (Khevenhiller, Balade Petrice Kerempuha)

Preface

All successful Ph.D. projects are the same, every problematic Ph.D. project is prob-lematic in its own way. The so-called Anna Karenina Principle, named after the firstsentence of the great book by Leo Tolstoy, applied in the context of a Ph.D. researchimplies that little can be said about a project that went according to plan during itswhole course. An interesting and well defined topic, good supervision and my pas-sion for railways and research made the previous four years an enjoyable and fruitfulperiod. Or is just my memory playing tricks because the work is finally completed?

The work presented in this thesis was carried out as a part of the joint project “Model-predictive railway traffic management” between the Department of Transport and Plan-ning (T&P) and Delft Centre for Systems and Control (DCSC) of the Delft Universityof Technology (DUT). The project was funded by the Dutch Technology FoundationSTW. The goal was to develop new models and a new model-predictive controller foranticipative management of railway networks. The work described in this thesis repre-sents the first step towards reaching this objective. It is planned to have the presentedmodels integrated in a closed-loop control approach that will be presented in a separatePh.D. thesis completed at DCSC.

There are many people who have directly and indirectly helped me to produce thisdissertation. My supervisors and colleagues deserve special gratitude for their helpand dedication. My direct supervisor Rob Goverde has been closely involved in thisresearch from the very beginning to the final approval of the thesis. He was alwaysavailable to help and I am very grateful for his contribution and guidance at the difficultpoints in my research. It was a great pleasure and an honour to work with him a learnfrom him. I would also like to thank my advisor Professor Ingo Hansen for his criticalpoint of view that was always followed by useful advice to help me improve my work.On a more general note, I am also grateful to him for the fact that his enthusiasmhelped to establish railway operations research as an independent scientific disciplinerepresented with the high quality journals and conferences.

I would furthermore like to thank the other people involved in the research project:Bart Kersbergen, Nicolas Weiss, Ton van den Boom and Bart De Schutter on behalfof DCSC. Keeping up to schedule was to a great extent helped by the fact that wepresented our main findings and research plans on a regular basis to the user commit-tee consisting of experts from academia and industry. The committee members: Bob

vii

viii Models for Predictive Railway Traffic Management

Jansen, Leo Kroon, Edo Nugteren, Alfons Schaafsma, Ello Weits, Jianxin Yuan helpeda lot with their comments, questions and advice. Direct support for this research wasprovided by ProRail, Dick Middelkoop in particular, who helped by providing the datasets needed to build and test our models.

Furthermore, I would like to thank Francesco Corman and Andrea D’Ariano for theirhelp and contribution to the part of this thesis related to real-time rescheduling. Work-ing with them at the early stage of my research was truly a lesson in efficiency, pre-cision and quality that helped me adopt such attitude in my work. I owe a lot ofgratitude to my dear colleagues from the rail group at T&P and the University of Bel-grade. Not a single part of this work remained undiscussed between us. From theproblem definition, via methodology and programming, to the clarity of the figures,they provided a useful feedback for each aspect at any time and place. I am very grate-ful to Daniel Sparing, Francesco Corman, Lingyun Meng, Egidio Quaglietta, NikolaBesinovic, Nadjla Ghaemi and Peca Jovanovic for their time and patience in manycasual brainstorming sessions. It was surely the most fun part of doing research. Fi-nally, I would like to thank all technical and administrative staff of T&P and TRAILResearch School for taking care of many practical issues, which allowed me to fullyfocus on the project.

During the last four years spent in the Netherlands I was lucky to be surrounded bymany wonderful people to rely on and have fun with at work and outside. My dearfriends in Delft, Rotterdam, The Hague, Amsterdam, Almelo and Groningen werethere for me to offer a good laugh and their advice and solution to all problems fromdoing laundry to weltschmertz and existential crises. Having them in my life is defi-nitely my most important achievement from this period. Having a delayed train is notthat bad if you’re in a good company. And of course, I am always most grateful to myfamily for their unreserved support and love that makes the physical distance betweenus seem so unimportant.

Pavle KecmanBelgrade, August 2014

Contents

Preface vii

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Railway traffic control in the Netherlands . . . . . . . . . . . . . . . 2

1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.1 Short-term traffic prediction . . . . . . . . . . . . . . . . . . 5

1.3.2 Network-wide traffic management . . . . . . . . . . . . . . . 6

1.3.3 Model-predictive control . . . . . . . . . . . . . . . . . . . . 7

1.4 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4.1 Research objective 1 – Monitoring and traffic state prediction 8

1.4.2 Research objective 2 – Rescheduling models for network-widetraffic control . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 Thesis contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.5.1 Monitoring and real-time traffic state prediction . . . . . . . . 12

1.5.2 Macroscopic models for network-wide traffic rescheduling . . 15

1.6 Thesis outline and scope . . . . . . . . . . . . . . . . . . . . . . . . 16

2 An overview of railway operation planning and control 19

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Terminology and basic concepts of railway traffic . . . . . . . . . . . 20

2.2.1 Railway timetable . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.2 Signalling and interlocking . . . . . . . . . . . . . . . . . . . 21

2.2.3 Blocking time theory . . . . . . . . . . . . . . . . . . . . . . 22

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x Models for Predictive Railway Traffic Management

2.2.4 Train position detection . . . . . . . . . . . . . . . . . . . . 24

2.2.5 Classification of train delays . . . . . . . . . . . . . . . . . . 26

2.2.6 Operational control of railway traffic and transport . . . . . . 26

2.3 Review of approaches for data mining of traffic realisation data . . . . 30

2.4 Review of approaches for process time estimation . . . . . . . . . . . 32

2.4.1 Running time estimation . . . . . . . . . . . . . . . . . . . . 32

2.4.2 Dwell time estimation . . . . . . . . . . . . . . . . . . . . . 33

2.4.3 Headway times . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5 Review of delay propagation analysis and prediction models . . . . . 35

2.5.1 Delay propagation analysis . . . . . . . . . . . . . . . . . . . 35

2.5.2 Identifying structural timetable errors and systematic delays . 37

2.5.3 Delay propagation models . . . . . . . . . . . . . . . . . . . 38

2.5.4 Models for delay prediction in real-time . . . . . . . . . . . . 41

2.6 Review of rescheduling models . . . . . . . . . . . . . . . . . . . . . 43

2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3 Process mining of train describer event data 51

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 Methodological framework of the process mining tool . . . . . . . . . 53

3.2.1 Process mining . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2.2 Process model . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.3 The Dutch train describer system . . . . . . . . . . . . . . . . . . . . 55

3.3.1 System architecture . . . . . . . . . . . . . . . . . . . . . . . 55

3.3.2 Data structure and information contained in log archives . . . 56

3.3.3 Shortcomings in TROTS log files . . . . . . . . . . . . . . . 57

3.4 Traffic monitoring on open track and in stations . . . . . . . . . . . . 58

3.4.1 Associating signal messages to train number steps . . . . . . 58

3.4.2 Logging of automatic block signal passing events . . . . . . . 59

3.4.3 Logging of station events . . . . . . . . . . . . . . . . . . . . 60

3.5 Train route recovery and route conflict identification . . . . . . . . . . 60

CONTENTS xi

3.5.1 Process mining train describer data . . . . . . . . . . . . . . 60

3.5.2 Main algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.5.3 Process discovery . . . . . . . . . . . . . . . . . . . . . . . . 64

3.5.4 Automatic identification of route conflicts . . . . . . . . . . . 65

3.5.5 Identification of hindering trains . . . . . . . . . . . . . . . . 65

3.5.6 Estimation of departure and arrival times . . . . . . . . . . . 65

3.6 Process mining tool . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.6.1 Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.6.2 Graphical user interface . . . . . . . . . . . . . . . . . . . . 67

3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4 Data analysis and estimation of process times 73

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.2 Methodological framework for statistical analysis . . . . . . . . . . . 75

4.2.1 Description of the data set . . . . . . . . . . . . . . . . . . . 75

4.2.2 Global model . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.3 Local model . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.3 Statistical learning methods . . . . . . . . . . . . . . . . . . . . . . . 77

4.3.1 Multiple linear regression . . . . . . . . . . . . . . . . . . . 77

4.3.2 Tree-based non-linear methods . . . . . . . . . . . . . . . . . 79

4.4 Process time estimates – global model . . . . . . . . . . . . . . . . . 81

4.4.1 Running time estimates derived from the global model . . . . 81

4.4.2 Dwell time estimates derived from the global model . . . . . 85

4.5 Process time estimates - local model . . . . . . . . . . . . . . . . . . 90

4.5.1 Estimation of running times over a particular block . . . . . . 90

4.5.2 Estimation of dwell times for a particular station . . . . . . . 93

4.6 Comparison of statistical models . . . . . . . . . . . . . . . . . . . . 95

4.6.1 Comparison of running time estimation models . . . . . . . . 95

4.6.2 Comparison of dwell time estimation models . . . . . . . . . 96

4.6.3 Comparison of prediction accuracy for scheduled processes . 96

4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

xii Models for Predictive Railway Traffic Management

5 Real-time prediction of train event times 101

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.2 Framework of the real-time prediction tool . . . . . . . . . . . . . . . 102

5.3 Microscopic graph based model . . . . . . . . . . . . . . . . . . . . 104

5.3.1 The graph model . . . . . . . . . . . . . . . . . . . . . . . . 104

5.3.2 Graph construction . . . . . . . . . . . . . . . . . . . . . . . 105

5.4 Computation of arc weights . . . . . . . . . . . . . . . . . . . . . . . 107

5.4.1 Running and dwell arc weights . . . . . . . . . . . . . . . . . 109

5.4.2 Headway and connection arc weights . . . . . . . . . . . . . 109

5.4.3 Online process time estimation . . . . . . . . . . . . . . . . . 110

5.4.4 Time loss due to route conflicts . . . . . . . . . . . . . . . . 110

5.5 Online prediction of event times . . . . . . . . . . . . . . . . . . . . 113

5.5.1 Prediction algorithm . . . . . . . . . . . . . . . . . . . . . . 113

5.5.2 Adjusting the running time estimates due to route conflicts . . 115

5.5.3 Adaptive adjustments of running time predictions . . . . . . . 116

5.6 Application on a case study . . . . . . . . . . . . . . . . . . . . . . . 118

5.6.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . 118

5.6.2 Description of the case study . . . . . . . . . . . . . . . . . . 118

5.6.3 Comprehensive analysis . . . . . . . . . . . . . . . . . . . . 119

5.6.4 Example of algorithm execution . . . . . . . . . . . . . . . . 122

5.7 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . 125

6 Rescheduling models for real-time traffic management in large networks 127

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.2 Macroscopic modelling of railway operations . . . . . . . . . . . . . 128

6.2.1 Timed event graphs . . . . . . . . . . . . . . . . . . . . . . . 128

6.2.2 Alternative graphs . . . . . . . . . . . . . . . . . . . . . . . 129

6.2.3 Conversion of timed event graphs to alternative graphs . . . . 132

6.2.4 Resources as building blocks of alternative graphs . . . . . . 133

6.2.5 Sequence-dependent setup times . . . . . . . . . . . . . . . . 136

CONTENTS xiii

6.3 Models examined . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6.3.1 Macroscopic models . . . . . . . . . . . . . . . . . . . . . . 137

6.3.2 Mesoscopic model . . . . . . . . . . . . . . . . . . . . . . . 141

6.3.3 Overview of the five models . . . . . . . . . . . . . . . . . . 141

6.4 Test case A: corridor Utrecht - Den Bosch . . . . . . . . . . . . . . . 141

6.4.1 Test case settings . . . . . . . . . . . . . . . . . . . . . . . . 142

6.4.2 Comprehensive evaluation . . . . . . . . . . . . . . . . . . . 144

6.5 Test case B: Dutch national railway network . . . . . . . . . . . . . . 146

6.5.1 Description of the tested instances . . . . . . . . . . . . . . . 146

6.5.2 Comprehensive evaluation . . . . . . . . . . . . . . . . . . . 147

6.5.3 Network-wide effects of reducing delay propagation . . . . . 149

6.6 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . 149

7 Conclusions 153

7.1 Summary of the main findings and contributions . . . . . . . . . . . . 153

7.1.1 Monitoring and traffic state prediction . . . . . . . . . . . . . 154

7.1.2 Network-wide traffic rescheduling . . . . . . . . . . . . . . . 157

7.2 Recommendations for future work . . . . . . . . . . . . . . . . . . . 158

Bibliography 161

List of acronyms 178

Summary 179

Samenvatting 183

About the author 187

TRAIL Thesis Series 189

xiv Models for Predictive Railway Traffic Management

List of Figures

1.1 Hierarchical structure of traffic control . . . . . . . . . . . . . . . . . 2

1.2 Railway map of the Netherlands . . . . . . . . . . . . . . . . . . . . 3

1.3 Workplace of a local traffic controller in Amsterdam . . . . . . . . . 4

1.4 Cascade MPC framework for traffic control . . . . . . . . . . . . . . 8

1.5 Research objectives integrated in a closed loop . . . . . . . . . . . . 9

1.6 Integration of requirements for real-time prediction tool . . . . . . . . 11

1.7 Flowchart of the thesis structure . . . . . . . . . . . . . . . . . . . . 16

2.1 Blocking time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Route conflict . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Blocking time stairways . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Infrastructure based train detection . . . . . . . . . . . . . . . . . . . 25

2.5 Regular time interval train detection . . . . . . . . . . . . . . . . . . 25

2.6 Structure and information flow within operational planning level . . . 27

2.7 Illustrative example of the parallel-shift prediction method . . . . . . 29

3.1 Process mining framework . . . . . . . . . . . . . . . . . . . . . . . 54

3.2 Events and processes in micro and mesoscopic models . . . . . . . . 54

3.3 Three-layer process model . . . . . . . . . . . . . . . . . . . . . . . 55

3.4 Screen shot of a TROTS log flle . . . . . . . . . . . . . . . . . . . . 59

3.5 Process mining TROTS data . . . . . . . . . . . . . . . . . . . . . . 61

3.6 Flowchart of the process mining algorithm . . . . . . . . . . . . . . . 63

3.7 Example network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.8 Observed area for the case study . . . . . . . . . . . . . . . . . . . . 67

xv

xvi Models for Predictive Railway Traffic Management

3.9 Graphical user interface . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.10 Train selection panel . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.11 Infrastructure selection panel . . . . . . . . . . . . . . . . . . . . . . 69

3.12 Time distance diagram . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.13 Blocking time diagram . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1 Regression tree for running time estimation . . . . . . . . . . . . . . 83

4.2 Relative running time prediction error depending on the tree size . . . 84

4.3 R2 of the running time model depending on the tree size . . . . . . . . 84

4.4 MSE of running time model depending on the number of trees . . . . 85

4.5 R2 of running time model depending on the number of trees . . . . . . 85

4.6 Regression tree for dwell time estimation . . . . . . . . . . . . . . . 88

4.7 Relative dwell time prediction error depending on the tree size . . . . 89

4.8 R2 of the dwell time model depending on the tree size . . . . . . . . . 89

4.9 MSE of the dwell time model depending on the number of trees . . . 89

4.10 R2 of the dwell time model depending on the number of trees . . . . . 90

4.11 Dependence of running time on delay (left) and box-plots of runningtimes for punctual and delayed trains (right) . . . . . . . . . . . . . . 91

4.12 R2 for prediction of running time on The Hague HS – Rotterdam corridor 92

4.13 Delay over corridor Leiden - Dordrecht for train line 2200 . . . . . . 92

4.14 R2 for prediction of dwell times on Leiden – Dordrecht corridor . . . 93

4.15 Dependence of dwell time on delay (left) and box-plots of dwell time(right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.16 Dependence of dwell time on scheduled departure time . . . . . . . . 94

4.17 Prediction error for dwell times of delayed trains . . . . . . . . . . . 95

4.18 Prediction error of running time estimation models . . . . . . . . . . 96

4.19 Prediction error of dwell time estimation models . . . . . . . . . . . . 97

4.20 Precision of dwell time and running time estimates . . . . . . . . . . 97

4.21 Precision of dwell time and running time estimates relative to sched-uled process time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.1 Monitoring and prediction components in the traffic control loop . . . 103

LIST OF FIGURES xvii

5.2 Space-based train separation . . . . . . . . . . . . . . . . . . . . . . 106

5.3 Time-based train separation . . . . . . . . . . . . . . . . . . . . . . . 106

5.4 An example of a mesoscopic DAG . . . . . . . . . . . . . . . . . . . 108

5.5 Time loss dependence on conflict duration: quadratic fit for short (up)and linear fit for long conflicts (down) . . . . . . . . . . . . . . . . . 112

5.6 An example of execution of Algorithm 2 . . . . . . . . . . . . . . . . 115

5.7 An example of route conflict prediction . . . . . . . . . . . . . . . . 117

5.8 A schematic example of adaptive prediction . . . . . . . . . . . . . . 117

5.9 Network and train lines for the case study . . . . . . . . . . . . . . . 119

5.10 Box plots of prediction error distributions for different prediction hori-zons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.11 Mean absolute prediction error depending on prediction horizon . . . 121

5.12 MAE comparison for adaptive and nonadaptive prediction . . . . . . 121

5.13 MAE of scheduled event times for a parallel shift strategy and the real-time prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.14 Time-distance diagram of predicted (at 7:13) and realised train paths . 123

5.15 Blocking time diagram predicted at 7:13 (up), realized blocking timediagram (down) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.16 Effects of adaptive prediction . . . . . . . . . . . . . . . . . . . . . . 125

6.1 Graph representation of resources with infinite capacity . . . . . . . . 133

6.2 Graph representation of resources with infinite capacity and headwayconstraint (left) and a possible selection (right) . . . . . . . . . . . . 134

6.3 Graph representation of resources with infinite capacity and FIFO con-straint (left) and a possible selection (right) . . . . . . . . . . . . . . 135

6.4 Graph representation of resources with finite capacity (left) and a pos-sible selection (right) . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6.5 Example of sequence-dependent setup times . . . . . . . . . . . . . . 136

6.6 Layout of the illustrative example . . . . . . . . . . . . . . . . . . . 137

6.7 Illustrative example - Model 1 . . . . . . . . . . . . . . . . . . . . . 138


6.9 Incompatibility graph of illustrative example . . . . . . . . . . . . . . 140


xviii Models for Predictive Railway Traffic Management


6.12 Layout of infrastructure and main stations . . . . . . . . . . . . . . . 142

6.13 Timetable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

6.14 Dutch railway network considered (in black), with main stations . . . 147

6.15 Maximum secondary delays without (left) and with (right) rescheduling 150

List of Tables

2.1 Summary of presented approaches for real-time rescheduling . . . . . 48

3.1 Train number messages generated by TROTS . . . . . . . . . . . . . 56

4.1 Summary of the training set for running time estimation . . . . . . . . 81

4.2 Summary of the LTS model for running time prediction . . . . . . . . 82

4.3 Summary of the training set for dwell time estimation . . . . . . . . . 86

4.4 Summary of the LTS model for dwell time prediction . . . . . . . . . 87

5.1 Model size for different prediction horizons . . . . . . . . . . . . . . 119

6.1 Operational constraints in models . . . . . . . . . . . . . . . . . . . 142

6.2 Quantitative assessment of the 5 models . . . . . . . . . . . . . . . . 144

6.3 Difference in orders between the mesoscopic and each macroscopicmodel. Direction Ht→ Ut . . . . . . . . . . . . . . . . . . . . . . . 146

6.4 Characteristics of the network-wide test case . . . . . . . . . . . . . . 148

6.5 Quantitative assessment of the macroscopic models on test case B . . 148

xix

xx Models for Predictive Railway Traffic Management

Chapter 1

Introduction

1.1 Background

A railway system integrates infrastructure, rolling-stock, staff and a set of strict op-erational rules into a functional system for transporting passengers and goods. Eachof the afore mentioned subsystems represents a very complex structure of intercon-nected entities. Following the directive of the European Commission (2001), a numberof railway systems in Europe are horizontally separated into infrastructure managers(IMs) and train train operating companys (TOCs). This reform was introduced in orderto improve the competitiveness and modal share of railways on the transport market(C. Nash, 2010). The IM is responsible for management and maintenance of railwayinfrastructure, allocating railway capacity (train paths) to TOCs and organizing andcontrolling traffic along the network. On the other hand, the main task of a TOC isplanning, operation and control of passenger and freight transport.

An IM has the task to coordinate train path requests of TOCs, allocate infrastructure ca-pacity through a timetable in the tactical planning stage, and control traffic in real timeat the operational planning level. A timetable in railway traffic is the master schedulethat reflects the relationship between the supply and demand in the railway sector. Itcontains the scheduled process time of each operation, i.e., a train dwelling in a sta-tion, running between two scheduled stops, passenger transfers, rolling-stock or crewconnections, etc. However, daily variations and unforeseeable disruptive events mayrender the planned timetable infeasible. Such events are inevitable in modern railwaysystems with many interacting processes that depend on human behaviour, technicaldevices, and the environment. In busy and heavily utilized networks, a deviation fromthe planned path of a single train can easily propagate as a secondary delay to othertrains that run over the same infrastructure or have a planned passenger, rolling-stockor crew connection. Prevention and minimisation of delay propagation, and main-taining timetable feasibility are the main responsibilities of operational traffic control(Pachl, 2009).

Railway traffic control is typically hierarchically structured into a local and a global

1

2 Models for Predictive Railway Traffic Management

(network) level (Figure 1.1). Local traffic control has the task to perform all safetyrelated actions, set routes for trains, predict and solve conflicts, and control processesthat take place on the designated part of infrastructure (Kecman, Goverde, & Van denBoom, 2011). A train typically crosses multiple traffic control areas controlled bydifferent local controllers (signallers and/or dispatchers). The global level (regional ornetwork controllers) comprises the supervision of the state of traffic on the networklevel, detection of deviations from the timetable, resolution of conflicts affecting theoverall network performance, handling failures and events that may have big impacton performance indicators, etc.

Networkcontroller

Localcontroller n

Localcontroller 2

Localcontroller 1

Figure 1.1: Hierarchical structure of traffic control

1.2 Railway traffic control in the Netherlands

The railway system in the Netherlands is a typical example of a highly interconnectedtransport and traffic network. It is one of the most densely utilized networks in theworld (Hansen, Wiggenraad, & Wolff, 2013). More than 3000 km of railway tracks thatconnect 404 stations in virtually all cities in the country (Figure 1.2), are managed bythe infrastructure manager ProRail (ProRail, 2013). With regard to the traffic volumes,i.e., the number of trains, train kilometres and the amount of passengers and goodstransported per line kilometre, the Dutch railway network performs almost as wellas Switzerland and Japan (Wolff, 2011). At any moment in time during peak hours,there are approximately 400 running trains, 93% of which are passenger trains, mainlyoperated by the national operator Netherlands Railways (NS) (NS Group, 2013).

In the heavily utilized Dutch network, trains are scheduled with short headway timesand small time supplements using the advanced timetabling tool Design of NetworkSchedules (DONS) (Hooghiemstra, Kroon, Odijk, Salomon, & Zwaneveld, 1999). Dueto dense traffic and interconnected services, delays and incidents that occur in onepart of the network may easily propagate through the whole network (Goverde, 2007).Therefore, operational traffic control has an important task to maintain the plannedschedule and recover from disruptions as quickly as possible in order to minimisedelays and increase traffic reliability.

Railway traffic control in the Netherlands is divided in two levels with 13 local trafficcontrol centres (Figure 1.3) and a network control centre Operational Control CentreRail (OCCR). Timetable updates are negotiated and determined in the OCCR between

Chapter 1. Introduction 3

In use for passenger and cargo trainsCargo trains only

Figure 1.2: Railway map of the Netherlands

the network traffic controllers of ProRail and transport controllers of NS. The networktraffic controllers receive information about the current delays and traffic conditionfrom the local level. Their task, in cooperation with the TOC, is to coordinate thedispatching measures that would decrease deviations from the planned timetable onthe network level. The controllers on behalf of NS verify that the proposed updatesare feasible with respect to rolling-stock and crew circulation plans. Finally, timetableupdates are transmitted to the local level for implementation.

Local traffic control centres are staffed with signallers, who are in charge of controllingthe signals and setting routes in stations, and dispatchers, who observe and supervisetraffic conditions and resolve conflicting train routes. In order to manage the complextasks of controlling dense traffic, controllers and signallers are supported by computertools for traffic monitoring, remote control of signals and switches, and automatic routesetting (Renkema & Van Visser, 1996). Process plans containing the planned routesand schedules for each train are transmitted to the traffic control centres one day inadvance. Train positions are monitored and reported by the train describer systemTrain Tracking and Observation System (TROTS). TROTS messages are received bythe traffic control system Verkeersleiding (VKL) that compares the train arrival anddeparture times with the daily process plan. Train delays are derived by the VKLsystem at home and exit signals, adjusted with a fixed correction term and rounded to


full minutes.

Figure 1.3: Workplace of a local traffic controller in Amsterdam (Source: ProRail,photo by Jos van Zetten)

The dispatching support system Procesleiding (PRL) is provided with the process planand actual train delays from VKL. It comprises the command and monitoring inter-face with the signalling and interlocking system. Traffic is visualised in the form of adynamic planned time-distance diagram. PRL is furthermore equipped with an auto-matic route setting system Automatische Rijweginstelling (ARI), which sets the routesfor trains according to the actual process plan and train delays (Berends & Ouburg,2005). Route conflicts are resolved according to the first-come-first-served principlebased on the current train positions or according to the relative train order definedin the timetable. Signallers may also use PRL to set the routes manually in order tomanage disruptions and resolve conflicting routes in the process plan. However, theyhave to rely on their own experience and a set of predetermined what-if scenarios.More details about the Dutch railway system and practice in traffic control are givenby Goverde (2005).

1.3 Motivation

While a timetable is carefully planned a year in advance using the sophisticated math-ematical models, the daily operational control of disruptions and delays still relies pre-dominantly on the predetermined rules and experience and skills of personnel. Traf-fic controllers do not commonly have any intelligent support tools such as short-termtraffic prognosis, conflict detection and prediction or optimal dispatching. Moreover,working in a preventive manner is poorly supported and train traffic controllers are usu-ally restricted to just solving problems as they occur (Kauppi, Wikstrom, Sandblad, &Andersson, 2005).


1.3.1 Short-term traffic prediction

Signallers typically do not have any intelligent decision support system to estimatethe expected running times. In the current Dutch practice, their situational awarenessabout current train delays is further limited due to the imprecision in the measurementsof actual delays. Local traffic control usually takes the expected arrival delay equal tothe current upstream delay as they have no information about the possible recoverytimes (except from experience) (D’Ariano, 2008). This method neglects the fact thatsome trains make up for their delays by running in the maximum performance regimeand exploiting the running time supplements incorporated in the timetable. On theother hand, other trains may get even more delayed due to a possible time loss in routeconflicts.

Delay propagation could be prevented or reduced if the traffic was managed proac-tively, i.e., if controllers had a reliable prediction of a route and connection conflictwith a possibility to prevent it. The main advantage of predictive traffic managementis that the traffic controllers can anticipate the occurrence of conflicts so that they haveenough time to prevent them using a conflict resolution method. Potential conflict-ing train paths in the current process plan need to be predicted in advance based onthe accurate monitoring of train positions, speed and infrastructure conditions such astemporary track or speed restrictions that can affect the process times. As a result,unscheduled stops before red signals could be avoided by resolving such conflicts inadvance using e.g. rerouteing, changing the train order at the conflict point, retimingor giving speed advice to the drivers.

Several approaches to traffic state prediction can be found in the current practice oracademic literature. Macroscopic models (Berger, Gebhardt, Muller-Hannemann, &Ostrowski, 2011; Hansen, Goverde, & Van der Meer, 2010) focus on predicting onlythe event times in stations (departures, arrivals and through rides). That way, the trainseparation principles cannot be accurately modelled and the route conflicts on opentrack sections (between two stations) cannot be predicted. On the other hand, the meso-scopic prediction models that are integrated in the traffic control systems such as RailControl System (RCS) in Switzerland (Dolder, Krista, & Voelcker, 2009), Styrningav Tag genom Elektronisk Graf (STEG) in Sweden (Isaksson-Lutteman, 2012) or theshort-term prediction module of the rescheduling system Railway traffic Optimizationby Means of Alternative Graphs (ROMA) (D’Ariano, 2008) may support the trafficcontrollers in conflict detection. Every signal passing event is explicitly included inthose models. However, the estimates of running and dwell times are computed inde-pendently from the actual traffic state. Different performance regimes between delayedand punctual trains, the impact of peak hours or behavioural factors are not consideredin the predictions. We use the terminology and definition of macroscopic and micro-scopic level of modelling described by Radtke (2008) and Schlechte, Borndorfer, Erol,Graffagnino, and Swarat (2011). Macroscopic models consider only station eventssuch as departures, arrivals and through rides. On the other hand, a train run is mod-elled microscopically on a detailed level of track-clear detection sections. In this aspect


we also define a class of mesoscopic models that model traffic on the level of blocksections and station routes. The different levels of modelling are explicitly defined inSection 3.5.

1.3.2 Network-wide traffic management

The current practice in operational control of disruptions and delays still relies pre-dominantly on the predetermined rules and experience and skills of personnel. Neitherlocal nor network traffic controllers have a reliable supporting tool to make despatch-ing decisions, predict their effect and evaluate them. For local traffic controllers, thatoften leads to creating new conflicts in the adjacent areas and suboptimal effects onthe network wide level. Even the advanced, recently developed tools that can pro-duce optimal solutions for traffic disruptions for a single traffic control area (Caimi,Fuchsberger, Laumanns, & Luthi, 2012; D’Ariano, Pranzo, & Hansen, 2007) or mul-tiple areas (Corman, D’Ariano, Pacciarelli, & Pranzo, 2012b) are not able to tacklelarge, network-wide instances, due to the demanding computational requirements ofinter-area coordination (Corman, D’Ariano, Pacciarelli, & Pranzo, 2014).

A decision support system for network-wide traffic management is required to con-tinuously supervise traffic on the network and create network-optimal updates to thetimetable, that can be used as a reference master schedule by the local control level.Due to a high combinatorial complexity of the train rescheduling problem (Tornquist,2006) the tools developed so far are not directly applicable for large and busy net-works. An important requirement for real-time railway applications is the knowledgeof the actual train positions, speed and the time needed for computing the solution,perception, decision and subsequent execution of the dispatching measure (e.g. lockof signal or set-up of a new route). A feasible or (near) optimal solution has to beproduced and implemented before it is outdated. In other words, the computation timemust not exceed the validity of prediction of the traffic state that is given as an input tothe rescheduling problem (Luthi, 2009).

Simplifications to the existing microscopic and mesoscopic tools that reduce the prob-lem complexity were therefore required for applications on the level of national net-works. A series of macroscopic models was developed that do not regard all capac-ity constraints on open track sections and in station areas (Tornquist, 2007; Van denBoom & De Schutter, 2007). Another stream of research was directed to so calleddelay management with the purpose to optimise passenger delays by controlling theplanned passenger transfer connections (Dollevoet, Huisman, Schmidt, & Schobel,2012; Schachtebeck & Schobel, 2010; Schobel, 2007). However, these macroscopicmodels for rescheduling were tested mostly on subnetworks of a national network orlarge urban networks. Therefore, the problem of controlling railway traffic on the levelof national network still remains unsolved.

An important aspect with high impact on applicability of the existing reschedulingtools in practice is the way they handle uncertainty. Running and dwell times are in


practice characterised by variability. Moreover, the interdependence of train runs mayincrease the uncertainty of delays in future. Apart from the recent contributions di-rected at non-anticipative delay management (Bauer & Schobel, 2014; Gatto, 2007),other rescheduling models assume full knowledge of current delays and their propaga-tion (with or without any rescheduling actions) which a limitation for practical appli-cation. For that reason, the accuracy of delay predictions is very important for validityof offline rescheduling models.

1.3.3 Model-predictive control

A possible way to model and optimize railway traffic control and overcome the prob-lem of uncertainty is through a closed-loop control paradigm, called model-predictivecontrol (MPC) (Maciejowski, 2002). The essential characteristic of the proposed frame-work is that it suggests proactive and anticipative (in contrast to reactive) traffic man-agement. Real-time information can be used to predict the occurrence of potentialconflicts. Moreover, delay propagation, resulting from route conflicts and plannedconnections, is prevented by computing optimal control actions.

The theoretical framework of the closed-loop railway traffic control is presented inFigure 1.4. A cascade control system is used to model the hierarchical relationship be-tween the global and a local control level Luthi (2009). Trains are operated accordingto a timetable and a daily process plan. Due to inevitable disturbances and deviationsfrom the planned schedule, train runs need to be continuously monitored. By moni-toring we assume keeping track of all performance indicators such as the actual trainpositions, delays, realised running and dwell times of all trains, etc. Monitoring there-fore provides the actual traffic state that can be used to predict the future evolutionof traffic on the network. A predictive traffic model continuously provides local con-trol level with the information about the expected traffic conditions. It can further beused to evaluate the impact of traffic control actions. In case of larger disruptions thatmay affect the traffic in a wider area, network traffic controllers can use the predictionmodel to optimise the traffic on the network, compute the network-optimal timetableupdates and transmit them as a reference to the local level. That way all traffic controlactions on the local level will lead to the network-optimal traffic state.

MPC has been implemented on the station level by Caimi et al. (2012) and on the levelof a corridor by Quaglietta, Corman, and Goverde (2013). Whereas the reschedul-ing models embedded in these approaches can efficiently control traffic in (multiple)control areas, the prediction component relies on the theoretical estimation of runningtimes and minimum dwell times. Variability of the process times is therefore not incor-porated in predictions and prediction accuracy has not been tested against the realisedtrain event times. Moreover, due to high computational requirements, these approachesare not directly applicable for controlling traffic on the level of national network.


Prediction

TimetableMonitoring

Localcontroller

Networkcontroller

Ref

eren

ce

Reference

Railway operations

Figure 1.4: Cascade MPC framework for traffic control

1.4 Thesis objectives

The main objective of the research presented in this thesis is to develop the systemsfor monitoring, traffic state prediction and network-wide rescheduling that can be em-bedded in the cascade MPC framework presented in the previous section. The mainobjective is divided into two research objectives:

• Research objective 1 (RO1) – Develop a tool for monitoring and traffic stateprediction

• Research objective 2 (RO2) – Develop a macroscopic model for network-widetraffic control

Research objectives integrated in a feedback loop are illustrated in Figure 1.5. Trainpositions are reported by a train describer system. The system for monitoring andtraffic state prediction (RO1) uses the live stream to determine the actual and futuretraffic conditions. In case of deviations with impact on a large part of the network, arescheduling tool (RO2) can produce a network-optimal timetable update as the newreference for railway operation.

1.4.1 Research objective 1 – Monitoring and traffic state predic-tion

The first research objective in this thesis is to develop a system for monitoring andtraffic state prediction. A way to overcome the drawbacks of the current practice andthe existing tools for monitoring and short-term traffic prediction (§1.3.1) emergedwith the availability of historical traffic realisation data. A real-time stream of raw traindescriber data can be processed in a way that extracts the actual traffic conditions in


the network: train positions, accurate estimates of current delays and realised runningand dwell times. Moreover, the archives of event logs can be used to learn how trainsbehave depending on the traffic conditions. The variability of process times can thusbe explained by isolating the factors with a high impact on the corresponding processtime. Estimates of future process times depend on the current or predicted valuesof explanatory variables. Therefore, the predictions will incorporate the empiricallydetermined variation of process times due to e.g. driving style, passenger behaviour orpeak hours.

In order to develop a system for for monitoring and traffic state prediction, a numberof requirements needs to be fulfilled.

The first requirement is to develop a data processing tool consisting of a detailedprocess model of railway traffic and an environment comprising the objects that rep-resent the infrastructure elements and trains. The archives of event logs of the Dutchtrain describer systems have already been used for reconstructing the realised trainpaths (Goverde & Hansen, 2000) and identifying route conflicts (Daamen, Goverde,& Hansen, 2008). However, the changes in the data structure and system architecturerequire a fundamentally different approach. Such environment should be compatiblewith an online stream of train describer messages. All objects need to be updated inreal time, thus providing the current state of traffic in order to raise the situationalawareness of controllers. Moreover, the data processing tool needs to be applicable forex post processing of traffic realisation data.

The second requirement is to derive robust estimates of process times. The appli-cation of the data processing tool results in the clean, structured data that are preparedfor analysis. The earlier efforts in punctuality analysis (Goverde, 2005; Yuan, 2006)focused on computing the descriptive statistical parameters and deriving probabilitydistributions. The resulting distributions can be used for an ex ante timetable analysisand development of stochastic models (Buker & Seybold, 2012; Medeossi, Longo, &

Liveydataystream

Monitoringyandyprediction

(RO1)

Actualyandyfutureytrafficystate

Networkywiderescheduling

(RO2)

Railwayoperations

Figure 1.5: Research objectives integrated in a closed loop


de Fabris, 2011). However, in order to develop the predictive models, it is necessaryto determine a set of explanatory variables and quantify their impact on process times.The aim is therefore to apply statistical predictive modelling on a training set of histor-ical traffic realisation data. The predictive models can be used to compute the estimatesof process times with respect to the actual values of explanatory variables that reflectthe state of the traffic on the network. An important requirement in predictive mod-elling of process times is that the resulting process time estimates need to be robustto noise, missing data and the outliers in the real-time data stream. The robustnessof the models is considered as one of the key criteria for selection of the appropri-ate statistical learning technique (§4.3). Robust estimates and coefficients that reflectthe dependence of process times on explanatory variables are stored in a database ofhistorical data.

The third requirement is to build a real-time prediction tool. A live stream of traindescriber data can be processed with the processing tool and give the actual state of thenetwork. Given the information on the current train positions, actual delays, and the re-alised running and dwell times, the robust estimates of process times can be computedin real time using the predefined predictive models. However, accurate modelling ofdependencies between processes of a single train as well as among multiple trains isrequired in order to predict traffic in large networks over long prediction horizons. Thethird requirement is therefore to create a fast prediction algorithm that calibrates therealistic traffic model in real time based on the current (future) traffic condition, andestimates the realisation times of all events within a prediction horizon.

The integration of the three requirements defined to reach the first research objective inthis thesis is illustrated in Figure 1.6. The approach consists of two parts. The offlinepart (dash-dot box) comprises data mining of a training set of raw train describer dataand creating a database of historical traffic realisation data. The online part (dashedbox) processes the live data stream, determines the traffic conditions in the network andpredicts the future traffic state using the historical database. Note that the processingtool can be used in both parts of the tool.

1.4.2 Research objective 2 – Rescheduling models for network-wide traffic control

The second research objective in this thesis is to develop and validate a macroscopicrescheduling model that can be applied for optimal control of traffic in large and heav-ily utilised networks. An approach of representing the railway rescheduling problemas a job-shop scheduling problem modelled with alternative graphs has been devel-oped by Mascis and Pacciarelli (2002) and Mascis, Pacciarelli, and Pranzo (2002). Ina series of improvements of the solution procedure, the model has been successfullyapplied for optimal control of traffic in station areas (Mazzarello & Ottaviani, 2007),on a corridor (D’Ariano, Pranzo, & Hansen, 2007) or in multiple traffic control areas(Corman et al., 2012b). However, the problem of controlling country-wide traffic is


Data processingLive data stream

Process timeestimates

PredictionDatabase

Future traffic state

Actual traffic state

Online Offline

Training data set

Figure 1.6: Integration of requirements for real-time prediction tool

still open since the coordination of local areas is hard to tackle within a short time andthere are multiple interdependencies between trains across the whole network. There-fore, the granularity of the alternative graph model needs to be modified in order tobecome applicable to problems of rescheduling trains on a large scale network-widelevel.

An important objective of this work is to search for a compromise between the precisemodelling of railway capacity constraints and a reasonable time to compute the alter-native solutions for the large scale railway traffic management instances. A suitablechoice of granularity of the macroscopic model is crucial in order to find the balancebetween limiting the problem complexity and maintaining the feasibility of producedsolutions.

1.5 Thesis contributions

This section presents the main theoretical, methodological and practical contributionsof the research project presented in this thesis. As outlined in the previous section,the research focused on studying, extending knowledge and improving the two mainaspects of operational traffic control.


1.5.1 Monitoring and real-time traffic state prediction

Data processing tool

The presented work on fulfilling this requirement provides an insight into data struc-ture and system architecture, and into the advantages and drawbacks of using the newDutch train describer system TROTS for traffic performance analysis. The previouslydeveloped algorithms for processing train describer event data (Goverde & Hansen,2000) and automatic conflict identification (Daamen et al., 2008) have been taken asa starting point in developing the new data processing tool. However, the new datastructure implemented in TROTS required a fundamental modification of the existingalgorithms. The tool is developed in an object-oriented environment which makes itsuitable for real-time application in monitoring train movements over the network. Inother words the tool is able to process large data sets in short time, thus it is applicablefor processing live data streams as well as large archives of traffic realisation data.

An important contribution is a data mining algorithm that can learn the mutual depen-dence between track sections and signals implemented in signalling and interlockingsystems from the TROTS data. This allows straightforward coupling of signal as-pect changes to the train numbers that have caused them, since TROTS data structuredoes not reveal a connection between messages coming from signals and train num-ber messages. Moreover, the automatic block signals on open tracks between stationsare not logged. This problem has been overcome by incorporating the signalling andinterlocking logic in the data mining algorithm, thus enabling accurate monitoring orreconstruction of the realised train paths even in these ‘dark territories’.

The methodology of process mining (Van der Aalst, 2011) has been applied for thefirst time for mining the train describer event data. This required a development of a3-level process model that reflects the majority of microscopic operational constraintsof railway traffic. The work resulted in a software tool for automatic recovery of trainpaths and route conflict identification. Application of the developed tool on a set oftrain describer data significantly increases the precision of delay estimates and enablesdistinction between primary and secondary delays.

The tool is equipped with a graphical user interface that simplifies analysis of the re-alised or actual traffic conditions. Traffic data for a particular corridor or station can beselected and visualised to enable the analyst to focus on a specific instance. Moreover,the tabular output of occupation and blocking times of infrastructure elements can beexported and used for analysis of process times and realised capacity utilisation. Re-alised train paths and route conflicts are visualised using time-distance and blockingtime diagrams.

The main contributions are summarised in the following list:

• process mining algorithm for TROTS data archives and live data stream


• recovery of process times on the level of signals and block sections in stationareas and open tracks

• automatic identification of route conflicts in station areas and open tracks

• computation of delays for all scheduled arrivals and departures

Robust estimates of process times

Advanced predictive modelling and statistical learning techniques are used to developprocess time prediction models with strong predictive power. Two different approachesare presented. A single general predictive model is developed that, given the currenttraffic condition, accurately predicts all running and dwell time estimates. The resultsof this generic approach can be generalised to the parts of the network and train linesthat are not included in the training set. Strong and quantified predictive power of thepresented models indicate the applicability of presented approach for deriving accurateprocess time estimates.

Moreover, the data structures obtained using the data processing tool motivated thedevelopment of separate statistical models for each block section (station route, plat-form) and each train line. The variability of running and dwell times was explainedwith greater precision by significantly reducing the number of predictors. Both ap-proaches are validated on an independent test set. We show that the application of thelocal statistical models produces more accurate predictions. Earlier approaches in thisdirection (Van der Meer, Goverde, & Hansen, 2010) are improved to include runningtimes on the level of block sections, headway times and time loss due to route conflicts.

Robust regression (Rousseeuw & Driessen, 2006), regression trees (Breiman, Fried-man, Ohlsen, & Stone, 1984) and random forests (Breiman, 2001) were used for com-puting the process time estimates. The resulting estimates are insensitive to outliers anddata errors which is crucial for real-time applications. Therefore, stability of processtime predictions is ensured, which is of utmost importance for reliability of estimatesand controlling the error propagation to other dependent processes. Moreover, all cap-tured dependencies and results are interpreted and validated using domain knowledge.


• a set of predictors for estimation of dwell times and running times on the levelof block sections

• global predictive models for process time estimation based on robust linear re-gression, regression trees and random forests

• robust regression models for process time estimation for each combination ofblock, station and train lines


Real-time traffic state prediction

A real-time prediction of train event times is the main contribution of this thesis. Verylittle work on real-time prediction exists in the current literature and the existing ap-proaches rely on the static predictions that are independent of the actual traffic condi-tions. Therefore, this work required a development of a new methodology to predictthe traffic state. The data-driven approach monitors the current traffic conditions onthe network and performs the prediction of the future events.

A mesoscopic traffic model is developed that reflects the microscopic traffic constraintson open track sections and in station areas. The graph model can be continuously up-dated with new information about the train positions or traffic control actions. Fur-thermore, a fast prediction algorithm has been implemented that in a single executioncalibrates the model and computes the predicted realisation times of all events within aprediction horizon. The model is calibrated depending on the actual traffic conditionson the observed parts of the network.

The mesoscopic character of the tool allows the accurate prediction of route and con-nection conflicts. For every predicted route conflict, the time loss of the hindered traindue to braking, re-acceleration, running with lower speed and unscheduled stops ismodelled realistically. The dependence of time loss on the conflict duration is deter-mined from the historical traffic realisation data and quantified. The train dynamics canthus be accurately modelled and the computationally demanding iterative approach toderiving the running times of hindered trains (D’Ariano, Pranzo, & Hansen, 2007) canbe avoided.

In order to further increase the accuracy of predictions in real-time, an adaptive onlineerror-smoothing component has been implemented. The prediction errors for runningtrains are monitored and an adaptive filter computes the adjustment to the downstreamprocess time estimates. The trains that significantly deviate from the estimated trajec-tories are therefore identified in real time and the prediction error for future processesis decreased.

A comprehensive analysis of algorithm performance has been carried out on a real-lifecase study. The computation speed and accuracy of predictions prove the applicabilityof the concept of data-driven predictions. The obtained results indicate a significantimprovement of precision compared to the approaches used in the current practice andimplemented in the relevant academic tools. The stability of predictions over differenthorizons is examined and the optimal prediction horizon is determined with respect tothe accuracy of predicted arrival and departure times and accurate prediction of routeconflicts.


• a mesoscopic traffic model that reflects microscopic constraints on open tracksections and in stations


• a prediction algorithm that can quickly predict the traffic evolution in large andbusy networks over a long prediction horizon

• adjustment of running times of the trains hindered in route conflicts

• adaptive adjustment of process time estimates in real-time

1.5.2 Macroscopic models for network-wide traffic rescheduling

The main methodological contribution of the work on this objective is a realistic macro-scopic model for real-time rescheduling that can solve the network-wide problem in-stances in short time. The appropriate macroscopic rescheduling model is created as aresult of investigating the trade-off between the quality of solutions and the computa-tion time. The effect of increasing the number of considered macroscopic constraintson solution quality, feasibility and the corresponding computation time is presented.The macroscopic models are validated by comparing their performance with the re-sults obtained using a detailed mesoscopic model model.

Aggregation of mesoscopic constraints to the macroscopic level was performed in arealistic manner that ensures the feasibility of the solutions produced by the macro-scopic model. This includes computation of minimum headway times with respect toblocking time theory instead of using the predetermined norms which is a commonapproach in current practice and academic research. The modification of the existingalternative graph models is therefore presented that enables computation of minimumheadway times with respect to train orders.

The feasibility of the approach is demonstrated by a real-world case study for theDutch national railway network. It is based on the DONS database represented in theform of a timed event graph (TEG) (Goverde, 2007). A data mining algorithm wasdeveloped that sweeps through a TEG, builds the macroscopic resources, i.e., stations,open track sections, and converts the TEG into an alternative graph based on running,dwell, headway and connection constraints. The model is applied to a substantialnumber of realistic disruption scenarios in a large instance that includes a peak hour oftraffic in the complete Dutch railway network.


• a mesoscopic alternative graph model (D’Ariano, 2008) modified in order toincorporate macroscopic operational constraints

• an approach to convert a timed event graph into an alternative graph

• four macroscopic rescheduling models created to investigate the trade-off be-tween solution quality and computation time

• the most complex model built with respect to macroscopic operational con-straints produces feasible solutions in short computation time


1.6 Thesis outline and scope

This thesis consists of seven chapters (including this one). Based on the content, thefirst two chapters can be grouped into an introductory part. Similarly the three chaptersfocusing on monitoring and traffic state prediction can intuitively be grouped into acoherent content. The structure of the parts and their relationship is illustrated in aflowchart in Figure 1.7. Related chapters are grouped and arrows indicate the order inwhich the chapters could be read.

Chapter 7Rescheduling models

for real-time traffic management in large networks

Chapter 8Conclusions

Chapter 2An overview of railway

operation planning and control

Chapter 1Introduction

Chapter 5Data analysis and

estimation of process times

Chapter 6 Real-time prediction of train event times

Chapter 4Process mining of

train describer event data

Figure 1.7: Flowchart of the thesis structure

Part I contains the first two chapters of this thesis. In Chapter 2 the main concepts ofrailway systems, definitions and terminology needed for understanding the remainderof the thesis are introduced. Moreover, a review of the most important contributions inthe scientific literature related to the problem of railway operation and traffic control ispresented.

Part II of the thesis consists of the chapters related to data-driven decision support sys-tems for monitoring and real-time traffic state prediction. Chapter 3 presents a processmodel that is used for mining the traffic realization data. The developed process miningmethod is applied for real-time monitoring of railway traffic and ex post analysis, i.e.


recovery of realized train paths and identification of route conflicts. The chapter firstdescribes the data structure of TROTS files, preprocessing steps and input preparation.Moreover, the underlying algorithms and procedures are described with a great levelof detail. Finally, the graphical user interface and visualisation component is presentedthat can be used to raise the situational awareness of traffic controllers or simplifyperformance analysis, depending on the application of the tool.

Chapter 4 focuses on statistical analysis of traffic realisation data and computing robustestimates of process times. The used statistical learning tools are described, followedby the the descriptive and inferential statistical analyses of process times and routeconflicts. Furthermore, we use the real-life data set to test and validate the commonassumptions used to describe the variability of process times. We test the impact ofdelays and peak-hours on process times. Finally, the results of model performance inan application to a test set of historical data are presented.

Chapter 5 gives a description of a real-time prediction tool as well as its position in therailway traffic control loop. The main prediction algorithm is presented followed by adescription of the adaptive components that modify the estimates of process times withrespect to the current (unexpected) traffic conditions. A real life case study is furtherdescribed that is used to test the performance of the complete tool for monitoring andtraffic state prediction. The integration of the components for data processing, analysisand prediction is described and model accuracy is extensively discussed.

Chapter 6 presents different rescheduling models for dynamic management of large-scale networks. The principles of deriving alternative graph models from macroscopicdata are described, as well as the procedure to convert a timed event graph into arescheduling model. Furthermore, this part focuses on the procedure to find an appro-priate level of granularity for modelling railway traffic on a macroscopic scale withrespect to the basic requirements for rescheduling problems such as the solution qual-ity and computation time. A comprehensive analysis of the model performance withrespect to the validated mesoscopic model is given, followed by the results of the ap-plication to a real-life case study of the Dutch national network.

Finally, Chapter 7 summarises the main findings and contributions of the thesis. Lim-itations of the performed research are also discussed and clear directions for furtherresearch are given.

As illustrated in Figure 1.7 there are multiple ways to read this thesis depending on theprior knowledge and interest of the reader. Readers with good knowledge of railwayterminology and system properties may proceed directly to Chapter 3. Similarly, read-ers with particular interest in rescheduling aspect of dynamic traffic control can, afterthe introductory part, proceed directly to Chapter 6.


Chapter 2

An overview of railway operationplanning and control

2.1 Introduction

The research motivation and main objectives addressed in this thesis were describedin the previous chapter. Before presenting the main contributions of this research inthe following chapters, it is important to define the problems of traffic control in moredetail and review the existing contributions from the scientific community.

This chapter first presents the adopted terminology and the basic concepts of railwaytraffic. The operational rules, implemented in the signalling system and timetable,are of crucial importance for developing new and analysing the existing mathematicalmodels of railway traffic. Moreover, the current practice of traffic control is presentedand the main problems are identified. The problems related to railway traffic controland performance analysis have been addressed by numerous contributions. We give acritical review of the existing approaches and emphasise the gaps in the state-of-the-artmodels that are filled by the tools presented in this thesis.

In the first part of the chapter, the basic definitions related to railway timetables, sig-nalling and safety systems, train delays and traffic control are given (§2.2). This isfollowed by a separate literature review for each research objective and the correspond-ing requirements. Section 2.3 gives the literature review of processing and mining thetrain describer and traffic realisation data. The description of running, dwell and head-way times, and approaches to their computation and estimation is given in Section 2.4.Section 2.5 presents the recent works on delay analysis, propagation modelling andprediction. The recent real-time rescheduling models are presented in Section 2.6. Fi-nally, we discuss the existing practice and models and analyse their applicability formonitoring, traffic state prediction and network-wide rescheduling (§2.7).

19


2.2 Terminology and basic concepts of railway traffic

2.2.1 Railway timetable

Railway traffic usually operates according to a timetable. The railway timetable in theNetherlands is periodic, meaning that the pattern of arrivals and departures of all trainsis repeated in regular intervals. The timetable construction for the Dutch network issupported by a sophisticated mathematical optimisation model based on the periodicevent scheduling problem (PESP) (Serafini & Ukovich, 1989), that was applied to thetrain timetabling problem by Schrijver and Steenbeek (1993). DONS database containsthe running and dwell times for each train, as well as the headway and connectionconstrains that need to be respected in order to design a feasible timetable for densetraffic of interconnected train lines (Hooghiemstra, 1996).

The running time comprises the period between the train departure and the completehalt at the arrival station. It contains the outbound running time from the platform trackto the departure signal, the running time from the departure signal to the home signalat arrival station and the inbound running time between the home signal until standstillat the platform track.

We distinguish between minimum running times and scheduled running times. Mini-mum running times are computed with respect to the defined maximum speed on thetrain route and dynamic properties of rolling-stock and infrastructure which reflect theacceleration and breaking characteristics (Brunger & Dahlhaus, 2008). In terms of dy-namic properties, a train run in full performance regime between two scheduled stopscan be distinguished into acceleration, cruising at the maximum speed and brakingcontinuously at the standard braking rate until stop at the platform (Albrecht, Goverde,Weeda, & van Luipen, 2006).

The scheduled running times are given in the timetable. In order to increase the reli-ability and robustness of the timetable to varying running times and decrease energyconsumption, the scheduled running times contain a certain amount of running timesupplements (Goverde, 2005). The value of the running time supplement, currently inuse in the Netherlands, is 5% of the minimum running time. The running time supple-ments can also be used for energy efficient driving. The typical strategies are cruisingat a lower speed than maximal and/or by coasting before braking to standstill (Albrechtet al., 2006).

The dwell time is the time between arrival of a train to standstill at the platform trackand subsequent departure after the scheduled stop. Weidman (1995) determined thefactors with high impact on the duration of dwell times. They include among other:the number, structure and distribution of passengers on the platform as well as thevehicle and platform design. Dwell times are modelled to a great level of detail by dis-tinguishing them into several sub-processes: door unblocking, door opening, passengerboarding and alighting, door closing and train dispatching (Buchmueller, Weidmann,& Nash, 2008).

Chapter 2. An overview of railway operation planning and control 21

In the Dutch practice of timetable design, minimum dwell times are determined basedon the train type, station type and estimated passenger demand. The dwell time bufferis introduced to absorb the seasonal and daily variation in boarding and alighting timewhich is the longest sub process of train dwell time. Moreover, similarly to the runningtime supplements, dwell buffer times can be used to partially or completely absorbarrival delays.

The scheduled dwell time may also be extended with the synchronisation times forpassenger transfers and rolling-stock or crew connections. Finally, all events in a pub-lished timetable (arrivals and departures) are usually rounded up to full minutes forpassenger convenience. The rounding procedure may affect the values of running anddwell time reserves and their distribution over the train route between terminal stations.

A timetable is a result of a careful planning process that may take several months tocomplete and is usually valid for one year (with possible minor modifications). How-ever, the final process plan, that may consider short-term allocated freight train pathsand track possessions due to maintenance works, is developed one day in advance.It contains a detailed plan of traffic execution and represents the reference for oper-ational traffic and transport control. A detailed description of the operational controllayer is given in Section 2.2.6 after explaining the basic constraints of railway trafficincorporated in the signalling and safety system.

2.2.2 Signalling and interlocking

Safety and signalling systems are an essential part of modern railways. Their mainpurpose is to ensure safe train runs by preventing derailments and collisions betweentrains that share the same infrastructure elements, and accidents between trains andother vehicles and objects. This overview is focused on the fixed-block signallingsystem that gives the movement authority for all trains on open tracks and in inter-locking areas. A comprehensive description of components and functions of safetyand signalling systems is given by Theeg and Vlasenko (2009). Bailey (1995) gives acomparative overview of the signalling systems in different infrastructure companiesin Europe.

The main signals in the Netherlands can be partitioned into automatic block signals onopen tracks and controlled signals in station areas. Automatic block signals operatebased on the information from train detection devices and interdependence with theneighbouring signals. Controlled signals are operated manually or activated by theautomatic route setting system ARI (Berends & Ouburg, 2005). They are dependenton the logic of interlocking systems with the purpose to prevent head-on, rear-end andflank collisions. A home signal is a signal that protects the station area and preventsthe incoming trains from entering if their route is not set up. The departure signal givesa movement authority after the corresponding outbound route has been locked.

A basic element of safety and signalling systems is the track-clear detection system.Railway tracks are divided into track sections. The task of the track-clear detection


systems is to detect the presence of a train on a track section. They provide the binaryinformation about the state of a track section which can be: (i) occupied if at least oneaxle is within track section borders or (ii) free if no axles are present at the section. Wedefine the moment when the first axle of a train occupies the section as occupation timeand the moment when the last axle leaves the section as release time. The presence ofa train is continuously monitored either by means of track circuits or axle counters ineach track section (Pachl, 2009).

Track circuits rely on the conductive properties of axles and tracks. The presence ofa train is detected when the electric circuit is closed between two rails and a vehicleaxle. On the other hand, axle counters detect the presence of a train on a track sectionby comparing the number of axles counted on each end of the section.

The interlocking is a safety system that integrates (interlocked) signals and switches toprevent conflicting or improperly set routes. Switches are movable track elements thatenable trains to move from one track to another. In order to be used safely, a switchneeds to be set in the appropriate position and locked. Track-clear detection of switchesis performed in the same way as for track sections. A comprehensive overview ofinterlocking systems and principles is given by Theeg and Vlasenko (2009). The Dutchsystem is described by Goverde (2005).

The safety principles required for route setting need to hold as long as the route isbeing used by a train or until it is cancelled by the controller. A route is released onlyafter the train has cleared it. In order to increase the capacity of interlocking areas,especially in complex and busy stations, the modern interlocking systems employ thesectional-release route setting principle. Each section of the route becomes availablefor another route as soon as it is released by the last axle on the rear of the train. Routeholding ensures that the occupied and non traversed sections still stay locked in theroute.

2.2.3 Blocking time theory

Fixed-block signalling is efficiently implemented in the railway traffic models usingblocking time theory (Hansen & Pachl, 2008). The blocking time can be defined asthe time during which a block between two signals is reserved exclusively to one trainand therefore blocked for all other trains. It consists of the sight and reaction timeof the train driver, approaching time, which is equivalent to the running time over thepreceding block, the running time, clearing time needed for the full train length toleave the block, and setup and release time of the signalling system (2.1). Note thata block is physically occupied only during the running and clearing time (representedby shaded box).

Using the blocking time theory, a route conflict between two trains corresponds to anoverlap of their blocking times. Figure 2.2 depicts an overlap of blocking times oftwo successive trains. The second train is within the sight distance of approachingsignal and the first train has still not left the block. Consequently, the aspect of the


Sightandreactiontime

Approachtime

Runningtime

Clearingtime

Releasetime

Sight

distance

Train

lenght

Time

Distance

Occupationtime

Setuptime

'y'

'r'

'g'

Figure 2.1: Blocking time

approaching signal is ‘yellow’, causing the second train to brake. The conflict durationis the width of the overlap indicated in red.

Time

Distance

Sightandreactiontime

Approachtime

Runningtime

Clearingtime

Releasetime

Hinderedtrain

Hinderingtrain

Duration TImeloss

'y'

'r'

'g'

Setuptime

Figure 2.2: Route conflict

A train run over the signalled open track section and interlocking areas can be repre-sented as a sequence of blocking times. That sequence models the time slots reservedfor train operation. It is represented by the blocking time diagram. Figure 2.3 shows


the blocking time diagrams of two successive trains. The minimum headway timebetween departures from the same station is determined by compressing the blockingtime stairways as much as possible without causing an overlap. The block where theblocking times would first overlap is called the critical block. The resulting minimumline headway can be used for time-based train separation.

Time

Distance

Minimumlineheadway

Criticalblockheadway

Figure 2.3: Blocking time stairways

2.2.4 Train position detection

Keeping track of train positions is a basic requirement for the monitoring of railwaytraffic. Traditionally, train positions were monitored only at staffed stations and othertimetable points. However, the recent developments in sensor and communicationstechnologies enable a more detailed observation of running trains.

Train positioning can be track-based or train-based (Luthi, 2009). Figure 2.4 illustratesthe track-based approach to train positioning. Train describers are the most commonlyemployed system for track-based train positioning (Exer, 1995; Pachl, 2009). A traindescriber system keeps track of train positions in discrete steps over the route based onthe messages received from the track-clear detection devices. Moreover, an importantfunction of train describers is logging of incoming infrastructure element messagesand the generation of train number messages.

The train describer system TROTS is used in the Netherlands since 2007 (ProRail,2008). Train number steps are followed on the level of track section, i.e. a messagereporting the new train position is recorded with every section occupation and release.Moreover, the system also logs binary messages reporting aspect changes of controlledsignals (‘stop’ or ‘go’), as well as a position change of switches (‘left’ or ‘right’).


A

B

time

Figure 2.4: Infrastructure based train detection

Alternatively, the actual train position may be determined with a certain frequency bymeans of the Global Positioning System (GPS), possibly in combination with an in-frastructure based detector to reduce the measurement errors (Figure 2.5). The exactposition of each train is communicated to the traffic control centre in regular intervalse.g. by means of the Global System for Mobile Communications-Railway (GSM-R)(Winter, 2009). Note that GPS signals may not be continuously available and suffi-ciently accurate to distinguish between parallel tracks. Therefore, GPS cannot ensuresafety of train operation in densely occupied railway networks.

A

B

timeDt Dt Dt Dt Dt Dt Dt Dt

Figure 2.5: Regular time interval train detection

For the purpose of this study, log archives of the Dutch train describer system TROTShave been made available by the infrastructure manager ProRail. Section 2.3 presentsearlier contributions related to data mining and extraction of information from histori-cal traffic realisation data.


2.2.5 Classification of train delays

Delays in railway traffic occur due to variability of process times, capacity and syn-chronisation processes, and dependence on availability of infrastructure, rolling-stockand crew. Small deviations from the scheduled process times as a consequence ofvariability result in disturbances. Goverde (2005) described disturbances as structuraldeviations that reflect stochasticity of process times due to internal and external fac-tors. The issue of minimising their impact on timetable reliability is addressed both inthe tactical and operational control and planning levels. Time supplements and buffertimes are added in the process of timetable construction as discussed in Section 2.2.1.Moreover, operational traffic control aims to minimise deviations from the timetableduring real-time operations (§2.2.6). On the other hand, disruptions are caused bymajor deviations of timetable and logistic schedules due to failures of infrastructure,rolling-stock, line blockages, extreme, weather conditions, etc. (Nielsen, 2011). Ma-jor disruptions in general do not happen frequently and they are resolved by specialdisruption and incident management strategies (Jespersen-Groth et al., 2009).

Primary delay is an extension of the scheduled process time caused by a disruptionwithin the process (Goverde, 2005). Primary delays may result in secondary (consec-utive, knock-on) delays. Occurrence of secondary delays is called delay propagation.Secondary delays occur as a result of interdependences between trains, i.e. due to routeconflicts or waiting for scheduled connections. They may be a consequence of primaryand secondary delays but also due to early trains and timetable errors. Capacity con-straints are a common reason for secondary delays. Extended running time of a trainmay cause knock-on delays to successive trains on the saturated line. Similarly, ex-tended dwell time in a station often results in consecutive delays of other trains in busystations due to occupied platform track or station routes. Whereas primary delays areindependent from traffic control, preventing delay propagation through the network isone of its most complex tasks that will be addressed in detail in Chapter 6.

If the time allowances, i.e. running time supplements and dwell buffer times are notsufficient to absorb the primary delay, the same train suffers follow-up (unavoidable)delays in subsequent stations. For example, extended dwell time in a station maycause a delay of the same train in other stations along its route until the running timesupplements and dwell time buffers have absorbed the delay. Note that the follow-updelays of an operating train cannot be reduced or avoided by any traffic control action.

2.2.6 Operational control of railway traffic and transport

Operational planning is performed by traffic control centres. Their task is to createupdates to the process plans determined on the tactical planning level. In case of dis-ruptions and disturbances, timetable, rolling-stock and crew circulations may becomeinfeasible. Controllers on behalf of an IM (traffic controllers) and the TOCs (transportcontrollers) need to perform rescheduling actions in real time.


Jespersen-Groth et al. (2009) presented the structure of an integrated operational con-trol level (Figure 2.6). The information flow between different levels of control, andIM and TOCs explains the process of disturbance and disruption management. Localtraffic controllers observe traffic in their area and implement the process plans derivedon the network level. Disturbances and disruptions with the effect that exceeds theirarea are reported to the network traffic control. The timetable updates, derived at thenetwork control level, are transmitted to local controllers who need to implement it.Computation of the working network timetable is a cooperative process between thetraffic and transport process control. The network traffic control derives the timetableupdates, whereas the network controllers on behalf of TOCs, create updates to re-source circulation schedules. In an iterative procedure, IM and TOCs derive a feasibleworking timetable that is given as a master plan for local control. On the local level,traffic and transport controllers cooperate in order to perform all necessary shuntingoperations.

IM TOC

Network

LocalLocal operations

control

Transport controller

Traffic controller

Signaller anddispatcher

Proposed timetable

Rolling -stock and crew

rescheduling

Shunting requests

Shunting time slots

Delays and traffic state

Actual tim

etable

Figure 2.6: Structure and information flow within operational planning level(Jespersen-Groth et al., 2009)

The problems of traffic and transport process control are highly interconnected both onthe network-wide and on the local level. However, a high complexity of each problemindividually prevents an integrated approach to computing the timetable and logisticplans adjustments simultaneously. In the current literature, the problems of real-timetransport and traffic control are addressed separately. It is assumed that a feasible so-lution to both problems is reached in a negotiation process by iteratively solving bothproblems in a closed loop until a feasible solution is found. A recent review on modelsfor crew rescheduling is given by Potthoff (2010) and Potthoff, Huisman, and De-saulniers (2010). Relevant contributions from the field of rolling-stock reschedulingare reviewed by Nielsen (2011) and Nielsen, Kroon, and Maroti (2012). Rolling-stock


and crew scheduling are beyond the scope of this thesis. However, the delay man-agement, with the purpose to decide which passenger connections to keep in case ofdelays, is closely related to network traffic control. TOC controllers perform delaymanagement to minimise passenger delays.

The main tasks of traffic controllers on both levels are monitoring, prediction andrescheduling (Luthi, 2009). The traffic state described by actual train positions andspeeds must be continuously observed in order to detect deviations from scheduledtrain paths. The consequences of such deviations need to be accurately predicted asthe rescheduling process is performed based on these predictions. Moreover, beforeimplementing a rescheduling decision, the effects on the corresponding area need tobe predicted.

Monitoring and traffic state prediction

Accurate information on train positions can be used to derive performance indicatorsand parameters needed for estimation of train running and dwell times such as: ap-proximation of train speed, actual train delays, registered values of train running anddwell times, etc. These parameters give an indication about the current traffic state onthe network that can further be used to predict the traffic in the period defined by aprediction horizon.

In the Netherlands, traffic controllers monitor train positions using infrastructure-basedposition detectors (§2.2.4). As explained in Section 1.2, the actual train delays aremeasured at home and departure signals, corrected with a fixed correction term androunded to full minutes. The precision of such measurements is insufficient for areliable estimation of the actual traffic state.

Traffic controllers use the actual traffic state to predict the future train positions and theevolution of traffic in their area of observation (D’Ariano, 2008). The accuracy of thesepredictions has a big impact on quality of traffic control decisions and reschedulingactions. Current practice in traffic state prediction has a macroscopic character andrelies on the so-called parallel shift method. The actual delay of a train, observed in atimetable point, is extrapolated to subsequent timetable points as illustrated in Figure5.13. This method neglects the fact that some trains may reduce their delays by runningwith maximum performance and using the running time supplements. Moreover, sometrains may get (more) delays due to route conflicts.

The improvement of the described drawbacks of the current practice in monitoringand traffic state prediction represents the first research objective of this thesis (§1.4).Sections 2.3–2.5 review the existing approaches relevant for developing the data-drivenmonitoring and prediction tool.

Rescheduling

After predicting the expected conflicts and delays that make the planned timetableinfeasible, traffic control needs to find a new feasible schedule for train operations.That procedure is called real-time rescheduling. It is performed both on the level of


Scheduleddeparture

Scheduledarrival

Realdeparture

Predictedarrival

A

B

Departure delay

Figure 2.7: Illustrative example of the parallel-shift prediction method

local and network traffic control. Operational requirements of rescheduling tasks oftraffic control are summarised, among others, by Cacchiani et al. (2014); D’Ariano(2008); Harrod (2012); Luthi (2009).

Network traffic controllers deal with disruptions and disturbances with effects that canpropagate and affect the global network performance. They need to take into accountmacroscopic constraints of railway traffic, such as running times of trains betweentimetable points, dwell times, minimum headway times between successive depen-dent events in timetable points, and synchronisation constraints. The objectives ofrescheduling on this level depend on the traffic situation and the magnitude of disrup-tion. They vary from minimising the deviations from the published timetable in caseof disturbances, to maintaining passenger flows and maximising throughput in case ofline blockages and major incidents. An important task of network traffic controllersis to coordinate the controllers on the local level whose situational awareness is lim-ited to their own area, and try to minimise delay propagation multiple areas. Apartform changing the scheduled times and relative train orders defined in the timetable,network traffic controllers may reroute trains over different lines, cancel or add trains,implement short turns, skip-stop operation, etc.

Local traffic controllers manage route conflicts, delays and disturbances within theircontrol area. Microscopic train routes, signalling and interlocking principles need tobe considered by traffic controllers on this level. The dispatchers and signallers in alocal traffic control area implement rescheduling decisions. That includes changingthe relative order of trains that simultaneously claim the same block (platform track orstation route), changing a train route in a station area or modifying departure times. Theobjective is to minimise the deviation from a target trajectory set by the hierarchicallyhigher network control level.

In the current Dutch practice however, traffic controllers do not have any decisionsupport to pursue the described objectives. In case of a major disruption, on the net-work level the tendency is to isolate the incident and prevent delay propagation to non-affected parts of the network. On the local level, traffic controllers rely on the ARI


system that automatically sets routes for the approaching and departing trains. Con-flicting routes are resolved using the predetermined rules depending on the magnitudeof delays. Specifically, the priority is given on the basis of the first come first served(FCFS) rule for routes crossing each other while for merging or identical routes theorders specified in the timetable are followed. For larger delays, dispatchers take trainordering decisions with the support of a list of what-if scenarios (Corman, D’Ariano,Pranzo, & Hansen, 2011).

The current practice in real-time rescheduling may produce suboptimal effects onpunctuality and reliability of traffic. The second research objective in this thesis aims todevelop a decision support rescheduling system for network traffic controllers (§1.4).Section 2.6 gives a review of the existing scientific approaches to real-time reschedul-ing.

2.3 Review of approaches for data mining of traffic re-alisation data

The first step in developing a data-driven tool for monitoring and traffic state predictionis to create a data mining procedure for processing the incoming messages about trainpositions, as well as the archives of historical track occupation data. This sectioncovers the relevant existing approaches for retrieval of traffic related information fromthe automatically logged event messages.

The historical traffic realisation data sources used in the current scientific literaturerange from the arrival and departure times recorded manually at specific stations to de-tailed traffic realization data extracted from train describer log files. Longo, Medeossi,and Nash (2012) classify the automatically collected railway operation data sources tosensors embedded in the infrastructure, sensors in rolling-stock and mobile GPS de-vices. We emphasise that the granularity of data from each data source varies depend-ing on the system employed by a particular infrastructure manager or train operatingcompany.

The most frequently used data source for recovery of realised train paths are traindescriber event log files. The level of detail in the data, as well as the structure of theresulting log files vary in different train describer systems. For that reason, a separateapproach is required, in order to develop a data processing algorithm, suitable for aspecific system. The purpose of such processing tools is to clean the raw data andproduce data structures that are convenient for performance analysis and developmentof data-driven models.

Train describer data were originally archived for maintenance and accident investiga-tion purposes. Their importance in direction of performance analysis has been recog-nised relatively recently. Goverde and Hansen (2000) presented a tool TNV-Preparethat couples infrastructure messages to train number steps. The track occupation andrelease messages, as well as signal aspect change messages are in the earlier Dutch


train describer system Treinnummer Volgsysteem (TNV) logged separately from trainnumber messages. The developed algorithms are able to assign infrastructure mes-sages reporting state changes of signals, sections and switches to the train numbersthat caused them. The application of this tool results in an ordered list of section andblock occupation and release times for each train run.

More insight in train interactions and route conflicts from historical track occupationdata was gained by expanding the data processing tool with signalling logic (Goverde,Daamen, & Hansen, 2008). Daamen et al. (2008) formalised the signalling logic modelthrough a coloured Petri net and implemented it in the TNV-Conflict tool. The maincontribution of this work is an automatic identification of all route conflicts that atrain suffered along its path. Hindering trains are also identified by finding the trainnumber that occupied the block section or route protected by the signal of conflict. Theidentification of route conflicts is a fundamental requirement for distinction betweenprimary and secondary delays and for developing accurate data-driven models thatneed to rely on conflict-free running times.

Results from processing train describer files in Switzerland are presented by Laber-meier (2013). The work exploits data from the traffic control system RCS that has beenin use as a dispatching system in Switzerland since 2010. Using the actual timetable,realized train event times and connection plans, the author is able to distinguish be-tween primary and secondary delays. Furthermore, a comparative analysis of primaryand secondary delays was performed. The results show that secondary delays that oc-cur due to waiting for late feeder trains are the main contributors to low punctualitylevels in Switzerland.

Train describer data often do not provide information about train runs on open tracksections because automatic block signals are not logged. Therefore, an alternativedata source for recovery of complete train paths with a great level of detail are trainevent recorders. The main advantage of using on-board train event recorders is thehigh frequency of incoming messages about train position and speed (Allotta, Toni,Malvezzi, Presciani, & Colla, 2001). Moreover, the actual stopping and departuretimes as well as the door opening and closing times are also recorded, thus enablingmore detailed modelling of train running and dwell times.

De Fabris, Longo, and Medeossi (2008) presented a method that enables the analysisof train event recorder data. The detailed recovery of train movements results in acontinuous estimation of speed profiles, acceleration rates and breaking curves. Dwelltimes are derived accurately from train door sensors. The tool is further applied forcalibrating the parameters that can improve the quality of microscopic simulation tools.

The described works on data mining train describer data archives in the enable a trainpath recovery, route conflict identification and separation between primary and sec-ondary delays. However, the implementation of the new train describer system in theNetherlands and corresponding changes in data structure and information contained inthe event logs, requires the construction of new algorithms for track occupation data


processing, discovery of processes, and route conflict identification. An importantdrawback of the Dutch train describer system TROTS is the fact that train events onopen tracks are not logged with the precision and frequency required to recover trainpaths and identify route conflicts. The existing approaches do not provide a solution tothis problem.

2.4 Review of approaches for process time estimation

The second step in reaching the first research objective of this thesis (§1.4) is estimationof process times. This section covers the most relevant approaches for running, dwelland headway time estimation.

2.4.1 Running time estimation

The minimum running times are usually computed by means of train motion equa-tions (Wende, 2003). This approach considers the dynamic properties of rolling-stockand infrastructure that are represented in equation parameters. The empirical param-eters for minimum running time computation are typically given for a particular lineor rolling-stock type and train composition. The parameters are usually determined byexperts and tuned in practical operation in a particular railway company. This methodis often used for minimum running time computation in the process of timetable con-struction (Hooghiemstra, 1996) and microscopic traffic simulation (A. Nash & Huerli-mann, 2004).

However, greater precision in calibrating the parameters of the train motion equationsfor different traffic conditions can be achieved using the actually realised running timedata derived from track occupation or train event recorders data. Longo et al. (2012)define a single parameter for each dynamic motion phase. The variability in runningtimes can be modelled by fine tuning the corresponding parameter. The parameters arecalibrated against the train event recorders data and corresponding probability distri-butions are derived. This approach is a convenient way of estimating the robustness ofrunning times in the timetabling stage.

Besinovic, Quaglietta, and Goverde (2013) extend this approach by calibrating eachtractive effort and resistance parameter separately. These parameters are optimised bya procedure that minimises the gap between the simulated and actual train positions andspeed profiles. A probability distribution is computed for each considered parameter.Moreover, the parameters with the greatest impact on variability of speed profiles areidentified, which can be useful for calibrating prediction models. The accuracy of themodel was tested in a real-life case study in the Netherlands.

Another stream of research in the modelling and analysis of realized train running anddwell times is related to defining explanatory variables and quantifying their impacton process times. The departure delay has been recognized as a potential predictor forrunning times of trains of a particular train line on an open track section. Similarly,


arrival delays and peak-hours are used to derive estimates of dwell times in a station.Van der Meer et al. (2010) presented an approach based on robust regression analysisto investigate the correlation between process times and delays. The results show astrong correlation between arrival delays and dwell times. The correlation betweenrunning times and departure delay is much weaker. Similar results are obtained fromthe set of track occupation data from Switzerland by Luthi (2009). Both approachesfor modelling running times rely on macroscopic data, aggregated over open tracksections.

The computational requirements for solving the train motion equation prevent straight-forward application of this method to simultaneous running time estimation of a largenumber of trains in busy networks. Moreover, such approach is static and offline in thesense that it does not consider the current traffic state and potential impact on runningtimes. Even the approaches based on data-driven calibration of train motion equa-tions for the purpose of running time estimation require computationally demandingmultiple simulations which makes them unsuitable for real-time applications. Thesedrawbacks are overcome by the data-driven approaches based on creating robust es-timates of running times dependent on current values of traffic state indicators. Eventhough this method gives precise free running time estimates on the macroscopic level,it lacks the exact modelling of train interactions on the line. Therefore, blocking times,minimum headway times and the time losses due to route conflicts cannot be captured.

2.4.2 Dwell time estimation

Current approaches for the estimation of dwell times used in timetable constructionand rescheduling rely to a great extent on the measurements of realised dwell times.Wiggenraad (2001) performed a detailed analysis of dwell times, and passenger board-ing and alighting processes using a set of manually collected data from seven busystations in the Netherlands. The impact of platform and vehicle characteristics, de-lays, station types and peak-hours was analysed with the purpose of detailed analysisof dwell times. The analysis determined the average boarding and alighting time perindividual passenger as well as per passenger within a cluster. An interesting insight isthat peak-hours do not have a significant impact on the duration of dwell times.

Lee, Daamen, and Wiggenraad (2007) performed a similar study using manually col-lected data from two busy stations in the Netherlands. They focused on the factors thatdetermine passenger behaviour and its influence on dwell times. Platform and vehicledesign, passenger mobility characteristics (age, disabilities, luggage) and crowding ef-fects were analysed in order to enable realistic modelling of dwell times. A non-linearrelationship between boarding time and the number of passengers was determined em-pirically.

Recent advancements in sensor technologies and availability of data from on-boardevent recorders inspired a stream of research on dwell time modelling. More preciseand larger data sources are analysed with the purpose of deriving general conclusions


about dwelling processes of trains in stations. Buchmueller et al. (2008) collected thedata from door sensors, passenger counters and train event recorders. They analyse theduration of each sub process separately with respect to vehicle and platform design,and passenger demand. The case study and data set for model calibration comprises alarge amount of data collected from different train lines in Switzerland.

Longo and Medeossi (2013) present a complex model for dwell time estimation thatseparates dwell time into a set of deterministic and a set of stochastic sub-processes.They focus on the detailed modelling of stochastic processes such as boarding andalighting time, waiting time and departure imprecision time. Boarding and alightingtime are considered to be dependent on the train set property and the number of pas-sengers. By treating the number of passengers as a random variable for different trainsets, estimates of stochastic sub processes of dwell times can be derived.

Detailed dwell time analysis of traffic realisation data in the Netherlands was per-formed by Stam-Van den Berg and Weeda (2007). The model relies on determiningthe exact location of access points to the platform and estimation of the actual stoppingpoint of the train. The authors approximate the running time of trains from the momentof occupation of the platform track section to the stopping point of the head of the trainby assuming constant deceleration. Similarly, they estimate the exact departure timeby assuming constant acceleration between the stopping point of the train and the firsttrack section after the platform track. Even though this approach reduces the estima-tion error based solely on track occupation data it relies on the knowledge of platformdesign and assumption about the stopping point of the train.

The limited scope of the studies that are based on manual data collection creates diffi-culties for deriving general conclusions. On the other hand, application of the detaileddata-based approach that relies on sensor and train event recorders data or platformlayout strongly depends on data availability. Finally, the approaches that incorporateuncertainty by computing probability distributions, possibly dependent on peak hoursand arrival delays, are not directly applicable for real-time application due to the largenumber of stochastic simulations required to derive robust estimates of dwell time du-ration.

2.4.3 Headway times

The estimation of minimum headway times depends on the level of modelling. Onthe micro or mesoscopic level, most models use a space-based separation of trains,which is analogous to the actual operation controlled by the signalling and interlock-ing systems. On the other hand, macroscopic models employ a time-based separationbetween trains, enforced between events at the relevant timetable points (arrivals, de-partures and through events) (Ciuffini, Longo, Medeossi, & Vaghi, 2013; Harrod &Schlechte, 2013).

The space-based separation fully corresponds to the requirements of signalling sys-tems (D’Ariano, Pranzo, & Hansen, 2007) and enables an accurate modelling of route


conflicts and speed profiles of hindered trains and conflict-free train runs. In micro-and mesoscopic models, that typically employ a space-based principle of train sepa-ration, a train cannot pass a main signal protecting a physically occupied or reservedblock and station route. Thus the collision prevention is accurately modelled. Theseparation with at least two free blocks between successive trains is used to modelthe conflict-free train runs (green wave policy). Corman, D’Ariano, Pacciarelli, andPranzo (2009) investigated the application of the green wave policy in real-time trafficmanagement on the mesoscopic level by incorporating a two-block separation betweensuccessive trains, including a time and distance, respectively for driver’s reaction timeand sighting.

The current practice and the majority of macroscopic models rely on time-based head-way computation based on the empirically determined norms. In the Netherlandsdifferent headway norms are applied for each type of conflicting train movements(ProRail, 2013). Time-based headways aim at separating events in stations to achieveconflict-free traffic on open tracks with all signals in the train route showing ‘green’ as-pects. In timetabling models, minimum headway time norms are increased with buffertimes (one or two minutes in the Netherlands) with the intention to absorb the variationin running times and prevent route conflicts in case of small deviations of train runsfrom their scheduled slots. Buffer times lead to a decrease of capacity. The problemof their optimal distribution reflects the compromise between schedule reliability andconsumed capacity (Yuan & Hansen, 2008).

Schlechte et al. (2011) presented a procedure for aggregating capacity constraints with-out compromising the feasibility of macroscopic models derived from the microscopiclevel. An earlier approach for the integration of the two levels of modelling was de-scribed by Kettner, Sewcyk, and Eickmann (2003). The minimum headway times areestimated on the basis of blocking times derived from microsimulation and may beused for optimisation of timetables and rescheduling.

2.5 Review of delay propagation analysis and predic-tion models

2.5.1 Delay propagation analysis

Traffic realization data can be used to analyse delays, punctuality and timetable ro-bustness and stability. Approaches based on historical data give insight into probabil-ity distributions of delays. Moreover, the mutual dependency between processes anddelays can be used for modelling delay propagation and traffic state prediction.

Goverde (2005) performed a statistical analysis of train delays in a complex and busystation of Eindhoven in the Netherlands. The purpose of punctuality analysis was todiscover and explain the systematic delay propagation resulting from minor distur-bances. Descriptive statistical analysis of arrival and departure delays, and dwell times


was presented. Moreover, corresponding probability distributions were computed to fitthe empirically observed values. The author selected the train lines with planned pas-senger connections and applied robust linear regression to investigate the correlationbetween arrival delays of feeder trains and departure delays of connecting trains.

Yuan (2006) contributed to detailed modelling of train delays in stations by incorpo-rating the microscopic layout of the station and route setting and release principles inanalysis. The main goal was to estimate the probability distributions of secondary de-lays due to route conflicts in complex and busy station areas. Statistical parameters ofarrival and departure delays, and dwell times were computed. An important objectivein this context was to investigate the impact of peak-hours on train delay propagation.A separate probability distribution for morning and evening peak, and off-peak periodwas computed. Delay propagation due to route conflict was analysed by identifyingthe critical points (switches or platform sections) that the two conflicting routes havein common. The time lag between release and subsequent occupation of critical pointswas determined and used to estimate the probability of route conflicts.

A punctuality analysis on a saturated corridor was performed by Richter (2013). Prob-ability distributions of running times were derived from the historical traffic realisationdata. Evolution of delays over a busy corridor in Denmark for individual train lines wasanalysed and correlation between delays of different trains was established. The anal-ysis was separated into several levels. First, the train lines with systematic departureand arrival delays were identified. The routes of selected train lines were analysed andpotential conflicting train lines were identified. Finally, linear regression analysis ofdelays of conflicting train lines was performed to prove the correlation and systematicdependency.

A generalised approach for timetable robustness and stability evaluation, based on traindescribers data in Switzerland was presented by Ullius (2004). Delays in stations andrunning times of trains on the corridor were analysed. Moreover, global punctuality in-dicators on the network level were computed. The methodology has been implementedin the OpenTimetable software (A. Nash & Ullius, 2004). Input files contain plannedand realized arrival and departure time for each train number. Users can query particu-lar corridors, time-slots and train lines. The output contains the realized time-distancediagrams, delay distributions and capacity utilization. A comprehensive evaluation ofthe tool and application on large data sets of realised traffic in Switzerland was pre-sented by Graffagnino (2012).

Goverde and Meng (2011) developed a data mining tool TNV-Statistics and applied iton a set of track occupation data in order to isolate secondary delays that occurred dueto route conflicts. The tool is equipped with a module that computes time loss, delayjumps and the number of conflicts per signal. An important feature of the tool is theidentification of conflict chains, i.e., linked lists of trains in successive route conflicts.The tool provides a convenient way to identify systematic delay dependencies due tocapacity constraints. Moreover, by analysing the number of route conflicts occurrenceper individual signal, the capacity bottlenecks can be identified.


The presented punctuality analysis methodologies can be used to identify typical delaypredictors and causes. Moreover, they are useful for developing stochastic and sim-ulation models of railway traffic that can be used to compute robustness measures oftimetables. However, their application for predicting delay propagation in real timerequires a (stochastic) model of railway traffic that would capture the complex in-terdependencies between train delays in busy networks. Thus they are not directlyapplicable for real-time traffic state prediction.

2.5.2 Identifying structural timetable errors and systematic delays

The identification of causes and prediction of delays that repeatedly occur on thenetwork-wide level is a complex task that involves applying advanced data miningtechniques for analysing historical traffic realisation data. Delay dependencies andidentified structural errors in a timetable, that result in systematic delays, can be effec-tively used not only for timetable improvement but also for real-time predictions.

Conte (2007) incorporated the dependencies of train events (due to headway or con-nection constraints) by modelling them with a stochastic Tri-graph approach. Indi-vidual dependencies are then incorporated in a large graph that models the traffic inthe observed part of the network. The tri-graph method was chosen to circumvent thedrawbacks that occur due to the complexity of the conventional conflict graph modelswhile exploiting their individual advantages. The method corresponds to a combineduse of a full conditional independence graph and covariance graph for modelling de-lay dependencies. Dependencies due to secondary delays are taken into account. Thisapproach was applied on a real-life case study of a large sub network in Germany. Theproblem size reduction as a result of using the tri-graph justifies the approach despitethe increase of prediction error.

Flier, Gelashvili, Graffagnino, and Nunkesser (2009) developed a data mining tool foridentifying delay dependencies in large networks. In this approach they distinguishbetween secondary delay due to capacity constraints and due to synchronisation con-straints. A separate model has been developed for each type of dependencies. Thesemodels are further used to sweep through the aggregated traffic realisation data in or-der to identify dependencies between delays. Further extensions include identifyingmultiple (capacity and connection) delay dependencies and improving robustness ofthe approach to measurement errors and outliers. The model was applied to a set oflarge-scale traffic realisation data. Important dependencies due to capacity and syn-chronisation constraints that were difficult to identify using correlation were discov-ered.

Cule, Goethals, Tassenoy, and Verboven (2011) applied pattern recognition algorithmsto isolate train delays that frequently occur in the network within a certain time interval.The large set of resulting patterns is further reduced by the closed episode miningalgorithm. However, since this method does not incorporate the operational constraintsof railway traffic, it is possible to discover mutually independent events within the same


pattern. The method is therefore only applicable for corridors or bottlenecks in whichall train events are dependent. The method was applied to a set of traffic realisationdata from Belgium. The validity of the discovered patterns of dependent delays wasensured by network decomposition and separate analysis of each interconnected subnetwork.

The described data mining approaches may be used for real-time predictions of traindelays in stations. However, the aggregated macroscopic models prevent prediction ofroute conflicts and train interactions on the level of block sections. For that reason,they are not applicable in the context of real-time traffic control.

2.5.3 Delay propagation models

Delay propagation models predict delay values for all trains within the observed partof the network and prediction horizon, based on the current traffic state and actual de-lays. The basic requirement of delay propagation models is an accurate traffic model.Mutual dependence of the process times of a particular train, as well as time reservesincorporated in the schedule need to be adequately considered. Moreover, the modelmust take into account all possible train interdependencies that can cause delay propa-gations over the network due to capacity or synchronisation constraints.

A possible way to compute delay propagation with an accurate model is by using mi-croscopic simulation tools (Janecek & Weymann, 2010; Middelkoop & Loeve, 2006;A. Nash & Huerlimann, 2004; Quaglietta, 2013; Siefer & Radtke, 2006). These mi-croscopic simulation models typically rely on detailed modelling of a train run withrespect to rolling-stock and infrastructure dynamic properties. On top of that, traininteractions are modelled on a detailed level by incorporating the signalling and in-terlocking principles. Microscopic simulation models can realistically represent traintraffic. However, computational requirements prevent the application of such modelsto dense traffic on large networks with strongly interconnected lines or long predictionhorizons.

In this review we cover the two fundamentally different approaches to the delay propa-gation problem. First, we focus on deterministic models with fixed relative train ordersand process times. In the second part, an overview of stochastic models is presentedwhere process times are modelled as random variables.

Deterministic models

Landex (2008) gave an overview of analytical approaches for computing delay propa-gation on a single line depending on traffic heterogeneity and type of the line (singletrack or double track). Given the initial delay, minimum headway times and buffertimes between trains, the sum of secondary delays is computed. Moreover, the delaypropagation between every pair of successive trains is given. Whereas this approachis useful for capacity analysis of a single line, real-time prediction of delays requiresgeneralisation on the network level.


Braker (1993) modelled the Dutch railway timetable as a discrete event dynamic sys-tem in max-plus algebra. Running, dwelling and connection precedence constrainsare included on a macroscopic level. Periodicity of the system is exploited to modelits dynamics using recursive max-plus relations. Timetable stability is evaluated bycomputing the maximum eigenvalue which is equivalent to minimum cycle time.

Goverde (2007) also exploited the convenience of using max-plus algebra for mod-elling periodic discrete event systems. A periodic timetable is modelled with a timed-event graph that includes running, dwelling, connection and headway constraints whilemaintaining the macroscopic level of the model. System dynamics is represented witha general higher-order max-plus linear system. Moreover, max-plus spectral analy-sis is used to evaluate stability and robustness of a timetable. Finally, a bucket-baseddelay propagation algorithm (Goverde, 2010) predicts the evolution of current trafficcondition over multiple periods in a time efficient manner.

A mesoscopic approach that integrates a microscopic simulation model (Siefer & Radtke,2006) with a macroscopic simulation tool for large networks (Kettner, Prinz, & Sew-cyk, 2001) is presented by Kettner et al. (2003). The accuracy of the macroscopicmodel that models railway traffic with a great level of abstraction is increased by com-puting all running and headway times with a detailed microscopic simulation tool. Thetwo-level approach enables modelling and simulating traffic in large networks with re-alistic process times. The required computational efforts for simulating process timesin large areas are distributed by using geographic decomposition of the network.

Stochastic models

Carey and Kwiecinski (1995) presented a stochastic model of a complex scheduledtransport system. The event times of all trains in the model are computed in a recursivemanner, based on the realised event times of preceding events, timetable, and processtimes modelled as random variables. The generic model is independent from the choiceof suitable probability distributions of running and dwell times. An important aspect ofthe model is probabilistic modelling of train orders which reflects the potential impactof traffic control decisions. The model was further used to develop and evaluate aseries of reliability measures for scheduled services (Carey, 1999).

Higgins and Kozan (1998) presented a stochastic delay propagation model and appliedit on a case study of a busy urban train network. The underlying traffic model includesthe basic dispatching actions. The delay of each train is estimated by summing up so-lutions to a set of equations that model the probability of primary delay, probability ofsecondary delay due to capacity constraints and probability of secondary delay due toconnection constraints. The solution is obtained using a numerical iterative refinementalgorithm.

Middelkoop and Bouwman (2001) presented a simulation tool Simone that simulatestrain running and dwell times over the complete Dutch network. The models aregenerated automatically from the Dutch timetable database that is used by DONS


(Hooghiemstra, 1996). Train interactions are modelled in stations only. Primary de-lays, defined by the user, are propagated through the rest of the network.

Yuan and Hansen (2007) described a detailed analytical stochastic delay propagationmodel for complex station areas. First, analytical formulas are given for deriving sec-ondary delays of departing and arriving trains separately. Conditional distributions ofarrival and departure times are computed using convolutions for computing the distri-bution of the sum of random variables. The model is validated on a case study from acomplex railway station The Hague HS in the Netherlands.

Meester and Muns (2007) formalised the model presented by Carey and Kwiecinski(1995) as a stochastic event graph. The distributions of free running times are given andthe process dependencies are computed as a mixture of the corresponding distributions.A set of performance measures is derived as a linear combination of delay distributions.The method for computing the values of proposed measures relies on approximatingdelay distributions with phase-type distributions. The upper bound of approximationerror is presented and the approach is applied on a small part of the Dutch nationalnetwork.

A stochastic delay propagation approach based on processed train event recorders datawas presented by Medeossi et al. (2011). Delay propagation is computed by means ofstochastic blocking times. The method relies on asynchronous simulation of individualtrain runs based on probability distributions of train motion parameters (Longo et al.,2012). Each simulation run generates a blocking time ‘stairway’. Superimposition ofblocking time stairways for each train run results in a blocking probability, as well asroute conflict probability when other train runs are considered.

Buker and Seybold (2012) modelled delays as random variables, described with suit-able distribution functions, and applied analytical methods to compute delay propaga-tion in a mesoscopic graph-based model. Running, dwelling, connection and headwayprecedence relations are included in the graph that comprises all scheduled events.Primary and secondary delay distributions are obtained by computing the conditionalconvolutions of corresponding extended exponential distributions. The model was ap-plied for timetable evaluation and prediction of event times on a real-life case study inSwitzerland.

The presented deterministic and stochastic delay propagation models rely on the sched-uled timetable, train orders, routes and connection plans. Therefore, the actual stateof traffic at the moment of prediction cannot be exploited to derive more accurate pre-dictions. Moreover, the large-scale character of the models does not allow precisemodelling of train operation, capacity constraints and the resulting impact on runningtimes. They are thus suitable for estimating timetable robustness and stability but ap-plications in real-time traffic control require more detailed modelling and continuousupdates of train positions and traffic control actions.


2.5.4 Models for delay prediction in real-time

Real-time prediction models can be mesoscopic or macroscopic depending on the traf-fic control level. Mesoscopic prediction includes predicting the train paths on a de-tailed level, i.e. each signal passage is predicted. Prediction of train operation withsuch a level of granularity can be used to detect and resolve route conflicts (Albrecht,2009) and conflicts due to synchronisation constraints. In order to do so, it is necessaryto take into account signalling and interlocking logic that controls train traffic in realtime. On the other hand, macroscopic predictions only estimate the realisation time ofstation events (departures and arrivals) and aim at predicting delay propagation overlarge networks.

Real-time models for traffic state prediction may rely on the actual train positions,speeds, relative train orders and routes. The prediction methods vary from simpleextrapolation of current delays to application of methods of statistical learning fromhistorical traffic realisation data. Real-time prediction models presented in this reviewcan be classified according to their granularity to mesoscopic and macroscopic.

Berger, Gebhardt, et al. (2011) created a stochastic graph-based macroscopic modelfor delay prediction. The approach is suitable for online applications where updatesabout train positions are frequent. Running times are modelled as random variableswith probability distributions conditional on departure time and train type. The ap-proach allows testing the model with different types of discrete distributions for run-ning times. By using a set of waiting policies for passenger connections, the futuredelay propagation of the current delays that are continuously updated can be predictedin the observed part of the network. The model has been applied on a large scale casestudy in Germany for predicting delays over the entire network over an hours longprediction horizon.

Another traffic state prediction approach that relies on the actual state of traffic andexploit it to derive estimates for train running and dwell times is presented by Hansenet al. (2010). A macroscopic model for prediction of train running times is calibratedfrom historical track occupation data. The robust estimates of minimum running timeson the level of open track sections are computed and used to predict subsequent arrivaltimes. The prediction algorithm estimates the realisation time of an event by computingthe critical path through the macroscopic graph starting from the last realised event.The main contribution of this data-driven approach is that the estimates of processtimes reflect phenomena of railway traffic such as the dependence on delay, peak-hours, weather, and rolling stock.

More detailed traffic prediction models have been in the focus of relevant literature dueto their applicability for real-time rescheduling models. Luthi and Laube (2007) stud-ied the role of real-time prediction systems in the traffic control environment. In thatcontext their purpose is twofold. The first requirement is prediction of train trajectoriesuntil the next controllable point on the network. In other words, train running times tothe next station or point in the network that can accommodate reordering or re-routing


need to be computed. That way the accuracy of the rescheduling models, that assumefull knowledge of future traffic state, can be improved. The second role is connected tothe procedure of finding a new feasible schedule as a result of the rescheduling process.During the optimisation stage, rescheduling systems evaluate different solutions in thesearch for the optimum. Traffic evolution according to each observed potential solutionis predicted and summarised in the corresponding value of the objective function.

A mesoscopic graph based rescheduling model (D’Ariano, Pranzo, & Hansen, 2007)that was further extended to distributed control over multiple traffic control area (Cor-man et al., 2012b), considers the majority of operational constraints of railway traffic.D’Ariano (2008) used the temporal decomposition to apply the model for predictionsover a time horizon of several hours. The model predicts the future traffic evolution foreach considered rescheduling action. Static arc weights in the graph require an iterativeapproach to recompute a feasible speed profile of a train based on the train dynamicsand detailed infrastructure data. Moreover, running times are estimated based on the-oretical values and dwell times based on minimum dwell times, which does not reflectthe impact of delays, peak hours and passenger volumes on process times.

Fukami and Yamamoto (2001) presented a real-time prediction tool for a high-speedline in Japan. The system follows positions of all trains in the network using traindescribers messages and estimates the speed of a running train by assuming a constantvelocity over track-clear detection sections. The train trajectories until the arrival at thenext station are then simulated with respect to all microscopic operational constraints.However, predicted arrival delays at the next station are extrapolated to succeedingstations by a simple parallel shift method. That drastically reduces the complexity ofthe computationally demanding simulations but also makes the system less reliable forlong corridors or complex networks.

An online prediction tool has been implemented in the Swiss traffic control systemRCS (Dolder et al., 2009). The prediction model is based on a directed acyclic graph,with nodes in the graph corresponding to arrival and departure events at timetablepoints and signals, and arcs representing precedence relations between nodes corre-sponding to running, dwell, headway and connection arcs. Arc weights are computedoffline by solving the train motion equations using a detailed description of infras-tructure and train characteristics. After each train position update, the running timesuntil the next station are computed and a critical path algorithm derives predictions ofall event times on the graph. Prediction errors smaller than 1 minute are reported forevents within a 10 min prediction horizon.

The granularity of the presented macroscopic real-time prediction models is insuffi-cient for applications in traffic control because the interdependencies of train runs onopen track sections and in stations cannot be accurately modelled. On the other hand,more detailed models are able to capture route conflicts. However, accurate modellingof train dynamics in route conflicts relies on the computationally demanding procedurefor solving train motion equation. Moreover, the predictions are performed based onthe pre-computed running and dwell times. Therefore, this method does not consider


the impact that the current traffic conditions, such as delays, peak hours and passengervolumes may have on process times. Finally, the real-time information about runningtrains is not used to adapt the process time estimates. Such models can therefore notbe adjusted online to capture a particular driving style or malfunctioning trains.

2.6 Review of rescheduling models

The second research objective of this thesis is concerned with the development of arescheduling model for network-wide traffic management (§1.4). In Section 2.2.5,capacity restrictions and synchronisation times are presented as the major reasonsfor delay propagation in railway networks. In the current literature, the problem ofrescheduling has been addressed mainly separately for each type of delay propagation.The delay management problem has been defined as deciding whether the plannedconnections should be kept or cancelled in order to minimise passenger delays andinconvenience in case of disruptions and delays (Schobel, 2007). The more advancedversions of the delay management problem model consider macroscopic capacity con-straints in a realistic manner (Dollevoet, Huisman, Kroon, Schmidt, & Schobel, 2014;Schachtebeck & Schobel, 2010). A recent overview of other relevant contributions todelay management is given by Dollevoet (2013).

The problem of optimising train traffic with respect to both connection and capac-ity constraints is too complex to tackle in an integrated formulation. Recently, Cor-man, D’Ariano, Pacciarelli, and Pranzo (2012a) described a bi-objective optimisationapproach where a Pareto front is obtained that minimises secondary delays and thenumber of broken connections. An iterative approach that integrates a mesoscopicrescheduling tool with a macroscopic delay management model was presented byDollevoet, Corman, D’Ariano, and Huisman (2013). However, these methods are onlyable to solve problems not larger than a single traffic control area due to high com-plexity of the problem and requirements for short computation times. Therefore, fornetwork-wide traffic control, the traffic and delay management problem are still ad-dressed separately.

In this thesis and literature review, we focus on real-time traffic rescheduling as a prob-lem of solving a possible schedule infeasibility caused by delays. Various formulationsof the rescheduling problem exist and most of them rely on mixed integer linear pro-gramming which belongs to a class of difficult NP-hard problems (Schrijver, 1986).The models most commonly contain a binary control variable that models the relativetrain order on an infrastructure resource or a broken or kept passenger connection. In anextensive review of applicable models and algorithms developed until 2006, Tornquist(2006) argues that problem complexity depends not only on the generic formulationbut also to a great extent on the actual instance that is modelled. The author states thatan increase in the number of binary variables does not automatically imply the increasein complexity due to interdependencies between binary variables and implications offixing a value for a binary variable. That is important because it shows that the domain


knowledge of railway operations and process dependencies can be employed to reducecomplexity of generic optimisation problems.

An important property of the real-time rescheduling models is the way they handleuncertainty. The majority of the existing models assume full knowledge of delays andtraffic evolution. In contrast to that, Gatto (2007) defined the online version of delaymanagement. In their approach, uncertainty of delay values, that are given as an inputto the optimisation procedure, is recognised as a major factor for model accuracy andapplicability. For that reason they developed a family of competitive online algorithmsthat do not anticipate any values of future train delays. Due to high complexity, thisapproach could only be applied for delay management on a single corridor (Gatto, Ja-cob, Peeters, & Widmayer, 2007) or a simplified suburban network (Berger, Hoffmann,Lorenz, & Stiller, 2011). A recent contribution to online non-anticipative delay man-agement problem focuses on defining online strategies and waiting policies (Bauer &Schobel, 2014). The main contribution of this work is the design and implementationof a learning strategy for online delay management.

Corman and Meng (2014) presented a comprehensive review and classification ofrescheduling tools and applications. The relevant models developed in the period 2007-2013 are classified by the problem scope, model and solution. A special focus in thisreview was on availability of information on current train positions and traffic stateprediction. Models were classified into those where a full deterministic knowledge offuture traffic condition is assumed, models with full but stochastic knowledge on futureand finally, models with continuous updates of the current and future traffic condition.The first two types are described as static (open-loop) models, whereas the third type asdynamic (closed-loop) models. Note that the rescheduling module of the most closed-loop models still assume full knowledge of the present and future traffic state. Therescheduling problem is solved after each update of traffic state estimate (prediction).The performance of the closed-loop rescheduling systems depends to a great extent onthe reliability of traffic state predictions.

In this literature review we discuss the existing contributions that are applicable fortraffic control of large networks or traffic control areas. The approaches for optimalcontrol of train traffic over junctions or single-track lines will not be covered. More de-tails on approaches for controlling railway junctions can be found in Rodriguez (2007)and Milinkovic, Markovic, Veskovic, Ivic, and Pavlovic (2013). Relevant contribu-tions from the field of optimal rescheduling on single-track lines include Sahin (1999),Zhou and Zhong (2007) and Meng and Zhou (2011). Since the purpose of this thesis isdevelopment of real-time models applicable for implementation in a model-predictivecontrol loop, a special focus in this review will be on closed-loop models.

Pellegrini, Marliere, and Rodriguez (2014) presented an approach that models trainruns on the level of track sections. The model is able to optimise train routes andrelative orders in a complex station area using a mixed integer linear programming(MILP) formulation. The authors consider two objective functions: minimisation ofthe total secondary delay and minimisation of the maximum secondary delay for any


considered train. The model is implemented in a rolling horizon framework. A twentyminute horizon is considered with a ten minutes update frequency. Finally, the modelperformance is assessed based on three types of disruption scenarios that differ bymagnitude and severity. The high granularity of the model prevents applications tolarger instances.

A different approach to microscopic rescheduling was presented by Caimi, Chudak,Fuchsberger, Laumanns, and Zenklusen (2010) who focused on rescheduling traffic inand around major stations (condensation zones). The approach represents a modifica-tion of the train routing problem that was previously presented by Zwaneveld, Kroon,and Hoesel (2001). In the latter approach, train routes are represented by vertices andconflicting routes are connected by arcs. The problem of finding conflict-free routingis then formulated as an NP-hard problem of finding an independent set. Caimi et al.(2010) improved this approach for use in real-time. First they apply time indexing andpredefine a number of possible routes (in space and time) for each train. A conflictgraph is then created for each used resource (block section). The problem is furtherformulated as finding an independent set in each resource graph of conflicting routesand solved using integer linear programming (ILP). The same model was recently in-cluded in a model-predictive control framework for closed-loop rescheduling (Caimiet al., 2012).

An influential MILP formulation of a train rescheduling problem on a macroscopiclevel was given by Tornquist and Persson (2007). Furthermore, the authors definedthree heuristics to reduce the search space and decrease the computation time. Eachheuristic limits the number of reordering and rerouting actions. All three methodswere applied to a case study of a subnetwork in Sweden and performance in termsof optimality margin and computation time was used to evaluate the strategies. Highquality solutions in short time were obtained by predefining a number of permitted re-orderings relative to the train that suffered primary delay. The most promising strategywas further extended in Tornquist (2007) by introducing a parameter that defines thenumber of permitted reorderings relative to trains suffering secondary delay. More-over, a comprehensive analysis of different objective functions and different lengthsof prediction horizon was presented. Tornquist Krasemann (2011) recently introduceda greedy algorithm to tackle the complex cases of the MILP formulation. The ideawas to obtain reasonably good feasible solutions in a very short time and use the restof the predefined computation time to try to improve it by backtracking and reversingdecisions made in the first stage.

Acuna-Agost and Michelon (2011) presented an extension to the MILP formulation ofTornquist and Persson (2007). The model is improved by increasing the granularityto the level of block sections. Furthermore, running time adjustments were imple-mented in case of route conflicts due to braking and reacceleration. Presented solutionapproaches include ‘right shift’ retiming, local search and iterative local search opti-misation. A local search approach looks for the solutions close to the planned schedulein the search space. An iterative local search improves the solution iteratively until a


time limit or other end criterion is reached. The model is applied on a corridor casestudy since the increase in model complexity came with a price in computation time.Further improvement of this approach is presented by Acuna-Agost, Michelon, Feil-let, and Gueye (2011). By analysing delay propagation in case of primary delays, theauthors are able to assign a probability of being affected to each event included in themodel. The probabilities are computed with logistic regression considering the pre-diction variables such as scheduled headway times around the considered event andtime window between the primary delayed event and the considered event. The searchspace can thus be reduced by focusing on events with high probability of sufferingsecondary delays.

Another extension of the Tornquist and Persson (2007) problem formulation and a newsolution approach was presented by Min, Park, Hong, and Hong (2011). The originalmodel is extended by introducing a constraint that models conflicts in stations betweentrains that depart to or arrive from different open track sections. On the other hand,the new model assumes infinite capacity of all stations and unidirectional traffic on alllines. By exploiting these assumptions, a decomposition of the problem to a number ofseparate subproblems is enabled. The authors prove that solving small separate prob-lems in topological order yields near-optimal global solutions. The proposed solutionmethod is column generation that was applied to a case study comprising a large urbannetwork of a metropolitan area.

Van den Boom and De Schutter (2006, 2007) presented a way to overcome the lim-itation of the conventional max-plus models that rely on a fixed structure, i.e., fixedtrain orders, sequences, and routes. They proposed an approach called switching max-plus linear systems that can be used to incorporate discrete dispatching actions, suchas changing the order of trains, cancelling a train or a connection, into the max-plusframework. In their approach, the structure of the timed event graph can be changed.Every change corresponds to a dispatching decision and results in a new structure(mode) which represents a railway traffic model with the specified order of events andsynchronization constraints. The system is managed by switching between differentmodes, thus allowing the inclusion of discrete decisions into the model. They recastthe optimal switching problem as an MILP problem and propose a commercial soft-ware or metaheuristic algorithms to obtain solutions. The model performance is testedon the intercity network in the Netherlands. Recently, different formulations of themodel and the resulting effect on the computation time were considered (Kersbergen, ,Van den Boom, & De Schutter, 2013). The explicit formulation of the model where thestate vector does not depend on the values in the previous period caused a considerateincrease of computation time.

A separate stream of research on real-time traffic rescheduling is characterised by thejob-shop scheduling formulation of the problem. The general problem can be definedas the problem of assigning a set of machines to a set of competing jobs where a ma-chine can handle only one job at a time. Mascis and Pacciarelli (2002) analysed thecomplexity of the job-shop scheduling problem with blocking and no-wait constraints.


Blocking constraints imply that a job keeps blocking a machine until the next machinein the sequence becomes available. A no-wait constraint implies that two consecutiveoperations of a job must be completed without any waiting time in-between. alterna-tive graph (AG) were introduced as a convenient way of modelling job-shop schedulingproblems with specific signalling and safety constraints. The resulting formulation wasexploited for applications in railway traffic rescheduling by Mazzarello and Ottaviani(2007). The AG representation of the job-shop scheduling problem was used to de-velop a mesoscopic model for optimal rescheduling of railway traffic. Apart from thestandard constraints for three aspect fixed signalling, a way to model green wave pol-icy and moving block signalling system was also presented. The model was calibratedusing a speed profile generation module and a heuristic approach for route conflict res-olution was presented. The approach was assessed on a case study of a bottleneck partof the corridor in the Netherlands.

D’Ariano, Pacciarelli, and Pranzo (2007) presented and efficient branch and boundalgorithm to minimise secondary delays in an alternative graph based reschedulingproblem implemented in the real-time traffic management decision support systemROMA. The problem is first reduced by exploiting the fact that a relative train ordercannot change on open track lines. The heuristic defined by Mazzarello and Ottaviani(2007) is used to compute the initial solution for the branch and bound algorithm. Thismodel is further extended with a speed coordination component (D’Ariano, Pranzo, &Hansen, 2007). The speed profiles of hindered trains are adjusted to model brakingand reacceleration. The conflict resolution and speed coordination components are in-tegrated into a closed-loop framework where the feasibility of the solution computedby the conflict resolution part is verified after computing the adjusted speed profiles.The model was applied on a realistic case study of a busy traffic control area. Optimalresults for different kinds of disruption scenarios were obtained in a short time.

The problem of coordinating two dispatching areas was tackled by Corman, D’Ariano,Pacciarelli, and Pranzo (2010). A coordination level was added to the reschedulingproblem that was formulated with a separate alternative graph for each local dispatch-ing area. The coordination level consists of a border graph that is used to verify theglobal feasibility of the outputs from each separate area. Global infeasibility is solvedby adjusting the solutions of the subproblems. This approach was further extended tocoordinate multiple traffic control areas (Corman et al., 2012b). Moreover, the coor-dinator graph formulation was also improved with optimality conditions. An iterativeapproach is adopted as a way of communication between each subproblem and thecoordination level. A branch and bound algorithm was presented that solves the coor-dination problem. This approach has been tested on a large and complex subnetworkin the Netherlands. The impact of number of dispatching areas and their sizes on thequality of solutions and computation time was analysed.

Other approaches with an alternative graph representation of the job-shop schedulingproblem include Mannino and Mascis (2009) who created a decision support systemfor train control in metro stations that is applied in practice. Moreover, Liu and Kozan


(2011) included train priories in their macroscopic model for train scheduling on asingle track corridor. Finally, a recent contribution focused on integrating an alternativegraph model into a closed-loop control framework (Quaglietta et al., 2013). Reorderingactions computed by ROMA tool (D’Ariano, 2008) are implemented in a microscopicsimulator (Quaglietta, 2011). The conflict detection component of ROMA predicts thetrain traffic during a rolling prediction horizon, based on the current train positionsobtained from the simulator. Predictions are performed in a time-driven manner aftereach predefined rescheduling interval. If route conflicts are predicted, a new scheduleis computed by ROMA.

Table 2.1: Summary of presented approaches for real-time rescheduling

Scope Dispatching area Subnetwork

DMGatto et al. (2007)Berger, Hoffmann, et al. (2011)

Schobel (2007)Schachtebeck and Schobel (2010)Dollevoet et al. (2014)Bauer and Schobel (2014)

TM

D’Ariano (2008) Tornquist and Persson (2007)Caimi et al. (2010) Min et al. (2011)Mannino and Mascis (2009) Acuna-Agost and Michelon (2011)Pellegrini et al. (2014) Corman et al. (2012b)

Table 2.1 summarises the delay management (DM) and real-time traffic management(TM) models presented in Section 2.2.6. The papers are classified by scope of appli-cation. Some papers focused on detailed modelling of infrastructure, train dynamicsor uncertainty but were able to cope with a problem size limited to a single dispatch-ing area. On the other hand, larger instances are tackled by macroscopic models witha great deal of abstraction. An exception is the work of Corman et al. (2012b) whocoordinated multiple detailed models to tackle the traffic rescheduling problem overseveral dispatching areas. However, the problem of controlling country-wide traffic isstill unsolved since the coordination of local areas modelled micro- meso-scopicallyis computationally demanding, while the presented macroscopic models are applied tosubnetworks of a national network or metropolitan area networks.

2.7 Discussion

This chapter presented the terminology and basic concepts of railway traffic. Theessential problems in the current traffic control practice were identified. Moreover, weanalysed the relevant scientific contributions directed at improvement of the currentpractice. Finally, the gaps in the current research were identified and translated intoresearch objectives of this thesis.

The drawbacks of the current traffic control practice in the Netherlands include thelack of intelligent computer-based support to traffic controllers to monitor the traffic


conditions on the network, predict the future train movements, reduce delays and re-solve route conflicts in a network-optimal way. Traffic monitoring consists of a delayregistration system with insufficient precision. Moreover, the controllers have no sup-port to predict the future evolution of traffic or the consequences of their dispatchingdecisions. Finally, dispatching actions are made based on the predetermined scenariosand rules-of-thumb which may lead to suboptimal effects on traffic state.

For each objective of this thesis a review of the existing literature was performed.Applicability of the existing data mining methods for processing and extracting infor-mation from the train describer logs depends strongly on the data structure and infor-mation logged by the system. Therefore, a new data mining approach for extractingtrain event times and route conflicts from the Dutch system TROTS is presented in thisthesis. The tool also overcomes the limitations of earlier approaches that were limitedto station areas and controlled signals. In the approach presented in this thesis, trainpaths and route conflicts can be recovered on open track sections. The full list of con-tributions is presented in Section 1.5.1 and a detailed description is given in Chapter3.

Static estimation of process times irrespective of the current traffic conditions of thenetwork was recognised as the main drawback of the existing approaches. The secondobjective of this thesis aims at bridging this gap in an accurate and computationallyefficient manner that relies on historical traffic data. Running and dwell times areestimated from the TROTS log files without relying on the manually collected data,on-board units or station design data. The detailed description of this approach isgiven in Chapter 4 and the main contributions are summarised in Section 1.5.1.

The analysis of the relevant literature on delay prediction identified the low granularityin modelling, fixed structure of the models, and high computational requirements asthe main drawbacks for straightforward application in real-time traffic control. Theresearch in this direction presented in Chapter 5 resulted in a model that can quicklyand accurately predict train event times over large areas and long prediction horizons.The considered level of detail is suitable for prediction of route conflicts which is animportant requirement to support traffic controllers. The model can be continuouslyupdated with incoming information on train positions or traffic control actions. Finally,the online character of the model allows adjustments of the process time estimates inreal-time thus overcoming the limitation of static models with pre-computed processtime estimates.

Finally, the relevant contributions from the field of real-time rescheduling were dis-cussed from the perspective of their applicability for rescheduling traffic over large-scale networks. None of the reviewed approaches is suitable for applications on thenetwork control level. In Chapter 6 we present a macroscopic model with an appro-priate level of model granularity that allows application of the previously developedprocedure (D’Ariano, Pacciarelli, & Pranzo, 2007) for solving large instances com-prising the Dutch national network.


Chapter 3

Process mining of train describerevent data

This chapter is an edited version of the article

Kecman, P. and Goverde, R. M. P. (2012). Process mining train describer event dataand automatic conflict identification. In C. A. Brebbia, N. Tomii, & J. M. Mera (Eds.),Computers in Railways XIII, WIT Transactions on The Built Environment (Vol. 127,pp. 227–238). Southampton: WIT Press.

3.1 Introduction

Monitoring of current and prediction of the future train positions and delays are im-portant tasks of traffic control, as discussed in the previous chapter. Train describersare a typical way of centralised monitoring of train positions in discrete points in thenetwork. A message is received in the traffic control centre after every available up-date of train positions. In complex and busy railway networks, multiple train describermessages can be received within a second. Consequently, message archives containseparate large text files for a particular area for each day.

Train describer messages and archives were recently recognised as an important sourceof information about train traffic (Goverde et al., 2008). Real-time stream of messagescan be used for monitoring traffic conditions in the network. At the same time, archivesof train event messages provide the necessary information for an ex post analysis ofthe realised traffic. Efficient data processing tools are thus necessary that are ableto extract the information from a train describer message in real time and update thetrain positions, actual delays and register route conflicts. Likewise, the tool has to beable to quickly process the large archives and retrieve all relevant information abouttrain traffic in a certain area and period. The necessary information include: realised

51


running and dwell times, headway times between trains in bottlenecks, actual arrivaland departure times, and delays (primary and secondary).

Automatic identification of route conflicts is an important requirement. A case studyon a busy corridor in the Netherlands showed that 55% of arrival delays exceeding 3minutes are caused by route conflicts (Daamen, Houben, Goverde, Hansen, & Weeda,2006). Registered delays at stations cannot be with certainty attributed to route con-flicts, therefore, it is difficult to identify and analyse them. Typically, train delays atstations are monitored and registered online using train detection at main signals andtimetable databases, but the accuracy is insufficient for process improvements. Rail-way operations thus require a feedback of operations data to improve planning andcontrol. Accurate data on the level of track sections and signal blocks can be used togain a better understanding of the realized train paths and conflicts between them.

In an earlier work, Daamen et al. (2008) developed algorithms for automatic routeconflict identification based on data records of the Dutch train describer system TNV,which were implemented in the tool TNV-conflict. The TNV system has recently beenreplaced by the new train describer system TROTS which contains an essential newapproach to train number steps. This came with a new format for the log files. Inparticular, train number steps are no longer given with respect to a route block to anext signal, but at section level. This means that a train number step does not predictto which signal the train is heading, as was customary with TNV. Thus, we cannotlook ahead at the aspect of the signal at the end of a block to identify a conflict. Thealgorithms described in Daamen et al. (2008) had to be modified in a way described inthis chapter.

In this thesis, a process mining (Van der Aalst, 2011) approach is applied on the logfiles of the Dutch train describer system TROTS. The resulting tool recovers and vi-sualizes the realized train paths, blocking times, and route conflicts, and thus providesessential information for analysing railway operations that can be used for fine-tuningthe railway timetable and operational processes or development of data-driven mod-els. The tool supports a tabular output for statistical analysis, as discussed in Goverdeand Meng (2011), and visualizations of the realized time-distance and blocking timediagrams with highlighted route conflicts. A separate procedure is presented for iden-tification of route conflicts suffered by departing trains after a scheduled stop becauseextended dwell time of a train cannot directly be attributed to a route conflict. More-over, several improvements to earlier approaches have been implemented in terms ofretrieving traffic information from open track segments where traffic is controlled bynon-logged automatic block signals. Blocking times over open track sections are deter-mined so that route conflict identification is applicable over entire corridors, including‘dark territories’ with aggregated track sections.

The remainder of the chapter is structured as follows. Section 3.2 describes the method-ological framework of the process mining tool and formalizes the blocking time theoryas the employed process model. Furthermore, Section 3.3 explains the system ar-chitecture, data structure and drawbacks of the Dutch train describer system TROTS.

Chapter 3. Process mining of train describer event data 53

Section 3.5 explains the process mining algorithm and subroutines. A case study witha description of the graphical user interface is given in Section 3.6. Finally, Section3.7 gives a brief summary and presents further application of processed train describerdata in the data-driven prediction tool.

3.2 Methodological framework of the process miningtool

3.2.1 Process mining

Process mining is a method for discovering processes and extracting information aboutthem from event data using a process model (Van der Aalst, 2011). It combines datamining with domain knowledge about the specific processes that are analysed. Theprinciple idea of the concept is to extract the necessary information from large datasets and obtain an output containing clean and structured data ready for analysis.

Figure 3.1 presents the background of process mining. Recent advancements in sensortechnology and telecommunications enabled continuous monitoring of processes incomplex systems. The corresponding software systems often store the event messagesand measurements of processes in event logs. Using a process model, which is builtbased on the domain knowledge of the real-world system, event logs can be searchedand relevant processes can be discovered and retrieved.

This recently developed data mining paradigm has been applied successfully in analysingbusiness processes (Van der Aalst et al., 2007) and activities in social networks (Medeiros,Weijters, & Van der Aalst, 2007). In this thesis, we apply this method to mining his-torical train describer event data, recovery of train paths and identification of routeconflicts. The following section gives more details about the process model, whereasthe event log files of the Dutch train describer system TROTS are described in Section3.3.

3.2.2 Process model

The process model is built according to the principles of signalling systems (§2.2.2)and timetables (§2.2.1). A three-layer model of railway traffic is used to representrailway operations on multiple levels. A microscopic traffic model represents a trainrun on the level of track-clear detection sections. Each track section occupation andrelease represents an event. A section is occupied between the occupation and releaseevents. By keeping track of section events, the actual position of the head of the trainis determined at every occupation event and the position of the rear of the train at everyrelease event.

On the mesoscopic level, a train run is modelled as a sequence of signal passages. Sig-nal passages are events that initiate processes such as blocking a part of the infrastruc-ture and running over a block. The topology of the signalling and interlocking system


Software systemReal world

process

Process model

event messagesmeasurements

knowledgeprinciplesoperational rules

Process mining

Event logs

Figure 3.1: Process mining framework

provides a way to directly map the microscopic layer of the model to mesoscopic level.A block is occupied when a train occupies the first section in the block. Similarly, ablock is cleared by a train when the last axle of the train clears the last section in theblock. Therefore, detailed knowledge of the infrastructure layout provides a way tobuild the mesoscopic model from the microscopic model in a straightforward manner.Blocking time theory provides the logic implemented in this layer of the process modelin order to identify route conflicts.

Figure 3.2 emphasises the events and processes in micro and mesoscopic models. Atrain run over a track or block section can be represented by occupation (o) and release(r) events that are connected by running and clearing processes.

o

or

running

clearing

time

Figure 3.2: Events and processes in micro and mesoscopic models

A macroscopic traffic model is the top level of the multilayer model. It represents atrain run over the network as a sequence of departure and arrival events separated by


running and dwelling processes. A similar bottom-up approach can be used to createthis layer from the low-level microscopic model. A way to do that is by incorporatingthe station layout and topology of track circuits. Departure and arrival events can thanbe determined by occupation or release events of the relevant track sections. Moredetails about the exact method for determining arrival and departure times employedin this thesis is given in Section 3.5.6. Processes in this level are the train runs betweentwo scheduled stops and dwellings in stations.

The superimposed three-layer model of a train run between two stations is depicted inFigure 3.3. Using the topology of the signalling system, the occupation and releasetimes of block sections can be directly derived from occupation and release times ofindividual sections. Moreover, the station layout allows attributing platform sectionevents to be arrival or departure events which allows direct computation of delays.Note that all boxes in the figure represent only physical occupation times of the cor-responding infrastructure elements. In order to enable identification of route conflictsusing blocking time theory, the mesoscopic model needs to be extended with additionaltimes as described in Section 2.2.3.

Station A Station B

time

D

A

D A

Micro

Meso

Macro

Figure 3.3: Three-layer process model

3.3 The Dutch train describer system

3.3.1 System architecture

The train describer system in the Netherlands TROTS keeps track of train movementsat discrete points in the network and monitors the state of infrastructure elements suchas track sections, signals and switches (ProRail, 2008). The system contains two com-ponents. The first component keeps track of the status of infrastructure elements. Ev-ery change caused by a train (section occupation or release), signalling system (signal


change to ‘stop’ or ‘proceed’) or traffic controller (switch position or signal change) isregistered and logged as an infrastructure message. The second component keeps trackof train number steps. A train is identified by its number which is inserted manuallyby the traffic controller before (or just after) the first departure. TROTS assigns eachtrack section occupation or release to the train number that caused it. These messagesare logged as train number steps.

The Dutch railway network is divided into 13 TROTS areas. Each area comprises oneor more major stations with complex topologies and 30–40 km of surrounding railwayinfrastructure. A communication protocol between the systems enables coordinationbetween adjacent areas so that a train number inserted in one area is transmitted toother areas that the train crosses on its route. In order to reconstruct the train traffic overmultiple TROTS areas, it is necessary to merge the corresponding log files. TROTSlog files are archived per day and area in large files of TROTS format of approximately75 MB.

An important improvement compared to the earlier TNV system (Goverde, 2005;Goverde & Hansen, 2000) is that the train number step messages are coupled to tracksection messages. Another modification is that the current train route from signal tosignal is no longer available in the system. Therefore a train step message does notpredict the destination signal any more. At any moment, only the past train step andinfrastructure messages are known which motivated a modification of the existing al-gorithms for recovery of train paths and route conflict identification.

3.3.2 Data structure and information contained in log archives

TROTS generates train number messages and infrastructure messages and logs theminto a comma separated values (CSV) file. The content of a train number message isgiven in Table 3.1. Each successive train number step message contains either a newoccupied track section at the front or a released track section at the rear.

Table 3.1: Train number messages generated by TROTS

Filed Message content1 Time stamp2 Message code3 Type: insert, remove, train step4 Running direction5 km position of last section6 km position of next section7 All occupied sections

Infrastructure messages contain binary values that indicate the state change caused bya train, signalling system or a signaller. The following information is contained: timestamp, event code, element type (section, signal, switch), element name, and new state


(‘occupied’/‘released’, ‘stop’/‘go’, ‘left’/‘right’). The event code of a train numberstep corresponds to a section message with the same event code. This coding is usedto match a message about a section occupation or release with a message of a trainnumber step. A train run can therefore be tracked along the route on the level of tracksections. Infrastructure element names are given in form of a string that contains thestation area code and a numerical element identifier (e.g. section RTD$282T).

3.3.3 Shortcomings in TROTS log files

There are several issues in the TROTS log files that represent a potential source ofinaccuracy and complicate the discovery of processes defined in Section 3.5 and sub-sequent performance analysis.

• Time-lag between infrastructure and train messages. The system architecture(§3.3.1) reveals that infrastructure messages and train number step messages aregenerated by different components of the system, which sometimes results in asignificant difference between the time stamps of the corresponding messages.Analyses show random delays of up to 7 seconds of the train number step mes-sages. In order to avoid the possible inconsistencies, the developed tool doesnot use the time stamps of the train number step messages but only the onesof the corresponding infrastructure element messages. This imperfection of thetrain describer system is in the remainder of this thesis considered as a source ofunavoidable errors with limited effects on the overall results.

• Signal messages cannot be coupled to train step messages. Infrastructuremessages of a signal aspect change to ‘stop’ cannot be coupled directly to anytrain number step or section occupation message. Therefore, the current datastructure of the log files does not allow identification of the signals passed alonga train route.

• Automatic block signals are not logged. Without intermediate logged signals,an open track segment between two stations can be regarded as one block fromthe exit signal at the station of departure to the home signal at the station ofarrival. Thus, route conflicts between successive trains on an open track sectioncannot be identified.

• Track sections on open track are aggregated. Moreover, multiple track sec-tions can be aggregated within the TROTS system. They are reported to beoccupied and released at the same time as a group. If a signal is located in themiddle of such group, the system misses the occupation and release times ofassociated track sections.

• Scheduled stops cannot be identified. In the infrastructure messages in TROTSlog files, no distinction can be made between platform tracks and other tracksections. Therefore, scheduled stops can not be detected in a straightforwardway.


3.4 Traffic monitoring on open track and in stations

The previous section presented the data structure and information contained in theTROTS log files. The train positions are reported with each occupation and releaseof a track section. However, the traffic performance indicators such as, actual delays,route conflicts, realised running and dwell times and headways require monitoringof the signal passing and station events (departures and arrivals) of each train. Theessential requirement for developing a tool for monitoring the traffic conditions on thenetwork is to overcome the listed limitations of TROTS related to signal and sectionmessages on open track and in stations.

3.4.1 Associating signal messages to train number steps

In order to determine train blocking times and identify route conflicts, signal passingtimes for each train need to be known. Level of information in TROTS log files doesnot allow straightforward identification of the signals passed on a train route. Signalmessages only indicate if the signal aspect is ‘stop’ or not. Signal change cannotbe associated to a passing train or a traffic control action. This can be overcome bycreating an additional input file that lists each signal together with the first section itprotects and the section that releases it. This enables a bottom-up derivation of themesoscopic model from the microscopic level.

The corresponding input file can be created automatically by data mining the TROTSlog archives in a preprocessing step. A pattern discovery algorithm has been developedthat finds events that frequently occur together within a predefined time window. Welook for section occupation messages from the corresponding station area, that are reg-istered shortly before or after a message reporting signal aspect change. A 10 secondswide window was used that is moved and positioned around each message that reportsa signal aspect change to ‘stop’. All relevant track section occupation messages withinthe window are noted. After parsing a significant number of messages for each signal,the section that most often gets occupied within the moving time window is registeredas the section protected by the signal. We use this input in the main algorithm to iden-tify the signal passing time of a train number via the corresponding section that gotoccupied.

Figure 3.4 presents a screen shot of a TROTS file that illustrates the procedure ofcoupling signals with the sections they protect. A time window around the selectedmessage is presented (highlighted). The message reports a change of signal DT$72 to‘stop’. A message reporting occupation of a section within the same area (DT$71BT)is discovered (boxed) and can be coupled to train number 2122 using the identicalmessage tag (BM3359596).


Figure 3.4: Screen shot of a TROTS log flle

3.4.2 Logging of automatic block signal passing events

The major limitation of using TROTS event logs for traffic monitoring is that eventsat automatic block signals on are not logged. This means that the train blocking timesand route conflicts on open track section cannot be determined form the TROTS data.Moreover, aggregation of track sections on open track additionally complicates thetrain path recovery if a signal is located in the middle of the group. An additionalinput, containing a list of automatic block signals, interdependent signals and sectionsand a list of aggregated sections is therefore required for keeping track of train runs onopen track.

Using the additional infrastructure data, passing times and aspects of automatic blocksignals can be determined based on the section occupation and release messages. Inorder to simulate the three-aspect fixed-block signalling based on track section mes-sages, each signal in the list needs to be connected with dependent track sections andsignals. The list therefore contains each block on the open track section defined withdelimiting signals and comprised track sections. Occupation time of the first section ina block can be interpreted as the switching time of the signal that protects the block to‘stop’. Similarly the release time of the last section in the block corresponds to signalchange to ‘proceed’. For distinction between signal aspects required to identify routeconflicts, interdependence with the neighbouring signals is used.


Passing times of signals that are located within the aggregated section groups cannotbe determined explicitly by relying on the TROTS section messages. In order to over-come this, a linear interpolation procedure can be used. The running time over eachsection is computed as a fragment of total running time over the aggregated group pro-portional to the section length. This approximation assumes constant speed over theaggregated section. After the running time over each section in the group is approx-imated, the three-aspect fixed-block signalling logic can be implemented in the waydescribed above.

3.4.3 Logging of station events

An important aspect of traffic monitoring is keeping track of actual delays, running anddwell times. Since TROTS log files make no distinction between platform tracks andother track sections, an additional data source is required to recognise station eventsfrom the event logs.

In order to determine the exact departure and arrival times for a scheduled stop of atrain, a list of platform sections in each considered station is necessary. Moreover,a timetable, which indicates the trains that are scheduled to stop in each station, isrequired. A registered occupation or release of a section in a station is a candidate eventthat represents an arrival or departure of the train. The exact procedure to estimate thetimes of station events from the list of candidate events is described in Section 3.5.6.

A timetable with scheduled arrival and departure times for each train is also needed tocompute delays. By comparing the realised with the scheduled event times, the actualdelays can be computed and updated.

3.5 Train route recovery and route conflict identifica-tion

3.5.1 Process mining train describer data

The concept of the process mining tool is presented in Figure 3.5. An important prop-erty is that this method can be applied both for processing a live stream of incomingtrain describer messages for the purpose of monitoring traffic, and processing archivesof log files to extract the structured historical traffic realisation data. The core of thetool is an environment containing section, signal, block and train objects. All objectsare created and updated on-the-fly while parsing a TROTS log file using the describedinfrastructure and timetable files.

Static attributes in each object are fixed when objects are created, using additional in-frastructure and timetable input files described in the previous section. Section objectsare attributed by name, platform flag that describes platform sections, open track (OT)flag that indicates aggregated track sections on an open track, and signal that protects


the section (only for the first section in a block). Signal objects are described by name,protected section (first section of the protected block) and previous section (last sec-tion of the previous block). The static attributes of block objects include the delimitingsignals of the block and comprised track sections. Finally, each train is described bythe corresponding object using the attributes number and timetable that contains thelist of scheduled arrival and departure times in stations.

S1 S2

TS1 TS2 TS3

TROTS

Block Section Signal

Stop/go list

Train

Realised delays of scheduled eventsRealised train paths (time-distance) and blocking timesRealised rоute conflicts

Process model

Output

Name

OTSignalPlatform

NameProtected sectionTrain list

Train listTrain list

Start signalEnd signal

Sections

NumberTimetableSection listSignal list

Figure 3.5: Process mining TROTS data

Each infrastructure object keeps track of occupation, release and passing times of alltrains that are reported by the train describer system. This data is stored in the train listof the corresponding object. The dynamic list ‘Stop/go’ in a signal object is updatedwith every signal message. Each row in the list contains the time of an aspect changeto ‘stop’ and subsequent change to ‘go’. A Train object is attributed with the lists oftraversed sections and signals, that are updated with every message from the log filerelated to the train.

Information passing between different object classes and methods within the sameclass reflect the operational constraints of railway traffic such as route setting and re-lease principles and train separation on open track according to blocking time theory.The output of process mining includes, realised running and dwell times, route con-flicts, realised departure and arrival times, as well as realised train paths (blocking timeor time distance diagram).


3.5.2 Main algorithm

For the purpose of this study, we simulate the real-time environment by parsing thechronologically ordered messages line-by-line. Since the time lag between two suc-cessive messages is often less than one second, an efficient algorithm is needed toextract the relevant information from each message, update the corresponding objectsand identify a route conflict or determine the actual event time. The relevant data fromthe log files are saved in the infrastructure and train number objects which enables thealgorithm to revisit them, and use and update the information therein (Daamen et al.,2008). At any moment in time the values of object attributes provide the current trafficstate with all train positions, actual delays and infrastructure availability. The majoradvantage of this approach is the data flow between objects. The subroutines depictedin the main loop of the algorithm (Figure 3.6) are implemented as methods for the cor-respodning object classes. They are able to compare the values of the correspondingattributes for the relevant objects and identify route conflicts, process times, and theactual arrival and departure times.

The algorithm first reads each line of the log file and updates the corresponding object.TROTS logs each section infrastructure message followed (one or more messages later)by the corresponding train step message. Thus after a train step message is received,the necessary information about the section event is complete, i.e. time stamp, sectionname, train number and event type are known. Signal passages can be registered usingthe predefined interdependence between signals and protected sections (§3.4).

The first step of information processing is to update the dynamic attributes of the cor-responding objects in the subroutine ‘updateObj’.The remainder of the algorithm con-tains subroutines that reflect the fixed-block signalling principles in order to detectroute conflicts and identify hindering trains. Sections that are relevant for identifica-tion of route conflicts are the sections interdependent with main signals. Occupationof the first section after each signal and release of the last section in a block initiate theaspect changes of the corresponding signals. These events are used for identificationof route conflicts. For occupations of other sections, the procedure ‘identifyHindering’is activated to identify the hindering train if a route conflict has been identified at theprevious signal passage.

The branch for an open-track section is applied for the non-logged signals, that are pro-cessed by the subroutine ‘logSignal’. The signal information is further treated in thesame manner as for logged signals. Other (non open track) relevant sections are pro-cessed if an occupation message is received. The subroutine ‘routeConflicts’ checksif the train is hindered by an earlier train. For departing trains a similar subroutine‘departureConflicts’ is activated after the exact arrival and departure times were de-termined by the ‘getEventTimes’ subroutine. For all identified conflicts a subroutine‘identifyHindering’ is activated.

All subroutines are explained in detail in the following subsections using the toy net-work depicted in Figure 3.7. The network consists of signals S1–S4, open-track sec-


read line

updateObj

open track?

occupied?

departure?

logSignal routeConflict

getEventTimes

identifyHindering

released?

departureConflict

relevant?

Y

Y Y

Y

N

N

N

N

N

Y

occupied?

N

Y

Figure 3.6: Flowchart of the process mining algorithm


tions TS1–TS4, platform track sections TS5–TS7 and section TS8 in the interlockingarea. Sections TS1 and TS2 are aggregated into TS1/TS2 and aspect changes of signalsS1 and S2 are not logged.

Platform

TS1/TS2 TS3 TS4 TS5 TS6 TS7 TS8

S1 S2 S3 S4

Figure 3.7: Example network

3.5.3 Process discovery

The discovery of processes on a micro and mesoscopic level is performed by subrou-tines ‘updateObj’ and ‘logSignal’. For each infrastructure and train message, ‘upda-teObj’ creates a new object or updates the dynamic attributes in the correspondingobject. Section and train step messages can be directly connected using the uniquemessage code and together they carry the complete information about a section event.Signal messages are only used to update the ‘Stop/go’ attribute of Signal objects sincea signal aspect of a controlled signal can be changed by traffic control and not only bya passing train.

The problems of non-logged signals and aggregated sections on open tracks are re-solved with the ‘logSignal’ subroutine. For each message reporting a release of thefirst or last section in a block on an open track, this subroutine updates the correspond-ing Signal and Train objects. The time of the aspect change to stop is equal to theoccupation time of the first section (e.g. in Figure 3.7 S2 changes aspect to ‘stop’when TS3 is occupied). Similarly, the corresponding object of a non-logged automaticblock signal is updated with an aspect change to ‘go’ at the time of release of the lastsection in a block (S2 changes to ‘go’ when TS4 is released).

Aggregated sections are occupied and released at the same time (e.g. for TS1/TS2,TS2 is occupied when a train occupies TS1, and TS1 is released when a train releasesTS2). In order to estimate the time of the aspect change of S1 to ‘stop’ (or previoussignal to ‘go’) we need to estimate the actual occupation time of TS2 (release time ofTS1). The procedure is performed at the moment of release of the aggregated segmentso the total running time is known. We exploit the assumption that trains move withconstant speed over the aggregated sections on an open track. The running time overTS1 is computed as a part of the total running time proportional to the length of TS1.

The presented subroutines perform full route recovery of a train run on a micro andmesoscopic level. Moreover, by keeping track of section occupation and release times,as well as signal passing times, the realised headway times between successive depar-tures, occupations of critical track sections and signals passages are implicitly deter-mined.


3.5.4 Automatic identification of route conflicts

This subroutine is activated for every signal passing event. Train separation principlesdescribed in Section 2.2.3 are incorporated in this subroutine. If a train did not have ascheduled stop in the previous block, the algorithm checks if a route conflict exists, i.e.if the current signal (e.g. S3 in Figure 3.7) displayed ‘stop’ at the moment when thetrain passed the previous signal (S2). The time stamp of the approach signal message ismodified with a constant value of 12 seconds, representing the sight and reaction time.If a route conflict is identified, the time of conflict is the passing time of the approachsignal (S2) by the hindered train.

Identification of route conflicts suffered by a departing train requires a different proce-dure. We assume that the departing train was hindered if the exit signal was showing‘stop’ at the earliest possible departure time. It is considered that the earliest departuretime equals the scheduled departure time if a train had the arrival delay that is smallerthan the dwell time buffer. Otherwise, the earliest departure time is after the minimumdwell time has passed since the arrival time. The subroutine ‘departureConflict’ listspotential outbound route conflicts. However, extended dwell times in stations cannotdirectly be explained by route conflicts. In order to exclude the trains that waited fora feeder train to realize a connection, or the ones that had an extended dwell time forsome other reason, additional information from signallers and dispatchers is necessary.If a route conflict is identified, the time of conflict is the earliest possible departure timeof the hindered train.

3.5.5 Identification of hindering trains

After a route conflict has been identified, the subroutine ‘identifyHindering’ identifiesthe hindering train. As the hindered train progresses along the block protected by thesignal of conflict (e.g. S2 in Figure 3.7), the algorithm compares the previous releasetimes of each section (TS3 and TS4) with the time of conflict (as defined in the previoussection). The train that released the section after the time of conflict is the hinderingtrain.

Identification of the hindering train completes the necessary attributes for a route con-flict object (Figure 3.1). Recall that the conflict duration is defined as an overlap ofblocking times of two trains (§2.2.3). For departure conflicts, the conflict duration is aperiod between the earliest possible departure time and passing time of the exit signal.

3.5.6 Estimation of departure and arrival times

This subroutine derives the realized arrival and departure times from TROTS log files.This corresponds to discovery of macroscopic processes, running and dwell times.When a train passes the exit signal (S4 in Figure 3.7) after a scheduled stop (i.e., amessage reporting the occupation of the first section after the exit signal is received)a list of times of all section occupations and releases in the platform block (including


the passing time of the exit signal) is created (sections TS5–TS8). Note that not allrelease times of platform sections are recorded by the time the train passes the exitsignal, however that does not affect the method we propose. The period of standstillis determined as the longest time gap between two successive events. The time of thelast section message before the standstill is set as the arrival time and the time of thefirst section message after the standstill is the departure time.

This method is an improvement of the current practice in the Netherlands which relieson the measurements of signal passing times adjusted with a fixed correction term(§1.2). Moreover, the approaches presented by Longo et al. (2012), Stam-Van den Bergand Weeda (2007) and Richter (2013) are based on occupation times of predeterminedsections. The approach described above is a generic procedure that relies not onlyon section occupation times but also on section releases times which increases theprecision of estimates and requires only train describer data as input without exactknowledge of station topology. The error of arrival (departure) time estimates dependson the number of platform track sections and the distance between the stop location ofthe rear (front) of the train and the used section border.

3.6 Process mining tool

The algorithms discussed in the previous section are implemented in a software tool forprocessing TROTS log files developed in MATLAB. The tool is able to process largesets of historical data and extract the relevant processes, route conflicts and delays.Moreover, for analysing traffic in particular instances, i.e. station areas or corridorsduring a specific time interval, a graphical user interface (GUI) has been developedthat simplifies selection of a particular instance and provides the graphical and tabularoutput.

3.6.1 Case study

This section illustrates the application of the presented algorithm in an ex post trafficanalysis for the TROTS areas The Hague and Rotterdam in the Netherlands. Thearea comprises the busy corridor Leiden–The Hague HS–Rotterdam–Dordrecht andsurrounding tracks. Figure 3.8 shows the macroscopic layout of the observed areawith indicated large stations. Since the messages from each TROTS area are loggedinto separate files, analysis of traffic over multiple areas requires merging the fileswhile maintaining the chronological order of the messages.

The performance of the tool is demonstrated by processing a data set for one day oftraffic. The algorithm parses the merged files and reconstructs the realized train pathsof 2048 trains on micro, meso ad macroscopic level. Moreover, all occupation timesof 1396 track sections and all blocking times of 733 blocks are determined, as well asthe aspect changes of 624 signals and the arrival and departure time estimates of alltrains at 21 stations. Finally, 1011 route conflicts are identified. The time required to


Leiden

Rotterdam

Dordrecht

H. v. HollandSchiedam

DelftThe Hague HS

The Hague CS

The Hague NOI

Figure 3.8: Observed area for the case study

process all 600 000 messages, describing the traffic over one complete day, was aroundten minutes.

3.6.2 Graphical user interface

In order to simplify the analysis of the output, a GUI has been created (Figure 3.9).The left part of the GUI contains tabbed panels for data loading (top left panel), visual-ization control (top right) and displaying results in tables (lower panel). The right partof the GUI is reserved for the visualization of traffic in either time-distance or blockingtime diagrams.

The tab panel for loading data enables the user to either load the raw data and startthe algorithm or load already processed data and display the results. In the lower tabpanel, the user can choose which results to display. In the tab Trains (Figure 3.10),a train line can be selected from the pop-up menu which enables selecting a trainnumber from the chosen line. We can then select the whole train path or a part of itby selecting a start and end station. The results are then displayed in the tables onthe left and the visualization panel on the right. The selected part of the train routeis visualized together with all other trains that operated on the selected corridor 15minutes before and after the selected train. The tables represent the list of conflicts inwhich the selected train participated, the running times on all sections, the blockingtimes, and actual arrival and departure times and delays at all stations.

The panel Infrastructure (Figure 3.11) enables the user to choose the corridor and the


Figure 3.9: Graphical user interface

Figure 3.10: Train selection panel


time interval and get the corresponding list of conflicts, list of sections, signals, blocks,and stations that were utilized by trains on the corridor within the selected time interval.Selection of the infrastructure element from the corresponding pop-up menu displaysall the state changes of that element with the associated train number and time instants(in seconds from midnight).

Figure 3.11: Infrastructure selection panel

The visualization control panel (upper right panel Figure 3.9) enables the user to switchbetween the blocking time diagram and time-distance diagram of traffic on the selectedcorridor and time interval. Also it is possible to turn on/off the zoom and pan tools androtate the axis of the diagrams. Finally the selection of the check-box Scheduled alsovisualizes the scheduled train paths.

Figure 3.12 shows the time-distance diagram on the busy corridor between The HagueHS and Rotterdam in the Netherlands between 9:00 and 9:40. The number of tracksbetween the stations is indicated (the number of lines between station name abbrevia-tions on the left side of the figure indicates the number of tracks) as well as the con-flicts (red squares on the hindered train path at the location of the signal of conflict).Intercity trains are presented in blue colour and local trains in magenta. Many minordisturbances are captured in the figure. Moreover, a major disruption, possibly due toa broken train just after departure from station Rotterdam (RTD) is visible. Finally, anon-scheduled overtaking of train 5133 by train 9220 occurred in station delft (DT).Closer analysis of the route conflicts requires a representation of the traffic situationusing blocking time theory.

Figure 3.13 displays the corresponding blocking time diagram for one direction thatappears after selecting the appropriate radio button on the visualization control panel.


Figure 3.12: Time distance diagram

Overlaps in blocking times indicating conflicts are denoted in red colour. Note thattrains on parallel tracks of four-track lines may overtake each other. Blocking timesthat appear to be overlapping but are not shown in red are non-conflicting parallel pro-cesses. The figure shows a departure conflict of train 5133 in station Delft. The trainwas hindered due to the unplanned overtaking. Moreover, a sequence of route con-flicts is captured in station Schiedam (SDM) where trains had to wait for an availableplatform track.

3.7 Conclusions

This chapter presented a tool for recovery of train paths and automatic conflict identi-fication based on process mining of train describer data. Historical archives from theDutch train describer system TROTS were used for developing the algorithms. Thedrawbacks of TROTS data for performance analysis have been overcome by includ-ing additional input containing the necessary infrastructure and timetable data. Thealgorithms have been implemented in a software tool for data processing and perfor-mance analysis. The tool provides flexibility in analysing particular train paths andtraffic on the corridor. Visual and tabular output simplify analysis and highlight severedisruptions as well as minor disturbances as a result of variability of process times.

The process mining method allows application of domain knowledge to data under-standing and extracting the relevant information which are the first essential steps forany data-driven application (Fayyad, Piatetsky-Shapiro, Smyth, & Uthurusamy, 1996).Moreover, model-based processing allows anticipation of a future event and thus sim-


Figure 3.13: Blocking time diagram

plifies the detection of errors in the data by detecting an unexpected event. This isof great importance for real-time applications that do not rely on clean and structureddata, but noisy live data streams that need to be quickly processed.

Straightforward applicability for other train describer systems strongly depends ontheir data structure. However, using the principles of blocking time theory as a processmodel in mining the event log files is a generic method for analysis of running timesand dwell times, and identification of route conflicts for fixed block signalling systems.Potential developments are mainly directed towards automatic analysis by providinguseful statistical indicators for structural flaws in the timetable, as well as detectingsevere disruptions and identifying primary delays, see also Goverde and Meng (2011).

Finally, the presented approach is important for development of the data-driven modelsdiscussed in the following chapters. The tool is used to process a large set of historicaldata comprising three months of traffic in Rotterdam and The Hague TROTS areas.Chapter 4 presents statistical models for analysing the processed data and derivingrobust estimates of process times. Moreover, the tool has been applied in the simulatedreal-time environment for monitoring train positions, infrastructure availability andactual delays (Chapter 5).


Chapter 4

Data analysis and estimation ofprocess times


Kecman, P. and Goverde, R. M. P. (2013). Calibration of a data-driven railway trafficprediction model. In T. Albrecht, B. Jaekel, & M. Lehnert (Eds.), Proceedings of the3rd International Conference on Models and Technologies for Intelligent TransportSystems 2013 (pp. 459–469). Dresden: DUTpress.

Submitted to Public Transport

4.1 Introduction

Processed historical traffic realisation data can be used to derive robust estimates ofprocess times. The tool for processing raw train describer data, presented in the pre-vious chapter, discovers train running times over track sections, blocks, and betweenscheduled stops. Dwell times at scheduled stops are also discovered, as well as allroute conflicts and their duration. An important property of the resulting data struc-tures is that they contain indicators of the traffic state for every discovered process.This enables analysis of processes depending on a particular train line, time of dayand actual train delays, which is described in this chapter. The work presented here iscarried out as a contribution to the second requirement in development of the tool formonitoring and traffic state prediction (§1.4.1).

Accurate estimation of running, dwell and headway times is important for all planningand control levels of railway traffic. The validity of capacity analysis and planningat strategic and tactical level depends to a great extent on the accuracy of processtime estimation (Abril et al., 2008; UIC, 2013). Similarly, timetabling models assume

73


full knowledge of process times. Moreover, stochastic models developed in order toimprove timetable robustness (Buker & Seybold, 2012; Medeossi et al., 2011) relyon probability distributions of process times derived from historical traffic realisationdata. Finally, on operational control level, process times are estimated for real-timetraffic prediction and conflict detection (D’Ariano, Pranzo, & Hansen, 2007; Dolder etal., 2009), as well as to provide reliable passenger information (Berger, Gebhardt, etal., 2011).

The relevant processes in railway traffic and earlier attempts in estimating their dura-tion are described in Section 2.4. The essential drawback of the existing approaches forestimation of running times (Brunger & Dahlhaus, 2008; Dolder et al., 2009) and dwelltimes (Buchmueller et al., 2008; Stam-Van den Berg & Weeda, 2007) is that they donot consider the actual traffic conditions on the network at the moment of estimation.In other words, process time estimates do not differ depending on the time of the day,train positions or delays. An initial work in overcoming this problem was presented byVan der Meer et al. (2010). However, the macroscopic character of the model preventsestimation of train runs on the level of block sections, which is essential for predictionof route conflicts. In this chapter we analyse the processed historical data and buildstatistical models for estimation of process times.

Two approaches for deriving process time estimates are examined. The global ap-proach consists of a generic statistical model applied on the aggregated set of histori-cal data. The data about all running times on the level of block sections and all dwelltimes are aggregated and used to train and validate the statistical models. A set ofpredictor variables is identified for the purpose of building the global model. A se-ries of advanced supervised learning methods is used for computing accurate processtime estimates. The accuracy of the robust linear regression model is improved usingstate-of-the-art tree-based regression methods (Hastie, Tibshirani, & Friedman, 2009).

On the the other hand, multiple local models are developed that estimate process timesfor particular blocks, stations and train lines. Each local model represents an inde-pendent statistical model. Robust linear regression is used to neutralise the impact ofoutliers which is important for real-time applications that need to process noisy data, aswell as missing values (Rousseeuw, 2005). The train describer log files are the singleinformation source for developing the models. The two approaches are compared bytheir accuracy and applicability for calibrating the real-time traffic prediction modeldescribed in Chapter 5.

The methodology used to build the statistical learning models is described in the fol-lowing section. Section 4.3 describes the advanced supervised learning methods forestimation of conflict-free running and dwell times followed by their implementationin the global (§4.4) and local model (§4.5). Model validation is presented in Section4.6. Finally, the main conclusions and recommendations for further research are givenin Section 4.7.

Chapter 4. Data analysis and estimation of process times 75

4.2 Methodological framework for statistical analysis

4.2.1 Description of the data set

For this study, a set of track occupation data comprising TROTS archives for threemonths (March – May, 2010) from the areas Rotterdam and The Hague (Figure 3.8)was made available by ProRail. The raw data archives are processed with the processmining tool (Chapter 3) resulting in running, dwell, blocking and headway times of alltrains. The data archives from 82 days was used to train and calibrate the statisticalmodels (training set). The remaining 10 days of data was used to test and compare theprediction accuracy of the models (test set).

In the processed files, running times are given on the level of block sections. Animportant aspect is the distinction between conflict-free runs and hindered train runs.Hindered train runs are filtered out and only conflict-free running times are includedin the data set. Dwell times at each station are provided using the method described inSection 3.5.6.

4.2.2 Global model

The global model for process time estimation aggregates the recovered process timesof all trains into a set of running times and a set of dwell times. A separate model iscreated for each process type.

Global model for running time estimation

Predictor variables used to estimate the train running time over a block are determined.An obvious indicator of train running times is the block length, which can be derivedfrom train number step messages (§3.3.2). Moreover, we include the block distancefrom the last scheduled stop, as well as the distance to the next scheduled stop inorder to include the effects of extended running times due to braking and acceleration.The distances are computed between the middle of the platform and the middle of theblock. Running times over blocks in a cruising stage depend on the maximum speedlimit. On the main lines in the Netherlands, excluding high-speed and freight lines, themaximum speed limit on is either 130 or 140 km/h (ProRail, 2013). Maximum speedlimit in the part of the network used for this case study is 140 km/h.

Furthermore, we consider the impact of peak-hours on train running times. A binaryvariable is created that indicates whether the observed process takes place during apeak-hour. The difficulty in separating the data set to peak and off-peak events stemsfrom the fact that the limits of peak hours can be fuzzy, as well as train line and stationdependent. The exact limits of peak periods are difficult to obtain without the addi-tional data sets that reflect passenger demand such as passenger counts, ticket salesinformation or smart card data. Therefore, in the global model, we use the definitionof peak-hours from the Dutch national train operator NS. Morning peak is the period


between 6.30 – 9.00 and the afternoon peak is between 16.00 – 18.30. Peak-hoursare considered only on working days, therefore, weekends and holidays have no peak-hours. Note that the drawback in accuracy of using the predefined limits for peakperiods has been overcome in the local model (4.5.2).

The categorical variable that indicates the train type is also considered as a predictor.In order to create a generic model, this variable has only two levels: intercity trainswith scheduled stops in large stations and local trains that stop in every station alongtheir route. Freight trains are not included in the data set due to a small correspondingsample in the considered area. Moreover, even though hindered train runs are excludedfrom the data set, the headway time between successive trains is included as a predictorthat may explain the impact of the preceding train on train running time. Headway timeis in this context defined as the time since the previous occupation of the same block.

Finally, we test the validity of the assumption that the running time of a train dependson the value of delay at the previous departure. It is assumed that delayed trains mayrun with full performance in order to use the running time supplements to reduce delay.On the other hand, trains running on time or ahead of their schedule run in a lower per-formance regime, thus avoiding early arrivals and achieving energy efficient driving.This assumption was not validated in earlier approaches (Luthi, 2009; Van der Meeret al., 2010) on the macroscopic level. In this thesis, the impact of departure delayson train running times over block sections is examined with respect to acceleration,cruising, coasting and braking.

Global model for dwell time estimation

Dwell time predictors, obtainable from train describer data are presented in this sec-tion. Scheduled dwell time for each scheduled stop is an obvious choice for a predictorvariable. Furthermore, the fact that trains do not depart before their scheduled depar-ture time indicates that arrival delay may have a major impact on train dwell time.Early trains have longer dwell times than scheduled in order to avoid early departures.On the other hand, trains with a positive arrival delay that is larger than dwell timebuffer spend a minimum dwell time in order to minimize the departure delay.

The impact of train and station type is examined by including corresponding two-levelcategorical variables. Stations are separated into small and large stations and trainsinto intercity and local trains. A station where only local trains stop (it is skippedby intercity trains) is considered as small. On the other hand, a station where bothlocal and intercity trains stop is considered as large. Finally, the impact of peak-hourson dwell times due to the increased number of alighting and boarding passengers isincluded in the same manner as in the described model for running time estimation.

Note that all considered predictors are obtainable from track occupation data and thetimetable. Dwell times are predicted as an integrated process since no rolling-stockor passenger data, needed to analyse sub-processes of train dwellings, were availablefor this study. Moreover, the imprecision in estimating the exact arrival and departuretimes , described in Section 3.5.6, may influence the accuracy of dwell time estimates.


The significance and predictive power of each presented variable is tested using thestatistical learning methods described in Section 4.3.

4.2.3 Local model

This chapter also focuses on the local model for running and dwell time prediction.The processed train describer data enable creating a separate process time estimationmodel for each block, station and train line. The goal of the local model is to explainthe variation of running times of trains of the same line over a particular block. Forthat reason, many of the predictors used for running time estimation in a global model,such as block length, distance to and from the last scheduled stop, train type, headwaybecome redundant. In order to estimate process times for a particular instance (trainline, block section or station), we investigate the impact of departure delay and attemptto verify the assumption that delayed trains run faster to reduce their delay. Similarly,the local model for dwell time estimation that is created for each station and train lineconsiders only the impact of arrival delay and peak-hours.

The applicability of such models is limited by data availability. For example a localmodel for estimating a process time of trains of a certain train line over a particularblock cannot be generalised to other block sections or train lines. Therefore, a suffi-cient amount of data is required to build each local model. It is important to have thisin mind because train lines operate with different frequencies and some parts of thenetwork may be utilised less than the busy main lines or station routes.

4.3 Statistical learning methodsThis section describes the statistical learning methods used in this thesis for develop-ing the predictive models for process time estimation. The criteria used to select thesemethods are: prediction accuracy, the simplicity of implementation, computationalrequirements and the interpretability of results. Moreover, an important aspect of su-pervised learning techniques is the trade off between bias and variance, i.e, betweenunderfitting and overfitting the models (Hastie et al., 2009). Due to the envisaged real-time application of the obtained process time estimates, it is essential that they arerobust against the outliers in the data. Thus the methods and models with high bias arefavoured compared to the models with high variance that overfit the data.

We first test the applicability of the linear models due to their simplicity and high bias.The accuracy of predictions is further tested with the regression tree based method,which can capture the nonlinear relations between the predictors and the response.Finally, the application of random forests, a method that overcomes the high varianceproperty of regression trees, is tested.

4.3.1 Multiple linear regression

Running and dwell times in the global model can be predicted as outcomes of a linearmodel. The approach relies on the multiple regression model due to its simplicity.


The individual impact of each predictor is computed as well as the goodness of fit ofthe global model. The generic model is given in equation (4.1) which estimates thevalue of the response variable Y with respect to p predictors. A regression coefficientβ j estimates the expected change in Y per unit change in X j, where j ∈ {1, . . . , p}assuming that all other predictors held fixed. Coefficient β0 is called the intercept andε is the error term.

Y = β0 +β1X1 +β2X2 + · · ·+βpXp + ε. (4.1)

The goal of multiple linear regression is to compute estimates β0, β1, . . . , βp based onn observations, so that the residual sum of squares (RSS) is minimal. RSS is computedas RSS = ∑

ni=1(yi− yi)

2, where y = β0 + β1x1 + β2x2 + · · ·+ βpxp.

Discussion of a multiple linear regression model requires analysis of overall modelaccuracy, as well as the analysis of impact of each of p predictors included in themodel. The model accuracy is reflected through the residual standard error (RSE)

RSE =

√1

n− p−1RSS (4.2)

and the fraction of explained variance of Y

R2 = 1− RSSTSS

. (4.3)

Total sum of squares (TSS) is computed by TSS = ∑ni=1(yi− y)2, where y is the mean

value of all observations of y, represents the sum of squares without any model.

Furthermore, the F statistic shows the predictive power of the model

F =(TSS−RSS)/pRSS/(n− p−1)

∼ Fp,n−p−1. (4.4)

The impact of each predictor X j is estimated by computing the p-value which indicatesthe probability of accepting the hypothesis that no relationship between X j and Y exists.More details on linear models and their interpretation can be found in Hastie et al.(2009).

Robust linear regression

Robust linear regression (Rousseeuw, 2005) represents a modification to the describedleast-squares method with the intention to identify outliers in the data set and excludethem from the computations. Estimates that are resistant to outliers both in x and ydirection can be obtained by fitting the regression curve to the majority of data andsubsequently identifying outliers as data points with large residuals from the robustsolution.


Rousseeuw and Driessen (2006) presented an efficient algorithm for computing ro-bust linear regression coefficients using the least trimmed squares (LTS) method. Theobjective is to find a h-subset of the data set n and minimise

h

∑i=1

(yi− yi)2i:n (4.5)

where (y1− y1)21:n ≤ ·· · ≤ (yn− yn)

2n:n are ordered squared residuals and h is a point

that reflects the percentage α of resisted outliers h = dn(1−α)e.

The simplicity of the linear model comes with a price of inaccuracy and inability tomodel interactions between predictors and their non-linear impact on the output vari-able. An example of the non-linear relationship between a predictor and the outputvariable are discrete categorical variables. Interactions between predictors indicatethat they are correlated and the impact of one predictor is dependent on the value ofanother. It is therefore difficult to distinguish the impact of correlated predictors sep-arately. An example of interacting predictors may be that delayed trains run faster inthe acceleration and braking phase. Thus the impact of block position with respect toprevious and next scheduled stop could indicate how important a departure delay ison running time estimation. The correlation between distance from the previous anddistance to the next scheduled stop is clear.

4.3.2 Tree-based non-linear methods

Regression trees

A way to overcome the drawbacks of linear methods emerged with the developmentof the tree-based methods (Breiman et al., 1984). The basic concept of these methodsand their application in regression is to segment the predictor space into simple regions.The output variable is predicted in each region separately.

The predictor space represents the set of values for X1,X2, . . . ,Xp which is dividedinto J distinct and non-overlapping regions R1,R2, . . . ,RJ . For every observation ofp predictors an appropriate region R j (terminal node in the tree) exists. The terminalnode for each observation is reached by applying splitting rules, i.e., binary decisionsat internal nodes that direct the observation towards its corresponding region. Theestimated value of the output variable is computed as the mean of the response valuesfor the training observations in R j.

Similarly to linear models, regression trees are created as a result of the optimisationprocedure that minimises RSS = ∑

Jj=1 ∑i∈R j(yi− yR j)

2, where yR j is the mean of alloutput values from training observations in R j. Due to the high computational com-plexity of this problem, an algorithm has been developed that recursively partitionsthe predictor space in a greedy manner (Therneau, Atkinson, & Ripley, 2014). Thetree is built by the following procedure: first a single variable X j and point s is found


that splits the data into two groups {X |X j < s} and {X |X j ≥ s}. The procedure is re-cursively repeated in each partition until a threshold is reached in terms of number oftraining observations in the region.

The described algorithm always selects the splitting variable that contributes to min-imisation of RSS the most. In principle that may cause that certain variables with lowcontribution to the main objective may be completely left out from the model and notchosen as splitting variables. An indicator of importance is obtained for each variableused for growing the tree. It is computed as the sum of improvements of the objec-tive function for each split for which the variable was used as the splitting variable.Furthermore, in order to increase the interpretability of a tree and avoid overfitting themodel to the training set, the tree can be pruned. The resulting tree has fewer regionsand performs better on the test set. More details on pruning can be found in Breimanet al. (1984).

The major advantage of regression trees is that they are transparent and easy to inter-pret and validate by experts. They are able to handle non-linear dependencies, interac-tion between predictors, and categorical variables. However, the prediction accuracyis often unsatisfactory when applied on a test set. Even after pruning the trees, theprediction in terminal nodes may be significantly affected by outliers.

Random forests

The drawbacks of regression trees can be overcome by generating a large numberof trees on the training set and using average values of all responses to estimate aninstance from the test set. The fundamental concept is called bagging and relies onrepeated sampling of the training set and obtaining B different training sets (Breiman,1996). Each sample Sb of size 2B/3 where b ∈ {1, . . . ,B} is used to build a regressiontree. The predicted response of the model to a test observation is computed as theaverage over all trees

y =1B

B

∑b=1

ySb (4.6)

In each sample the data that is left out is used to estimate the so called out of bag(OOB) error. The response for the bth observation is predicted using each regressiontree for which this observation was left out from the training set (B/3 observations onaverage). All errors are averaged to obtain the OOB error as a cross-validated indicatorof model accuracy.

Random forests have been introduced by Breiman (2001) in order to further improvethe accuracy of bagging models. They rely on randomisation of the previously de-scribed recursive algorithm for construction of each tree. The major modification isthat not all predictors are considered for choosing the best split of the predictor spacebut only randomly chosen m variables. The prediction is again performed by aver-aging the response of each of the B trees thus further reducing the response error ofregression trees.


4.4 Process time estimates – global model

Predictor variables used to derive process time estimates form the global model weredescribed in Section 4.2.2. This section presents the results of applying the statisticallearning methods described in the previous section on the available data set (§4.2.1).The algorithms for creating the statistical models have been implemented in a pro-gramming language for statistical computing R (R Core Team, 2013). The packagesfor robust linear regression (Rousseeuw et al., 2014), regression trees (Therneau et al.,2014) and random forests (Liaw & Wiener, 2002) were used to build the respectivemodels.

4.4.1 Running time estimates derived from the global model

Table 4.1 summarises the training set used to derive running time estimates. Responsevariable ‘running time’ represents the running time of a train over a block. It is pre-dicted with respect to departure delay (‘departure delay’), block length (‘block length’),distance from the last (‘distance from’) and to the next (‘distance to’) scheduled stop,and time headway from the preceding train (‘headway’). Two categorical binary vari-ables: train type (68% of data points are related to intercity trains), and peak-hours(27% of data relate to peak-hours) are also included in the model. Training data setcomprises 101481 data points describing the running times of nine train lines over 143blocks in 82 days.

Table 4.1: Summary of the training set for running time estimation

Mean Median St. Dev. Min Max

running time (sec) 43.16 41.57 19.10 10.01 179.35departure delay (sec) 100.29 53.97 148.90 −147.73 1199.13block length (m) 1137.82 1185.00 384.70 255.00 1915.00distance from (m) 5300.93 3685.00 5291.24 131.00 24440.00distance to (m) 6986.98 5140.00 5500.12 1190.00 2376.00headway (sec) 691.58 610.58 556.48 93.66 21349.03

Robust linear model for running time estimation

Results of applying LTS robust multiple linear regression (Rousseeuw et al., 2014) tofit the data are given in Table 4.2. The coefficient is given for each variable. Moreover,we give an indicator of importance of a particular variable for the overall model, whichis a representation of the corresponding p-value. Note that the categorical variables arepresented with only one level since the variable value for the second level is equal tozero.

The results indicate that all considered variables have a significant impact on runningtimes. The running times during peak-hours are slightly shorter than off peak. A neg-ative correlation with departure delay is determined which indicates that in general,


Table 4.2: Summary of the LTS model for running time prediction

Dependent variable: running time

Coefficient p-value

peak hour = 1 −0.1608 ∗∗∗

departure delay −0.0019 ∗∗∗

headway −0.0013 ∗∗∗

distance to −0.0002 ∗∗∗

distance from −0.0002 ∗∗∗

block length 0.0239 ∗∗∗

train type = ‘local’ 0.6803 ∗∗∗

Intercept 13.0600 ∗∗∗

R2 0.6514Residual Std. Error 6.5810F Statistic 19320.0800 ∗∗∗

Note: ∗∗∗p<0.01

delayed trains run slightly faster to recover the delay. Furthermore, a negative correla-tion between running times and headways can indicate that in case of short headwaysafter the preceding trains, trains tend to run slower to reduce the possibility of run-ning into a route conflict. The position of the block with respect to the station of theprevious and next scheduled stop may reflect the phase of running time as defined inSection 2.2.1. Negative coefficients of the corresponding variables indicate shorterrunning times with increased distance from/to the scheduled stop. Furthermore, blocklength has an expected positive impact on train running times. Finally, local trains areestimated to have slightly longer running times than intercity trains.

The lower part of Table 4.2 presents the predictive quality of the model. The R2 valueindicates that 65% of variation of running times can be explained by the presentedmodel. Having in mind that the variation within the training set is relatively low (Table4.1), this implies that the presented model is useful for estimating running times. Thisis also demonstrated by the low RSE of less than 7 seconds. Large F statistic and lowp-value indicate strong correlation between response and explanatory variables.

Regression tree model for running time estimation

The non-linear relationship between predictors and response, as well as interactionsamong predictors can be resolved using regression trees. Figure 4.1 presents the treeobtained after applying the recursive partitioning algorithm (Therneau et al., 2014) onthe training set.

The large training set enabled the construction of a complex regression tree with 16internal nodes (splits), indicated by oval nodes, and 17 terminal nodes (rectangularnodes). Each node contains the mean value of response (running time) and the numberof data points n in the corresponding region. The tree indicates the relative impor-


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Figure 4.1: Regression tree for running time estimation


tance of the variables: ‘length’ (41%), ‘distance from’ (21%), ‘distance to’ (18%),‘train type’ (11%), ‘headway’ (5%) and ‘delay’ (4%).

The data is split throughout the tree in accordance with the interpretation of the resultsof linear regression for important variables. However, the final terminal nodes thatare split according to the ‘length’ variable show inconsistencies with the assumptionthat running time is positively correlated with block length. In case of short headways(<214.4 sec) and blocks close to the scheduled stop (<1970 m) the running time overshort blocks tends to be longer. However, the large mean squared error (MSE) obtainedafter 10-fold cross-validation of the tree indicates that these regions may be affectedby outliers and therefore produce inaccurate estimates.

The overall quality of the model is presented in Figure 4.2 which shows improvementof error after performing each split. Prediction error is presented relative to the initialestimation error equal to the mean of all observed running time in the training set. Eachsplit contributes to reduction of prediction error. Figure 4.3 presents the improvementof R2 depending on the number of splits. The maximum value of R2 = 0.697 is obtainedfor 16 splits.

0 5 10 15

0.2

0.4

0.6

0.8

1.0

Number of Splits

X R

elat

ive

Err

or

Figure 4.2: Relative running time prediction error depending on the tree size

0 5 10 15

0.0

0.4

0.8

Number of Splits

R−

squa

re

0 5 10 15

0.0

0.4

0.8

Figure 4.3: R2 of the running time model depending on the tree size

Even though the predictive quality of the linear model is improved by using a regres-sion tree, the effects of outliers still may present a source of inaccuracy for estimatingrunning times.


Random forest model for running time estimation

Random forests provide a further increase of prediction accuracy and improve the re-sistance of regression trees against outliers. The training set (Table 4.1) is used tocreate a random forest model with 300 trees (Liaw & Wiener, 2002). Each split is per-formed using the best of three randomly chosen variables from the full set of predictors.Unlike the LTS regression and regression trees models that are created instantaneouslyeven for a large training set, creating the random forest model took around 5 minutes.

The MSE depending on the number of trees in the forest is presented in Figure 4.4. Asignificant error decrease of 30% is visible for increasing the forest size up to 100 trees.Further increase of the number of trees has a limited contribution to error reduction.

0 50 100 150 200 250 300

8090

100

110

120

Number of trees

MS

E

Figure 4.4: MSE of running time model depending on the number of trees

Figure 4.5 shows a significant improvement of R2 compared to the approach with asingle regression tree. The effects of increasing the number of trees above 100 aresmall. The value of R2 = 0.780 indicates that 78% percent of running time variationcan be explained with predictor values. The relative variable importance is obtainedafter computing the OOB error and does not differ from the single tree case.

0 50 100 150 200 250 300

0.66

0.70

0.74

0.78

Number of trees

R−

squa

red

Figure 4.5: R2 of running time model depending on the number of trees

4.4.2 Dwell time estimates derived from the global model

Continuous variables of the training set for dwell time estimation are shown in Table4.3. The training set contains 145807 points that describe the dwell times of 9 train


lines in 19 stations (5 of which are large) over 82 days. The variable ‘scheduled time’is given as a continuous variable even though scheduled dwell time is usually givenin full minutes. The reason is that the number of levels may significantly increasethe number of dummy variables used to model a discrete variable and consequentlyincrease the complexity of the underlying optimisation algorithms. Moreover, dwelltimes of local trains in the Netherlands are scheduled as so-called short stops, meaningthat train arrival and departure time are scheduled to occur within one minute. Suchscheduled dwell times are in this model considered to be equal to the minimum dwelltimes of 30 seconds.

Moreover, we include categorical variables for train type and station type with twolevels each. Only intercity (47% of data points) and local trains are considered invariable ‘train type’. Stations are divided into small (60% of data points) and largestations and included in variable ‘station type’. Finally, the importance of peak-hoursis incorporated with a binary indicator (24% of data points from peak-hours).

Table 4.3: Summary of the training set for dwell time estimation

Mean Median St. Dev. Min Max

dwell time (sec) 136.60 114.72 80.17 10.01 599.66arrival delay (sec) 8.48 -16.60 131.05 −299.94 1199.04scheduled time (sec) 70.20 69.60 65.40 30.00 360.00

Robust linear model for dwell time estimation

LTS robust multiple linear regression (Rousseeuw et al., 2014) is used to fit the datafrom the training set. The results show that all predictors have a strong impact onresponse ‘dwell time’ (Table 4.4). The relatively large intercept can be explained bythe unavoidable error of dwell time estimation using the procedure described in Section3.5.6. The realised dwell times are clearly closely correlated with the scheduled dwelltimes. Dwell times in small stations, as well as dwell times of local trains are estimatedto be slightly larger than scheduled. Moreover, arrival delay is negatively correlatedwith dwell times. That finding reflects the fact that early trains have to wait for thescheduled departure time and late trains tend to depart as soon as possible to reducetheir delay. Finally, dwell times during peak-hours are estimated to be longer than inoff-peak periods.

Indicators of the predictive quality of the model (lower part of Table 4.4) show highpredictive power of the model with 73% of response variation explained by explana-tory variables. The high value of the F statistic also indicates the relevance of selectedpredictors on the response value. However, the possible interactions between explana-tory variables can not be determined using the linear model which is why non-linearpredictive models are also tested.


Table 4.4: Summary of the LTS model for dwell time prediction

Dependent variable: dwell time

Coefficient p-value

peak hour= 1 5.2223 ∗∗∗

arrival delay −0.1163 ∗∗∗

train type = ‘local’ 2.2810 ∗∗∗

station type = ‘small’ 7.4580 ∗∗∗

scheduled time 1.0070 ∗∗∗

Intercept 38.7810 ∗∗∗

R2 0.7281Residual Std. Error 31.5000F Statistic 73700.2481 ∗∗∗

Note: ∗∗∗p<0.01

Regression tree model for dwell time estimation

The recursive partitioning algorithm (Therneau et al., 2014) is used to optimise regionsin the prediction data space with respect to prediction error. The resulting regressiontree containing 8 splits (9 terminal nodes) is presented in Figure 4.6. Relative vari-able importance is also determined: ‘scheduled time’ (56%), ‘station type’ (24%),‘arrival delay’ (19%) and ‘train type’ (1%).

Correlations between scheduled dwell times, arrival delays and response variable de-termined using robust linear regression are visible from analysing the internal nodes ofthe tree. The interpretation of the splits is therefore consistent with the interpretationof correlation coefficients. However, terminal nodes and splits on the lower level of thetree did not manage to capture dwell time dependence on peak-hours. Moreover, traintype does not influence any split of the tree. That can be explained with the correlationbetween station type and train type. In particular, data points for small stations implylocal train type.

The overall quality of the regression tree model is determined by 10-fold cross-validation.Figure 4.7 shows the decrease of prediction error with increasing number of splits inthe tree.

Figure 4.8 shows the increase of R2 with the tree size. For the optimal number ofsplits 70% of variation of dwell time from the training set can be explained using thepresented regression tree model.

The application of the regression tree method for prediction of dwell times resolvedthe issue of mutually correlated and interacting predictors, and non-linear impact onthe response variable. The resulting tree is easy to interpret and relative importance ofeach considered variable is given. However, the predictive power of the global modeldid not improve. We assume that sensitivity to outliers especially in lower internal andterminal nodes may cause inaccuracy of prediction.


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0 2 4 6 8

0.2

0.4

0.6

0.8

1.0

Number of Splits

X R

elat

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Err

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Figure 4.7: Relative dwell time prediction error depending on the tree size

0 2 4 6 8

0.0

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Number of Splits

R−

squa

re

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0.0

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Figure 4.8: R2 of the dwell time model depending on the tree size

Random forest model for dwell time estimation

We attempt to improve robustness against outliers and prediction accuracy of the globalmodel by applying the random forest method on the training set (Liaw & Wiener,2002). The resulting random forest contains 300 trees. Each split in each tree is createdby choosing the best out of three randomly selected predictors.

The indicators used to examine the quality of the model are MSE and R2. Figure4.9 shows the reduction of MSE with increasing number of trees in the forest. Nosignificant decrease of error is achieved for forests larger than 100 trees.

0 50 100 150 200 250 300

1500

1700

1900

Number of trees

MS

E

Figure 4.9: MSE of the dwell time model depending on the number of trees

The coefficient of determination R2 is also significantly improved for forest size ofup to 100 trees (Figure 4.10). The final value shows that by using the random forest


algorithm, 76% of dwell time variability can be explained and predicted. Thus, the pre-dictive power has been improved compared to the regression tree model. This comesat the cost of computation time which is much longer than for the tree model or LTSrobust regression.

0 50 100 150 200 250 300

0.70

0.72

0.74

0.76

Number of trees

R−squared

Figure 4.10: R2 of the dwell time model depending on the number of trees

4.5 Process time estimates - local model

The data structure resulting from the process mining algorithm (Chapter 3) can beexploited to derive a separate statistical model for each process. A running process isdefined by the train line and block section, and a dwell process by the train line andstation of the scheduled stop. The LTS robust linear regression model is used to predictrunning and dwell times depending on departure and arrival delay, respectively. Theassumption about the different behaviour of delayed (delay larger than 60 seconds)and punctual or early trains is tested by separating the set of observed running anddwell times into corresponding sets of delayed and punctual trains and applying theWilcoxon rank-sum test at 5% significance level. The null hypothesis is that sampleshave continuous distributions with equal medians.

4.5.1 Estimation of running times over a particular block

The difference in running times is expected to be the largest in the last part of theopen track section before the scheduled stop where punctual or early trains have longerrunning times due to coasting or cruising with lower speed. In Figure 4.11, the realisedrunning times are presented relative to the departure delay. A weak correlation betweenrunning times and departure delays was found on the level of block sections. This isillustrated in Figure 4.11 (left) which shows the dependence of running time over thelast block before the scheduled stop in Delft station of train line 2200. The solidred line in the left part of the figure represents the robust fit. The black dashed linerepresents the 10th percentile of running times. The small percentile is selected andused as a robust estimator of minimum running times Van der Meer et al. (2010).It used in real-time running time predictions as the lower bound in order to avoidunrealistically low values for large delays.


The Wilcoxon rank-sum test rejected the null hypothesis with p ≈ 0 thus indicatingthe different distributions of running times of delayed trains. Box-plots in Figure 4.11(right) show small differences in distributions of six data samples specified based onthe value of departure delay. The box-plots used in this thesis indicate the median (linein the middle of the box), the 1st and the 3rd quartiles (upper and lower bound of thebox) and data maximum and minimum (ends of the upper and lower whisker). Notethat the outliers are excluded from the plots for the sake of clarity of the figures. Out-liers are detected in a conventional procedure by adding (subtracting) the interquartiledifference multiplied by 1.5 to (from) the upper (lower) quartile. All values outside ofthe obtained range are considered as outliers.

Departure1delay1from1The1Hague1HS1of1line122001[s]

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Figure 4.11: Dependence of running time on delay (left) and box-plots of runningtimes for punctual and delayed trains (right)

Figure 4.12 shows weak correlation between running times and departure delays forall train lines on the corridor The Hague HS – Rotterdam. Each circle corresponds toa train line and block pair. All blocks on the corridor, represented by the start and endsignal code, are given on the horizontal axis. The colour of each circle represents thevalue of R2 for the particular local model, according to the colour map given on theright side of the figure.

Since no or only weak correlation between running times and actual delays was dis-covered, it is important to determine how the running time supplements are actuallyused. In order to do so, delay accumulation over all scheduled stops for each line wasanalysed. Figure 4.13 shows how the delay of line 2200 trains changes over the routealong the corridor Leiden – Dordrecht. The solid red line indicates the mean of delaychange over distance. No distinction can be made between early, punctual and delayedtrains. It is visible that time reserves are spent on extended dwell times. Trains gener-ally run with full performance thus compensating for departure delay (delayed trains)or having more slack during dwell times (punctual trains).


Block

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Figure 4.12: R2 for prediction of running time on The Hague HS – Rotterdam corridor

LEDN LAA GV DT SDM RTD RTB RLB DDR-200

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Figure 4.13: Delay over corridor Leiden - Dordrecht for train line 2200


4.5.2 Estimation of dwell times for a particular station

Availability of data from door sensors and on board equipment has inspired recent re-search in detailed modelling of train dwell times (Medeossi et al., 2011). In this thesiswe rely solely on train describer data, thus a detailed analysis of different phases ofdwelling in scheduled stops was not possible. The dependence of dwell times on ar-rival delays was examined. Figure 4.14 shows the correlation between arrival delayand dwell time for each observed train line and station pair. The correlation is partic-ularly strong for the large stations Leiden (LEDN), The Hague HS (GV), Delft (DT),Schiedam (SDM), Rotterdam (RTD) and Dordrecht (DDR). In smaller stations whereonly local trains are scheduled to stop, no significant correlation between dwell timesand arrival delays was established. That can be explained by the fact that these stopsare scheduled as short stops as described in Section 4.4.2. The trains only stop forboarding and alighting and depart as soon as possible.

LEDN

DVNK VS

TLAA GV

GVMW

RSW DT DT

ZSDM

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Figure 4.14: R2 for prediction of dwell times on Leiden – Dordrecht corridor

Figure 4.15 (left) shows the dependence of dwell times on arrival delays for the trainline 2200 in station Delft. The horizontal black dashed line represents the 10th per-centile of all dwell times, whereas the red line represents the robust linear fit for punc-tual trains. The scheduled dwell time is 60 seconds. Strong correlation (R2 = 0.8704)was captured for early and punctual trains. The Wilcoxon rank-sum test rejected thenull hypothesis (p≈ 0) and different distributions of dwell times for punctual and latetrains are clear from the box-plots in Figure 4.15 (right). However, the variation ofdwell times for delayed trains needs to be explained by other factors and therefore, thedata set is divided into a set of punctual and delayed trains at the threshold of 60 sec.


Arrival delay of 2200 train line in Delft [s]

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Figure 4.15: Dependence of dwell time on delay (left) and box-plots of dwell time(right)

The variability of dwell times of delayed trains is explained by modelling dwell time asa time series to determine the dependence on the peak-hours. Dwell times of delayedtrains normally equal the minimum dwell time required for passenger operations androute setting if the delay exceeds the dwell buffer time. We assumed that passengervolumes and consequently the time needed for alighting and boarding increases duringpeak-hours. Figure 4.16 shows dwell times (weekends and holidays were not consid-ered) relative to scheduled arrival times of the train line 2200 in Delft. The increasein dwell times during peak-hours is clearly visible. The red line indicates the mediandwell time.

Scheduled9arrival9time9to9Delft

Rec

ord

ed9d

wel

l9rim

es9o

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09tr

ains

9[s]

6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 24:0050

100

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Figure 4.16: Dependence of dwell time on scheduled departure time

This clear distinction between causes of variability of dwell time for punctual anddelayed trains requires a separate approach to prediction of dwell times. Therefore,for punctual and early trains, dwell time can be predicted based on the correlationwith arrival delay. On the other hand, dwell time for a delayed train is estimatedfrom historical data based on dwell times of the same train number and adjacent train


numbers of the same series (e.g. if train 2245 arrived with a delay, the dwell time willbe predicted as the average dwell time of trains 2243, 2245 and 2247 obtained from thedata set of delayed trains). The reason for including the data from the adjacent trainnumbers is to ensure the sufficient sample size and robustness of the moving averageestimate. Note that the described moving average smoothing method incorporates theeffects of the peak hour dependence of dwell times without assuming a clear limit forpeak periods. That way the limitation of including the peak-hour dependence in theglobal model as a categorical variable has been overcome (§4.2.2).

Figure 4.17 shows the effects of using the described moving average approach forpredicting the dwell times of delayed trains on a test set. The prediction accuracy iscompared to the approach based on LTS robust regression. The prediction error iscomputed by subtracting the estimate from the realised dwell time. Positive bias ofthe LTS estimate error indicates that dwell times of delayed trains are underestimated.This approach assumes the minimum dwell time for delayed trains thus disregardingthe effects of peak-hours. The moving average approach significantly improves theprediction accuracy.

LTS regression Moving average

−80

−40

040

80

Pre

dict

ion

erro

r (s

ec)

Figure 4.17: Prediction error for dwell times of delayed trains

4.6 Comparison of statistical models

All presented global and local models for estimating running and dwell times are val-idated on a test set consisting of processed data for 10 days of traffic in TROTS areasRotterdam and The Hague. The test set for running time estimation contains 18684data points. The size of the test set for dwell times is 12225. The results of the indi-vidual local models are combined in one data set in order to be comparable with theglobal model.

4.6.1 Comparison of running time estimation models

Figure 4.18 shows the distribution of prediction error of each model for running timeprediction. Random forests clearly give the most accurate estimates of running timeswith respect to other global models. The performance of random forests is comparableto the performance of local models that give the most accurate predictions of running


times. The most significant predictors used in the global model are block length andposition with respect to the previous and the following scheduled stop. These predic-tors do not need to be considered in the local models that are created for a particularblock and train line pair. The correlation with other explanatory variables such as de-parture delay in both model types is weak and therefore the two models give similaroutput. Note the very small prediction errors within±10 seconds for the local LTS andrandom forest estimates.

Global LTS Random forest

−10

010

2030

Pre

dict

ion

erro

r (s

ec)

Regression tree Local LTS

Figure 4.18: Prediction error of running time estimation models

4.6.2 Comparison of dwell time estimation models

Similar results are obtained for dwell time estimation (Figure 4.19). Random forestsare the best performing global model. However, local models, consisting of a LTSrobust linear regression model for punctual trains and a time series (TS) model for de-layed trains, give more accurate estimates of dwell times. A high standard deviationof prediction error even for the most precise model indicates that relying on train de-scriber data as the sole source for developing prediction models may not be enough foraccurate estimation of dwell times.

An important aspect for comparing the global and local models for dwell time estima-tion is how sensitive they are to imprecision in estimating actual arrival and departuretimes. As explained in Section 3.5.6 the measurement error depends on the topologyof track circuits, stopping position of the train and train length. It is expected that forthe trains of a single train line in the same station these measurement errors are iden-tical. Therefore, the accuracy of local models is not significantly affected. However,the global model, that aggregates the dwell time data from all stations and train lines,may have lower prediction accuracy due to measurement errors of actual arrival anddeparture times.

4.6.3 Comparison of prediction accuracy for scheduled processes

Finally, we compare the accuracy of dwell time and running time estimates. The qual-ity of the presented models for estimating the duration of scheduled processes can thusbe analysed. Recall that the running times analysis presented in this chapter relates


Global LTS Random forest

−10

00

5010

0

Regression tree Local LTS+TS

Pre

dict

ion

erro

r (s

ec)

−50

Figure 4.19: Prediction error of dwell time estimation models

to running time over blocks sections. This is important for calibrating the mesoscopictraffic prediction model presented in the next chapter. However, in order to offer a faircomparison of the presented models, the accuracy of scheduled process time estimatesneeds to be considered.

The running time between two scheduled stops can be computed as the sum of therunning times over blocks in the train route including the outbound route from thestation of departure and the inbound route at arrival station. In order to exclude theimpact that other trains may have had on the running times of trains in the test set, allhindered train runs are excluded from analysis. Figure 4.20 shows a comparison ofprediction error for dwell time and running time estimates. The approach based on thelocal LTS models is selected for the analysis. Running times between two scheduledstops are clearly predicted more precisely than dwell times. This is also demonstratedin Figure 4.21 which compares the relative errors for dwell time and running timeestimates. The relative errors are obtained with respect to the scheduled time of thecorresponding process. The errors of running time estimates are within 10% of thecorresponding scheduled running times. The variability of the relative error of dwelltime estimates is much larger. The errors of dwell time estimates may be even largerthan the corresponding scheduled dwell times.

Dwell time Running time

−40

020

40

Pre

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ionn

err

or (

sec)

−20

Figure 4.20: Precision of dwell time and running time estimates


Dwell time Running time

−1.

00.

00.

51.

0

Rel

ativ

e pr

edic

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−0.

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Figure 4.21: Precision of dwell time and running time estimates relative to scheduledprocess time

4.7 Conclusions

This chapter presented two data driven approaches for estimation of conflict-free run-ning times and dwell times. Global models are developed by collecting all runningtime and dwell time data from the training set and creating a separate predictive modelfor estimation of each type of process times. Advanced supervised learning methodswere tested and compared by predictive power, interpretability of results, and accu-racy. On the other hand, the data structure and large size of the test set were exploitedto develop local running time and dwell time models for a particular block and station.Both approaches are validated on the test set. Estimates of the local models providedon average more accurate predictions of process times.

The running times showed small variation which was to a great extent explained bypredictors in both models. Weak dependence on actual delays has been establishedfor running times. The analysis on one corridor showed that the majority of trainsrun in full performance regime regardless of departure delays. In the last few years,NS, the main train operator in the Netherlands, is promoting the concepts of energyefficient driving which may have an effect on the running times of punctual or earlytrains (Scheepmaker, 2013). Furthermore, running times seem to be weakly affectedby peak-hours and do not have a significant daily variation. An interesting observationis that even for conflict-free train runs short minimum headway after the precedingtrain may cause extended running time in order to prevent a route conflict.

Dwell times of punctual trains show strong correlation with arrival delays, in particularin large stations. On the other hand, the dwell times of delayed trains are more sensitiveto impact of passenger volume variability in peak and off-peak periods. Despite thestrong predictive power of the presented models, the validation on an independenttest set showed that variability of dwell times cannot be fully explained by selectedpredictor variables. Dwell times need to be modelled with a higher precision since thevariation of prediction error is significantly larger than for running times. One way to


do it is to include other data sources on platform design and rolling-stock to estimate.That would enable computation of more precise estimates of arrival and departureevents. Moreover, the data sources related to behavioural properties of passengers andtrain drivers can be used to derive more accurate estimates of dwell times.

Finally, we discuss the advantages of the two presented approaches based on the localand global models. The major advantage of the global model is that the results canbe generalised and applied to other parts of the network and different train lines thatwere possibly not included in the training data set. However, the accuracy of processtime estimation is the most important criterion for selecting the appropriate model.Since the running time and dwell time estimates are used for real-time calibration ofthe traffic prediction model presented in the following chapter, the overall accuracyof the model can be severely affected by propagation of process time estimation errorover the prediction horizon. Moreover, calibration of the global model as well as theapplication in real-time is computationally more demanding than creating the multiplelocal models and using them for prediction. The approach based on the multiple localmodels is therefore used for calibrating the traffic prediction model presented in thenext chapter.


Chapter 5

Real-time prediction of train eventtimes


Kecman, P. and Goverde, R. M. P. (2014). Online data-driven adaptive prediction oftrain event times. IEEE Transactions on Intelligent Transportation Systems. (in press)

5.1 Introduction

Real-time prediction of train positions in time and space is a basic requirement foreffective route setting, traffic control, rescheduling, and passenger information. Theprevious chapter described how conflict-free running times and dwell times can bepredicted from historical traffic realisation data. However, accurate prediction of trainevent times, requires detailed modelling of other operational constraints of railwaytraffic such as interdependencies between trains that share the same infrastructure orhave a planned synchronisation constraint.

Railway traffic controllers in the Netherlands currently have no support to predicttrain traffic or the effects of their control actions. Train positions are monitored us-ing the train describer system and actual delays are measured with low accuracy androunded to full minutes (§2.2.4). Existing tools developed in Switzerland (Dolder etal., 2009), Sweden (Isaksson-Lutteman, 2012) and Japan (Fukami & Yamamoto, 2001)provide controllers with real-time traffic prediction and conflict detection. Moreover,conflict detection modules of the state-of-the-art rescheduling models (Caimi et al.,2012; D’Ariano, 2008) predict train event times and route conflicts in order to deriverescheduling actions. However, these approaches do not exploit the dependence of pro-cess times on the actual traffic state or the interdependence with other trains. Processtimes are predicted based on theoretically obtained values independent of the actual

101


condition of traffic on the network. Running times are typically estimated using pre-determined empirical values or microscopic simulation. Similarly, fixed scheduled orminimum dwell times are used to estimate the duration of a scheduled stop for eachtrain.

In this chapter, an online approach to traffic state prediction is presented. The mainidea is that the prediction is performed by propagating the actual traffic information(current train positions, process times, delays) through a realistic, mesoscopic modelof railway traffic. The level of detail included in the model is an essential differencefrom the earlier approaches (Van der Meer et al., 2010). We use the actual route plans,timetable and current positions of all trains to build a graph model. Microscopic opera-tional constraints are reflected in the graph topology that captures all scheduled eventsand signal passages. Modelled processes represent the precedence relations betweenevents such as train runs and stops, connections, and minimum headways. The graphis calibrated dynamically, in real-time, using historical track occupation data with pre-determined and quantified dependency of running and dwell times on departure andarrival delays, respectively. When an update of train positions becomes available, adepth-first search based algorithm sweeps through the graph. Robust estimates of arcweights are computed in real-time using the estimates derived with the LTS method asdescribed in Chapter 4 and an efficient algorithm computes the predicted realizationtime for all events within the prediction horizon.

This approach is extended by precise modelling of route conflicts and incorporatingtime losses, due to braking and re-accelerating of hindered trains, in the predictions.Moreover, we present an adaptive component that exploits feedback information aboutthe actually realized blocking times of running trains. The realized process times aremonitored and trains with process times that continuously deviate from computed es-timates in a certain pattern are detected. The estimates of downstream process timescan subsequently be adjusted to minimize the expected prediction error.

The described prediction tool is tested on a busy corridor Leiden – Dordrecht in theNetherlands. The accuracy of predictions, size of the model and computation speedare presented and analysed depending on the length of the prediction horizon.

The next section (§5.2) describes the framework of the system design. Sections 5.3 and5.4 give a detailed description of the model and data-driven calibration, respectively.The online prediction algorithm is presented in Section 5.5 and its performance in real-life case study in Section 5.6. Finally, Section 5.7 summarises the presented model andgives guidelines for further research and improvements.

5.2 Framework of the real-time prediction tool

The main components of the tool in the real-time environment and the flow of databetween them are depicted in Figure 5.1. The parts of the tool presented in this chapterare shown with shaded boxes. The traffic model is based on a directed acyclic graph

Chapter 5. Real-time prediction of train event times 103

(DAG) with dynamic arc weights. The graph topology is built and updated based onthe actual process plan (train orders, route and connection plan) and current positionsof trains on the network. We assume that the actual route and connection plans arecontinuously provided by traffic control for the duration of prediction horizon. Theroute plan for a train is given as a planned sequence of block sections in the train route.A route plan can be translated to the level of track sections (Chapter 3) and used todetermine the necessary headway arcs for routes with common track sections. Eachchange of the actual plans or information from the real-time operations, i.e., changingthe relative order of trains, adding or cancelling trains, modifying train routes, updatingconnections, and removing passed events, results in an update of the graph topology.

Traffic modelMonitoring

Route conflictadjustment

Arc weights computation

Railway operations

Rea

lise

d pr

oces

s ti

mes

Pre

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roce

ss ti

mes

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co

nflic

ts

Orders

Routes

Connections

Pre

dict

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vent

tim

es

Timeta

ble

Actual process plan

Trafficcontrol

Adaptiveadjustment

Actual traffic state

Figure 5.1: Monitoring and prediction components in the traffic control loop

Arc weights represent the estimated process times which are computed based on theactual (predicted) traffic state and processed historical data. The actual traffic state,comprising the current train positions and delays, is provided continuously by the mon-itoring component and the future traffic state is obtained from the traffic model. Theweight of an arc is time-dependent and assigned in a dynamic way depending on the(estimated) starting time of the modelled process (Nachtigall, 1995). By comparing theactually realised event times with the scheduled times, the actual delays are obtained.Similarly, we obtain predicted delays by subtracting the predicted event times from thescheduled ones. Arc weights are computed from the database of historical data thatcontains the predetermined dependencies of process times on delays. The database is


obtained using the methodology described in the previous chapter. This way the de-pendence of running and dwell times on the current (predicted) delays is incorporatedin the model.

This primary prediction loop is extended with an adaptive component (Section 5.5.3)that compares the actually realised process times of the running trains with the pre-dicted values and adapts the running time until the next scheduled stop to minimiseprediction error. The adaptive component of the prediction model enables online de-tection of the train runs with process times that continuously exceed or fall behind thecomputed estimates, and adjusts the predictions of future train behaviour accordingly.

Furthermore, the accuracy of predictions is increased by adjusting the running timesover the approaching block for the hindered trains (Section 5.5.2). Route conflict du-ration is predicted and the corresponding adjustment factor is retrieved from the pre-determined dependence of running time increase on conflict duration.

After every graph update, a prediction of event times of all reachable events is per-formed by applying a depth-first search based algorithm on the graph-based trafficmodel (Section 5.5).

5.3 Microscopic graph based model

5.3.1 The graph model

The railway traffic, represented as a discrete-event dynamic system is modelled witha DAG G = (V,E), where V is a set of nodes and E is a set of arcs. Each event ismodelled by a node. We distinguish between signal events (passing of a signal by arunning train) and station events (arrival and departure to and from a platform track).The microscopic graph model needs to support rescheduling actions such as reorder-ing, rerouting, revising services (cancelling transfers or trains, adding extra trains) andretiming. Therefore, graph G is constructed in a form of an adjacency list which is asuitable data structure that supports operations on dynamic sets (Cormen, Leiserson,Rivest, & Stein, 2009). The existing routines for implementation of the dispatching ac-tions in a graph-based traffic model represented as an adjacency list are thus applicable(Van der Meer, 2008).

A node i ∈ V is described by (ni, infrai, typei, previ, nexti, t predi , trec

i ), representingthe train number, infrastructure element (signal or platform track), type, direct pre-decessors, direct successors, predicted realization time and the recorded time (whenavailable), respectively. Nodes that model scheduled events, i.e., arrivals and depar-tures are also attributed with the scheduled event time tsch. By comparing the recorded(predicted) event times with the scheduled event times, the current (predicted) delayis obtained for a specific train and used to estimate the duration of its subsequent pro-cesses (dwell and running times). Scheduled departure times are also used to incor-porate the timetable constraints (a train cannot depart before the scheduled departuretime).


An arc models a precedence relation between events. Apart from modelling the run-ning and dwelling processes related to a specific train, directed arcs are also used tomodel interactions between trains, namely minimum headway and connection con-straints. Connection arcs can be used to model synchronisation constrains such aspassenger transfers, and rolling-stock and crew circulation constraints. Arc (i, j) ∈ Eis described by (i, j,wi, j, typei, j) representing the tail event, the head event, the arcweight and the arc type (‘dwell’, ‘run’, ‘headway’, ‘connection’).

5.3.2 Graph construction

The graph is constructed based on the actual process plan that includes the given trainroutes, scheduled event times (actual timetable) and connection plan (§2.2.1). Theconnection plan contains all planned synchronisation constraints. A train route is rep-resented as a sequence of track sections and signals. For events belonging to the sametrain, running arcs connect all signal passing events, as well as signal passing eventswith station events. Dwell arcs connect station events, i.e. an arrival event with a sub-sequent departure event. An inbound running arc connects a home signal event with asubsequent arrival event, whereas an outbound running arc connects a departure eventwith a subsequent exit signal event.

Headway arcs separate the successive occupations of a block between two signals ora station route by different trains. Typically, a signal changes to a permissive aspectas soon as all sections in a block (station route of the approaching train) protected bythe signal, have been released. As discussed in Section 2.4.3, minimum headwaysneed to be modelled differently for interactions of trains on open track or station areaswith overlapping and merging routes on the one hand, and for interactions of trainswith diverging or intersecting routes on the other. Note that the relative train orders oneach infrastructure element (switch, track section, block, platform track) are neededto construct the headway arcs. The relative orders can be determined from the actualprocess plans (train routes and actual timetable).

On open tracks and for station routes with the same end signal, the critical section thatconstrains a signal release is the section before the end signal of the block or route.This situation holds for trains that run over the same block or station route or for trainswith merging routes (routes that have different starting signals and the same end signal)in interlocking areas (Figure 5.2). An accurate space-based train separation is ensuredby adding a headway arc that constrains the realisation of a signal passing event of anapproaching train until the protected block was cleared by the previous train. The headevent is the start signal passing event of the approaching train, the tail event is the endsignal passing event of the preceding train.

However, in station areas, conflicting routes are often diverging (with the same startingsignal and different end signals, as shown in Figure 5.3) or intersecting (different start-ing and different end signals). For such route interactions, the ‘sectional release’ routelocking principle applies. Since all events in the mesoscopic model are signal passages


S1 S7

S5

S3

S2

S4

S6

S8TS1

TS2

TS3

TS4

TS5

Train1-route TS1 TS3 TS5S1 S7


Train1

Train2

S1 S7

S7S3

r

r

h r - running time h - clearing time+ signal release time

Figure 5.2: Space-based train separation

or station events, the event of the critical section release has not been included. Wemodel the train separation in a time-based manner by adding a headway arc betweenpassing events of signals that initiate running processes over the protected switches.The head event and the tail event are the start signal passing events of the approachingand the preceding train, respectively. The procedure to compute the weights for bothtypes of headway arcs is described in Section 5.4.2.

S1 S7

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S3

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S4

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S8TS1

TS2

TS3

TS4

TS5



Train1

Train2

S1 S7

S5S1

r

r

h r - running time h - 10th percentile from the data

Figure 5.3: Time-based train separation

Finally, a connection arc models the commercial constraints (passenger transfers), orlogistic constraints (rolling-stock and crew connections). The arrival event of a feedertrain is the tail event and the departure event of a connecting train is the head event.

The graph can be constructed based on the train list (each train is described by the


route and timetable), train orders, and the list of planned synchronisation constraints.Given G = (V,E), the dynamics of railway traffic can be simulated with the followingconstraints:

t predj ≥ t pred

i +wi, j,∀i, j ∈V,(i, j) ∈ E (5.1)

t predi ≥ tsch

i , i ∈ {V | typei = ‘departure’}. (5.2)

Constraint (5.1) defines the precedence relation between the tail and the head event ofan arc. Inequality (5.2) represents the timetable constraint for all departure events.

Figure 5.4 shows an illustrative example of a directed acyclic graph for two trains. Theplanned route for each train can be described by the sequence of signals: S1,S2,S3,S4,S6 for train T 1 and S1,S2,S3,S5,S6 for train T 2. Every signal passage is modelled asa node. Both trains have a scheduled stop at the station which is modelled with arrivaland departure nodes. Each node is represented as an object with the correspondingattributes and their values. Time related attributes were left out from the figure forthe sake of clarity. Nodes belonging to one train run are connected by running anddwell arcs. Since the trains run over the same infrastructure, the necessary minimumheadway times are ensured with headway arcs. The route between signals S1 and S3is the same for both trains, thus requiring at least one block separation between trains,which is modelled with headway arcs (T 1,S2)→ (T 2,S1) and (T 1,S3)→ (T 2,S2).Recall that for conflict-free traffic, the two-blocks separation is required (§2.2.3). Thesectional release principle between diverging inbound routes of two trains is enabledwith the headway arc (T 1,S3)→ (T 2,S3). Finally, train T 1 can leave the station whenthe block between S5 and S6 has been released by train T 2, which is modelled by theheadway arc (T 2,S6)→ (T 1,S4).

A planned connection is secured with the arc between the arrival event of T 1 and thedeparture event of T 2. Note that the direction of the headway arcs indicate the orderof trains. In Figure 5.4 train T 2 overtakes train T 1 in the station.

The graph topology is continuously updated according to the rolling prediction horizonand traffic control decisions. Possible new trains, planned to operate within the actualhorizon, are added to the graph with their planned route on the level of block sections.The necessary headway arcs are built per block between consecutive trains that use atleast one shared track section covered by the block. With each update of train positions(signal passage, departure or arrival of a train), the nodes describing events from thepast and their incoming and outgoing arcs are removed from the graph (and storedwith the realized event times). The size of the graph is thus stable within a certain timeinterval.

5.4 Computation of arc weightsTrack occupation data, obtained by processing the train describer log files of the Dutchtrain describer system TROTS (Chapter 3), are used to calibrate the graph model with


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)}next =

{(T2,S6

)}

S1

S2

S3

S5

S4

PLA

TF

OR

M

S6

Figure 5.4: An example of a mesoscopic DAG


actually realized rather than theoretical process times. Three months of data (March –May 2010) from the busy corridor between Leiden and Dordrecht in the Netherlandswere used to develop statistical models for estimation of process times depending onthe actual traffic conditions (Chapter 4). Recall that the route conflicts were identifiedand only conflict-free process times are used in the analysis of process times and modelcalibration.

In order to include the dependence of process times on actual traffic conditions, a dy-namic, time-dependent computation of arc weights (Nachtigall, 1995) is implementedin the prediction algorithm. The main idea behind this approach is that the running anddwell time of a train may vary depending on the current delay of the train, time of theday, realised process times and route conflicts.

5.4.1 Running and dwell arc weights

Track occupation data were analysed separately for each train line, thus ensuring thatthe stopping pattern and routes of all observed trains are the same. Correlations be-tween running and dwell times with actual delays are determined using LTS robustlinear regression resisting 25% of outliers (Rousseeuw & Driessen, 2006).

For the purpose of obtaining the weight of a running arc dynamically, each block sec-tion and station route in the infrastructure database has been attributed with regressioncoefficients a0 and a1 that are computed for each train line. For a known delay value zn

of a train n, the expected running time over a block can than be computed as a0+a1zn.We also include the 10th percentile of a process time and use it as the absolute mini-mum process time to avoid infeasible predictions in case of large delays.

Recall that the method for dwell time estimation depends on the actual delay valueof a train (§4.5.2). Dwell time of early or punctual trains (delayed less than 60 sec-onds) is computed using the robust linear regression coefficients as b0 + b1zn. Theregression coefficients b0 and b1 are computed for each station and train line. On theother hand, dwell time of a delayed train is computed using the moving average over acorresponding time series as a function of the train number n.

5.4.2 Headway and connection arc weights

Headway arc weights

The weight of a headway arc that models space-based train separation represents theminimum time from the moment when the head of the first train leaves a block sectionto the moment when the next train can occupy the same block. The arc weight equalsthe sum of block clearing time by the first train, and setup and release time of thesignalling system (§2.2.2). In this thesis a constant value of 2 seconds is used for thesetup and release time on open track and 12 seconds for route setting time in stations.Clearing time is estimated from the data as the 10th percentile of the clearing times of ablock by a specific train line. Note that this approach only models the constraint of the


signalling system that does not allow multiple trains in the same block. The identifica-tion of route conflicts is not possible without including the remaining components ofthe blocking time. In Section 5.5.2 the approaching time, as well as sight and reactiontime of the train driver are included in the module for route conflict identification.

In order to model the principle of sectional release using time-based train separation,the minimum headway time between two trains with diverging or intersecting routesis estimated from the data as the 10th percentile of the time headways between trainruns of the corresponding train lines from the historical track occupation data. Bychoosing a small percentile of the realised time headways, the impact of buffer timeson minimum headway times estimates is excluded.

Connection arc weights

The weight of a connection arc is equal to the minimum transfer time for passengerconnections or the time needed to perform activities that enable planned rolling-stockand crew circulations, for logistic connections.

Minimum connection times do not depend on the current delay of trains and the pos-sible effect of delays on headway times was not considered in this work. Therefore,these values are computed offline and the corresponding arc weights are fixed.

5.4.3 Online process time estimation

The regression coefficients used to predict running and dwell times based on actualdelays, time series models. as well as the 10th percentiles of process times and headwayand connection arc weights are precomputed using the method described in Chapter 4and stored in the data structure of processed historical data W . The database contains aseparate object for each block section, inbound and outbound route, and station. Eachobject is attributed with a process time estimate and coefficients for each train line.

We define a separate mapping for retrieving the necessary regression coefficients and10th percentiles for each process type of arc (i, j). Running time estimates are obtainedby fr(W,(i, j)); fd′(W,(i, j)) is used for dwell time estimates for punctual and earlytrains, and fd′′(W,ni) for dwell time estimates for delayed trains. Finally, f f ix(W,(i, j))is used for fixed values of headway and connection time estimate from W .

The procedure to estimate process time for arc (i, j) from the historical database Wbased on the actual (predicted) delay zni is given in Algorithm 1. Running time es-timation is presented in lines 2–4, dwell time in lines 5–10 and fixed estimates forheadway and connection times in line 12. Note the different method for estimating thedwell times for delayed trains (line 10) that is based on the train number as explainedin Section 4.5.2.

5.4.4 Time loss due to route conflicts

The running time estimates are computed based on the free running times. Therefore,if a route conflict is detected, the arc weights that model the running processes of


Algorithm 1 ESTIMATEPROCESSTIMES

1: Input: W , zni , (i, j)2: if typei, j =‘run’ then3: (a0,a1, p10)← fr(W,(i, j)) {retrieve the coefficients}4: wi, j←max(p10,a0 +a1zni) {compute the estimate}5: else if typei, j =‘dwell’ then6: if zni ≤ 60 then7: (b0,b1, p10)← fd′(W,(i, j)) {retrieve the coefficients}8: wi, j←max(p10,b0 +b1zni) {compute the estimate}9: else

10: wi, j← fd′′(W,ni) {retrieve the estimate for delayed trains}11: else12: wi, j← f f ix(W,(i, j)) {retrieve the fixed estimate}13: return wi, j

the hindered train over the affected blocks need to be adjusted. The running timeadjustments need to incorporate time loss in running time estimates of the hinderedtrain. The time loss consists of braking, possible waiting time in front of the signal,running at a lower speed and re-acceleration.

The impact of a route conflict on the running time of the hindered train over the sub-sequent block depends on the conflict duration and the route and running time of thehindering train. The typical situation that occurs in practice when the two conflict-ing trains follow the same route is the ‘conflict wave’, where the hindered train keepspassing signals that show yellow aspect and is thus unable to re-accelerate to full speed(Goverde & Meng, 2011). We therefore consider the time loss due to re-accelerationonly after the hindered train has passed a green aspect signal.

In order to estimate the effects of route conflicts on train running times, all route con-flicts within 82 days of traffic on the busy corridor Leiden–Dordrecht in the Nether-lands were filtered out (Chapter 3). A quadratic robust fit was used to determine thecorrelation between conflict duration and the resulting time loss. Time loss is obtainedas the difference between the realized running time over a block and the predictedconflict-free running time derived depending on the current train delay.

Figure 5.5 shows the regression analysis that was performed based on 20130 datapoints split into conflicts shorter (left) and longer than 150 seconds (right). A ro-bust quadratic fit resisting 25% of the outliers showed the best performance in termsof coefficient of determination R2 = 0.79 for conflicts shorter than 150 seconds. Eventhough the data points are scarce for conflict durations longer than 150 seconds, thelinear regression line (R2 = 0.92) can be interpreted as the waiting time in rear of thesignal, which is the greater part of time loss in long conflicts. This approach enablesthe adjustment of running time estimates for hindered trains after a route conflict andits duration have been predicted.


Conflict duration [s]

Tim

e lo

ss [s

]

0 50 100 1500

50

100

150

200

250

300

350

Conflict duration [s]

Tim

e lo

ss [s

]

200 300 400 500 600 700 800 900 10000

200

400

600

800

1000

Figure 5.5: Time loss dependence on conflict duration: quadratic fit for short (up) andlinear fit for long conflicts (down)


5.5 Online prediction of event times

This section describes the online prediction based algorithm for prediction of eventtimes over graphs with dynamic arc weights. When an event happens, the correspond-ing node is selected as a root node. The algorithm then visits all reachable nodes inthe graph with dynamic arc weights and predicts all event times within the predictionhorizon. If route conflicts are predicted, the running times of affected trains are ad-justed. Finally, the actual information from the running trains is used for smoothingthe prediction error for future process times.

5.5.1 Prediction algorithm

The two typical methods of traversing the graph are breadth-first and depth-first search(Cormen et al., 2009). A recursive depth-first search (DFS) is chosen as the methodof traversing the graph, due to its low memory requirements, which is an importantconstraint for large graphs. This version of the DFS algorithm does not rely on queuesor stacks to keep track of the already visited nodes. Moreover, the prediction algo-rithm needs to traverse the graph in the topological order and DFS is typically used todetermine the topological structure of a graph.

After each event realisation, the reachable set of nodes is traversed, where the rootnode is the node that models the realised event. The prediction algorithm then updatesthe predicted event times of all events in the reachable set. Note that if a node isnot reachable, the corresponding event time can in no way be affected by the newinformation. Therefore, it is not necessary to visit that node in the prediction process.

The weights of running and dwell arcs are determined online with every graph traversalusing the functional dependence of process time on the current train delay (§5.4.3).During the algorithm execution, the predicted event times of a scheduled event willprovide predicted delays of trains. Therefore, subsequent process time estimates arecomputed with respect to z which is a vector that contains the predicted delays foreach train. For implementation purposes, an attribute colour is added to each arc. Itsvalues:‘white’ and ‘black’ indicate that the arc has not been discovered or has beendiscovered (appropriate weight has been assigned), respectively.

Finally, every first node in the planned route of a train, modelling the entrance time ofthe train (the first departure or the first event within the observed network), is connectedto a dummy node 0 by an arc with weight that is equal to the expected entrance time.After processing each event realization, the graph is updated by removing the realizedevent together with all incoming and outgoing arcs. An arc between node 0 and thenext node in the event sequence of a train is added. The weight of the added arc is equalto the predicted realization time of the next event of the train. Moreover, every trafficcontrol action also results in a graph update. The process times of each added train areinitially calibrated with respect to the actual delays and expected entrance times.


When an update about the occurrence of event i ∈ V arrives, a set of reachable nodesV is computed that comprises all nodes reachable from and including i. The recordedevent time is set t pred

i ← treci and colour attribute of each arc in the subgraph is set to

‘white’. If typei ∈ {‘departure’,‘arrival’}, the current delay value of the correspondingtrain is updated zni ← trec

i − tschi . The information is propagated through the graph and

predicted event times of all reachable events are computed according to Algorithm 2.

Algorithm 2 PREDICTEVENTTIMES

1: Input: G,V ,W,z, i,Thor2: z← z3: for all j ∈ nexti do4: wi, j← EstimateProcessTimes(W, zni,(i, j)) {arc weight}5: colouri, j =‘black’6: if colourk, j =‘black’, k ∈ prev j∩V then7: t pred

j ← maxk∈prev j

(t predk +wk, j) {predicted event time}

8: if type j ∈ {arrival,departure} then9: if type j = departure then

10: t predj ←max(t pred

j , tschj ) {timetable constraint}

11: zn j ← t predj − tsch

j {predicted delay}12: if t pred

j ≤ Thor then13: PredictEventTimes(G,V ,W, z, j,Thor) {recursive call}14: return G, z

The main loop of the prediction algorithm is initiated in line 3. In line 4 the actualweight of an outgoing arc is computed using the procedure described in Algorithm 1.If all constraints on the event realization time are known, i.e., all direct predecessorswithin the subgraph were visited and all incoming arcs traversed (line 6), the predictedevent time is computed in line 7. Otherwise, a new iteration of the main loop is ini-tiated. The timetable constraint for departure events is included in line 10. For allscheduled events, the predicted delay vector is updated in line 11. Finally, if the pre-dicted event time is within the prediction horizon Thor, a recursive call of the algorithmis performed in line 13.

Note that the predicted event time may also depend on events that are not reachablefrom the realized event and thus do not belong to the subgraph. For that reason it isrequired to explicitly define the set of reachable nodes V . In such cases arc weightwk, j for k ∈ prev j \ V in line 7 can be computed using the same procedure wk, j ←EstimateProcessTimes(W, znk ,(k, j)). The predicted event time of k is is retrieved fromG as a prediction during an earlier algorithm call.

Since the Algorithm 2 represents a modified version of a DFS algorithm, its complexitycan be determined in a similar way Cormen et al. (2009). The modification restrictsthe generic DFS algorithm to follow the topological order of the graph. The predictionalgorithm sweeps through the subgraph of reachable nodes V and it is called exactly


once for each node (line 6). For an algorithm call for node i ∈ V , the main loop (lines3–13) is called |nexti| times. Since ∑i∈V nexti = E, where E = {( j,k) | { j,k} ∈ V}, therunning time of Algorithm 2 is O(|E|).

Figure 5.6 shows an example of algorithm performance when event (q,S1) is realized.Solid arcs illustrate arcs with computed arc weights. The weights of dashed arcs arestill unknown. The events with predicted event times are shown in grey colour. Notethat an event time can be predicted only after all incoming arcs in the correspondingnode are solid. This is visible in the figure when the algorithm backtracks after step4 to determine the weight of (q,S2)→ (r,S2) in order to compute the predicted eventtime of (r,S2).

S1 S2

S4

S3

(q,S1) (q,S2) (q,S3)

(r,S1) (r,S2) (r,S4)

(q,S1) (q,S2) (q,S3)

(r,S2) (r,S4)

(q,S1) (q,S2) (q,S3)

(r,S2) (r,S4)

(q,S1) (q,S2) (q,S3)

(r,S2) (r,S4)

(q,S1) (q,S2) (q,S3)

(r,S2) (r,S4)

(q,S1) (q,S2) (q,S3)

(r,S2) (r,S4)

(1) (2)

(4)(3)

(5) (6)

Figure 5.6: An example of execution of Algorithm 2

5.5.2 Adjusting the running time estimates due to route conflicts

The prediction of route conflicts can be performed by extending the microscopic modelwith the principles of blocking time theory. Section 5.4 describes how running andclearing times, and setup and release times are determined for each train run over ablock. After including sight and reaction, and approaching time, the blocking timescan be determined. Route conflicts are identified by the overlapping blocking times(Figure 2.2).

Since the running time estimates are computed based on the free running times, arcweights that model the running processes over affected blocks need to be adjusted totake into account braking (and possible waiting time in front of the signal), running ata lower speed, and re-acceleration for every predicted route conflict. Algorithm 2 is


therefore extended with a running time adjustment procedure. For each predicted routeconflict, the increase of running time of the hindered train is computed depending onthe conflict duration.

In this thesis we consider a conventional three-aspect signalling system. The weightwi, j of running arc (i, j) needs to be adjusted if it is estimated that Signali will beshowing a ‘yellow’ aspect at the moment when the train arrives at the sighting distanceof the signal. This moment is obtained by modifying the predicted signal passing timet predi with a fixed value of 12 seconds for the sight and reaction time of the train driver.

The signal aspect can be determined by comparison with the release time (switch to apermissive aspect) of the following signal, Signal j,

trelSignal j

= maxk∈{prev j\i}

(t predk +wk, j). (5.3)

The procedure for adjustment of the running time of hindered trains is shown in Algo-rithm 3.

Algorithm 3 ROUTECONFLICTPREDICTION

1: Input: t predi , trel

Signal j,wi, j

2: if t predi −12 < trel

Signal jthen

3: d← trelSignal j

− (t predi −12) {compute duration}

4: ∆← f (d) {compute time loss}5: wi, j← wi, j +∆ {update arc weight}6: return wi, j

If a route conflict is predicted (line 2) the duration d of the conflict is computed in line3 and the predicted time loss ∆ as a function of d determined from historical data asexplained in Section 5.4.4, in line 4. The running time estimate is updated in line 5.

An example of a route conflict prediction is given in Figure 5.7. The graph showsthree trains q,r,s (the trains are planned to pass signal S2 in that order) with theirplanned routes over the given subnetwork. Using the introduced notation, we denoteby t pred

8 the time when train s passes signal S2. A route conflict can be identifiedby comparing the passing time of train s at signal S1, t pred

7 with the earliest possiblerelease time of signal S2 due to minimum headway times after passing of trains q andr, max(t pred

3 +w3,8, tpred5 +w5,8). If train s passes signal S1 before the release time of

S2 the conflict is identified and the running time estimate of train s between signals S1and S2 can be adjusted according to lines 3–5 in Algorithm 3.

5.5.3 Adaptive adjustments of running time predictions

In the presented prediction model, the estimated running times over block sectionsdepend on departure delay from the last scheduled stop. In order to exploit the real-time information received since the last departure, an adaptive component has been


v1=(q,S1)

S1 S2

S4

S3

v2=(q,S2) v3=(q,S3)

v4=(r,S1)v5=(r,S2)

v6=(r,S4)

v7=(s,S1) v9=(s,S3)v8=(s,S2)

Figure 5.7: An example of route conflict prediction

developed that keeps track of the actually realized running times of a running train andadjusts the running times estimates until the next scheduled stop. A moving averagesmoothing method is used to incorporate the prediction error observed during the trainrun into future predictions until the next stop.

A schematic example of adaptive prediction is given in Figure 5.8. The running traindeparted from station A and, in the situation from the figure, has just cleared the jth outof m blocks to station B where it is scheduled to stop. The grey solid line starting atstation A represents the predicted running time of the train based on the actually regis-tered departure delay. For the sake of clarity, for subsequent realized signal passagesonly the predicted running time over the following block is shown.

bj+1 bi bmbjb1

A B

δ1 δj-1

δj

Time

j+1i-1

im-1

m

Figure 5.8: A schematic example of adaptive prediction

The prediction error of the running time over block bk is denoted by δk and computedafter each observed signal passage. For subsequent blocks until some block m′ ∈ { j+1, ...,m} we derive the estimated prediction error δ and adjust the estimates of running


times over the remaining blocks by

δi =1l

j

∑k= j−l

δk,∀i = j+1, ...,m′ (5.4)

where l is a parameter l ∈ {1, ..., j−1} that specifies the length of the moving average.A separate value of parameters l and m′ is selected for each train type. The red dottedline in Figure 5.8 denotes the adjusted prediction of running times to station B.

By applying this adaptive prediction strategy, the continuous delay sources of theconflict-free run of a single train (e.g. due to particular driving style or defectiverolling-stock) as well as temporary speed restrictions (due to infrastructure malfunc-tions or maintenance), will be possible to identify and include in the predictions.

5.6 Application on a case study

5.6.1 Experimental setup

In order to test the performance of the described algorithms, an experimental environ-ment was set up that includes a static and a dynamic component. The static componentconsists of the database of historical track occupation data used for dynamic arc weightassignment and running time adjustments (Section 5.4).

The dynamic component of the experimental environment consist of the actual processplans for all trains within the prediction horizon and actual train event times. Theactual route for each train is given on the level of track sections, which is crucial foraccurate modelling of route conflicts and building the mesoscopic graph model. Asthe prediction horizon moves, new trains are added to the model and passed events areremoved.

As explained in Section 3.3.1, the train describer log files contain chronologically or-dered infrastructure and train step messages. We created a real-time environment formodel validation by sweeping through the train describer file for one day of traffic.Every train step message (signal passage) represents the new information that is prop-agated through the graph using Algorithm 2. The actually realized train event timesare used to test the accuracy of predictions.

5.6.2 Description of the case study

The experimental setup was built for the busy corridor Leiden–The Hague–Rotterdam–Dordrecht in the Netherlands. The 60 km long corridor is (partially) traversed daily byapproximately 300 trains per direction. Figure 5.9 shows the schematic representationof the observed network along with the train lines and the corresponding stopping pat-tern for the 2010 timetable, which was available for this study. The thin line illustratesa train line that runs once per hour, whereas the other lines operate twice per hour.


Sch

ieda

mvC

entr

umDen

vHaa

gM

oerw

ijkR

ijsw

ijk

Del

ftZu

id

Del

ft

R’d

amvB

laak

R’d

amvZ

uid

R’d

amvL

omba

rdije

n

Bar

endr

echt

Zwijn

drec

ht

Dd

ht

Den

vHaa

gvC

entr

aal

Leiden

Den

vHaa

gvH

S

Rot

terd

amvC

entr

aal

Dor

drec

ht

DenvHaagLaanvvanvN.O.I

DenvHaagMariahoeve

Voorschoten

DevVink

Figure 5.9: Network and train lines for the case study

The selected corridor and train routes enable testing the model with all possible traininteractions – merging, diverging and intersecting routes. The part of the corridorbetween Delft and Rotterdam Centraal as well as the branches towards Den Haag Cen-traal is a double track line. The remaining part is a four-track line, where two tracksare dedicated for each direction.

5.6.3 Comprehensive analysis

This section presents a comprehensive analysis of the prediction tool performancebased on the application to one day of traffic on the corridor. The prediction algorithmis initiated and the rolling horizon moves after receiving each of the 9776 messagesthat report the realization of signal and station events that occurred on the observedday. Table 5.1 shows the average number of events that are predicted in each algorithmexecution, and the average number of arcs for prediction horizons of 2 hours, 1 hour,30 minutes, 20 minutes and 10 minutes. The average number of nodes and arcs aremonotonically decreasing as shorter prediction horizons are considered.

Table 5.1: Model size for different prediction horizons

Prediction horizon [min]120 60 30 20 10

Average no. events 1040 532 269 180 90Average no. arcs 2288 1117 590 389 202

Figure 5.10 shows the box-plots of errors of event time predictions for each consid-ered prediction horizon. The prediction error is computed as the difference betweenthe actually realised event time and the predicted event time. The standard deviationof prediction error reduces with the decrease of horizon length. The median of theprediction error also follows a monotonically decreasing trend as a smaller prediction


horizon is considered. Medians in each box plot show a slight positive bias. In orderto explain this, we define a negative error that occurs if the predicted event occurredearlier then predicted and the positive error if it occurred later then predicted. Thus thenegative error of a process time estimate is bounded by the physical and operationalconstraints for the duration of the corresponding process. On the other hand, no suchbound exists for the positive error, which explains the positive bias of prediction errors.

Prediction horizon [min]

Pre

dic

tion

erro

r [s

]

120 60 30 20 10-150

-100

-50

0

50

100

150

200

Figure 5.10: Box plots of prediction error distributions for different prediction horizons

The accuracy of predictions is indicated by the mean absolute error (MAE). The pre-diction horizon of 120 minutes is divided into 10 second wide intervals. The absoluteprediction error is computed as the absolute value of the difference between the actu-ally realised event time and the predicted event time. MAE is obtained in each intervalby computing the mean value of all corresponding absolute prediction errors. The de-pendence of the MAE on the length of the prediction horizon is shown in Figure 5.11.The MAE is within 45 seconds even for the longest prediction horizon. The accuracyof predictions that are within a 30 minutes prediction horizon is significantly increasedsince more accurate information is available on events that have a direct impact on therealization time of an event. For the prediction horizons shorter than 30 minutes, theMAE is monotonically decreasing with horizon length.

We obtain an average error shorter than 1 minute for all prediction horizons. The 10minutes horizon shows that in terms of average prediction error, our model outperformsthe approach of predicting event times using train motion equations (Dolder et al.,2009).

The benefit of adaptive prediction when applied to all observed train runs in one day oftraffic is shown in Figure 5.12. Improvements are noticeable for a prediction horizon ofup to 10 minutes due to parameter l that defines the width of the moving average and m′

that defines the smoothing horizon (Section 5.5.3). Different combination of parameter


0 20 40 60 80 100 1200

5

10

15

20

25

30

35

40

45

Prediction horizon [min]

Mea

n ab

solu

te e

rror

[s]

Figure 5.11: Mean absolute prediction error depending on prediction horizon

values were tested. Values l = 3 and m′= 3 for intercity trains and l = j−1 and m′=mfor local trains showed the best performance in terms of MAE. Therefore, the runningtime estimates are adapted for the next three blocks for intercities and until the nextscheduled stop for local trains. Similarly, the moving average is computed over the lastthree block sections for intercities and over all blocks since the last departure for localtrains.

0 100 200 300 400 500 600 700-5

0

5

10

15

20

25

NonadaptivelpredictionAdaptivelprediction

Predictionlhorizonl[s]

Mea

nlab

solu

telle

rror

l[s]

Figure 5.12: MAE comparison for adaptive and nonadaptive prediction

The accuracy of route conflict predictions for different prediction horizons is stronglycorrelated with the mean absolute error. For prediction horizons longer than 30 min-utes, approximately 80% of route conflicts longer than 30 seconds are accurately pre-dicted. As shorter prediction horizons are considered, the accuracy of route conflictsprediction increases. For a 10 minutes horizon, 95% of route conflicts are accuratelypredicted.

The running time adjustment does not show a noticeable global effect when the MAE


of all predictions of all events is considered. However, an accuracy analysis performedon the isolated set of running times of hindered trains, shows an increase in predictionaccuracy of 8 seconds on average for a 30 minutes prediction horizon and 13 secondsfor 10 minutes prediction horizon.

Since the prediction algorithm is linear, the computational complexity, which dependson the size of the input graph, is not considered as a criterion for choosing the mostappropriate prediction horizon. Even for the longest prediction horizon, the algorithmexecution takes less than one second.

Finally, Figure 5.13 shows the comparison of prediction accuracy of the model pre-sented in this chapter with the conventional parallel shift strategy, which is typicallyapplied for estimating train arrival and departure times. The analysis is performedfor scheduled event times only. The benefits of real-time prediction are noticeable forevery prediction horizon.

0 1000 2000 3000 4000 5000 6000 7000 80000

20

40

60

80

100

120

Prediction-horizon-[s]

Mea

n-ab

solu

te--e

rror

-[s]

Parallel-shiftReal-time-prediction-tool

Figure 5.13: MAE of scheduled event times for a parallel shift strategy and the real-time prediction

5.6.4 Example of algorithm execution

An example of predictions is shown in Figure 5.14. The presented time-distance di-agram shows the predicted train paths (solid lines). The realized train paths in spaceand time are presented with dashed lines. The prediction is performed at the departureof train ST5025 from Den Haag HS (GV). The complete routes of the seven trains thatenter the network within the 30 minutes prediction horizon are included in the predic-tions. The mean absolute prediction error for 161 predicted events (including signalpassages) is 19.33 s, while the maximum prediction absolute error is 68.71 s.


ST5025

ST5025

ST5025

IC1925

IC1925

IC1925

IC1925

S2227

S2227

S2227

S2227

IC9216

IC9216

IC9216

IC9216

ST5127

ST5127

ST5127

IC2127

IC2127

IC2127

IC2127

ST5027

ST5027

ST5027

07:13 07:21 07:30 07:38 07:46 07:55 08:03 08:11 08:20

GV

RSW

DT

DTZ

SDM

RTD

GVMW

Figure 5.14: Time-distance diagram of predicted (at 7:13) and realised train paths

The major advantage of the presented model for traffic controllers is the ability topredict all route conflicts within the prediction horizon. We use the principle of over-lapping blocking times (Hansen & Pachl, 2008) to predict and visualize route conflicts.

Figure 5.15 shows the predicted (up) and realized (down) blocking time diagram. Localtrains are presented in magenta and intercity trains in blue. Overlaps in blocking timesthat indicate route conflicts are given in red. The three out of the four major routeconflicts that occurred, one in Schiedam (SDM) and two in Rotterdam (RTD), werepredicted by the model. The fourth conflict that was not captured occurred more than30 minutes after the moment of prediction. The very short running time of IC2127 be-tween stations Delft South (DTZ) and Schiedam (that is visible in Figure 5.14) causeda route conflict with the preceding ST5127 at SDM, which was not captured by themodel.

An example of adaptive prediction that minimizes the prediction error for runningtrains is shown in Figure 5.16. The example considers intercity train IC1919 thatdoes not have scheduled stops between The Hague HS (GV) and Delft (DT). The firstprediction, derived at the moment of departure from The Hague HS, is represented bythe blue line. After three corrections of running time estimates resulting in predictions,the prediction error of less than 1 second was achieved (the final running time estimatepractically overlaps the realized running time given with dashed line). The predictedarrival time error is monotonically decreasing as the train progresses towards stationDelft. Therefore the propagation of prediction error to connected events of other trainsis reduced thus affecting the overall performance of the model.


ST5025

ST5025

ST5025

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Figure 5.15: Blocking time diagram predicted at 7:13 (up), realized blocking timediagram (down)


IC1919

05:56:40 05:58:20 06:00:00 06:01:40 06:03:20

GV

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Figure 5.16: Effects of adaptive prediction

5.7 Conclusions and outlook

This chapter presented a tool for accurate prediction of event times based on a directedacyclic graph with dynamic arc weights. The process times in the model are obtaineddynamically using processed historical train describer data, thus reflecting all phenom-ena of railway traffic captured by the train describer systems and preprocessing tools.The graph structure of the model allows applying fast algorithms to compute predictionof event times even for large and busy networks.

The main contribution of this approach is the dynamic estimation of process times foreach train by using the predetermined functional dependence of process times on actualdelays. Train interactions are modelled with high accuracy by including the mainoperational constraints and relying on the actually realised corresponding minimumheadway times (obtained from the historical data) rather than on theoretical values.The recursive depth-first search algorithm with dynamic arc weights gives predictionsfor all event times within the horizon.

The predictive traffic model supports route setting and traffic control decisions andcould be interactively used by signallers and traffic controllers. First, the model pre-dicts route conflicts for a given actual route plan and train positions. This could beused by the signaller to pro-actively resolve the conflict by e.g. changing routes or theorder of trains. The impact of any control decision can be checked by an update ofthe predictive model leading to new conflict and arrival time predictions. If a control


decision leads to satisfying results it can be implemented in the actual process plan.If on the other hand a route conflict cannot be avoided, the signaller could give speedadvice (or new target passage times) to the relevant train drivers so that the impact ofthe route conflict is minimal and energy can be saved by preventing unnecessary brak-ing and re-acceleration. Second, the arrival time predictions could be used to checkconnections in the case of arrival delays. When a connection conflict is detected, thesignaller may decide to secure or cancel a connection in advance. This way up-to-date passenger information can be provided, both at stations and in the delayed trains.Similarly, endangered logistic connections (crew or rolling-stock) can be predicted inadvance.

The model has been applied in a case study on a busy corridor in the Netherlands in areal-time environment using train describer log files, and produced accurate estimatesfor train traffic and route conflicts within 30 minutes. Application of the model to awider area is possible either by enlarging the observed area or by coordinating multipleareas. Finally, the model structure enables straightforward application of the network-wide delay propagation algorithm (Goverde, 2010) to estimate the further effect ofcurrent traffic conditions (or examined traffic control actions).

For larger examples that model dense traffic, it is expectable that more events can oc-cur almost simultaneously, i.e., more than one update can arrive within one second.The presented event-driven prediction algorithm can be modified to a time-driven ver-sion where the prediction process is performed in regular time intervals based on theinformation that arrived within the interval.

Finally, performance analysis has been conducted using raw data from train describerlog files. Even though data are very detailed and of high quality, various errors inlogging of event times still occur which may affect the accuracy of subsequent predic-tions. In future research robustness of the model to noise and errors in the data need tobe increased in order to provide more stable and accurate predictions.

Chapter 6

Rescheduling models for real-timetraffic management in large networks


Kecman, P., Corman, F., D’Ariano, A., and Goverde, R. M. P. (2013). Reschedulingmodels for railway traffic management in large-scale networks. Public Transport, 5(1-2), 95–123.

6.1 IntroductionReal-time rescheduling of railway traffic is an important task of traffic controllers witha great impact on punctuality and reliability of train traffic. Reliable predictions and in-formation from the monitoring system, that are described in the previous chapters, arecrucial for developing robust rescheduling models. In case of disturbances, accuratepredictions of train delays may serve as an input for traffic controllers or reschedul-ing models that aim to reduce delay propagation and deviation from the scheduledtimetable. This chapter focuses on rescheduling models that can be integrated in aclosed loop with monitoring and prediction systems as described in Figure 1.4.

In current practice, traffic controllers attempt to reduce the effects of disruptions anddelays using a set of predetermined rules and their own experience. Traffic in localcontrol areas or on the network level is controlled without a reliable supporting tool tocompute optimal control decisions. That often leads to creating suboptimal solutionswith new conflicts and effects on the network level. This problem has been tackledby numerous approaches available in the academic literature (§2.6). The scope of theexisting models is limited to a single traffic control area (Caimi et al., 2012; D’Ariano,2008; Pellegrini et al., 2014) or a subnetwork (Corman et al., 2012b; Tornquist Krase-mann, 2011). The resulting solutions are (near) optimal in the respective areas. How-ever, Goverde (2010) showed that in large and busy networks delays often propagate

127


across multiple traffic control areas and, depending on their magnitude, often have animpact on the network level. We therefore aim at developing a global, network scaleoptimization tool that optimizes the actual state over the overall network and controlsthe traffic from a global perspective with adjustments to the timetable.

In this chapter, we examine the applicability of macroscopic models for reschedulingrailway traffic at a network-wide level. Railway traffic is represented by a timed eventgraph that allows computing delay propagation in large and strongly interconnectednetworks in a short time. The timed event graph is then converted to four alternativegraph models with different operational constraints. An efficient solution algorithmD’Ariano, Pacciarelli, and Pranzo (2007) is applied on the alternative graph modelsto optimize the rescheduling actions. All presented models have been tested on a se-ries of delay scenarios, compared to each other, and evaluated by comparison to themesoscopic model of D’Ariano (2008), that takes into account detailed infrastructuredata and train dynamics. All comparisons have been performed in terms of resultingsecondary delay and dispatching decisions on a case study of the corridor betweenUtrecht and Den Bosch in the Netherlands. Moreover, the macroscopic models havebeen applied on a test case of one peak hour of the Dutch national timetable in orderto test their applicability on large and busy networks.

An important objective of the work presented in this chapter was to investigate thetrade-off between precise modelling of operational constraints of railway traffic andthe time needed to compute a (near) optimal solution for a large network. Macroscopicmodels with different levels of abstraction, result in different quality of solutions andcomputation time. The aim is to select such level of the granularity of the macroscopicmodel that enables computing a feasible solution of high quality in short time.

The next section describes the general approach to macroscopic modelling of railwayoperations as well as the procedure used to solve the rescheduling problem and obtainthe new schedule. Section 6.3 gives a specific description of presented models. Sec-tions 6.4 and 6.5 report on a comparison of the models on a railway corridor and onthe whole Dutch network, respectively. Finally, we discuss the performance of eachmodel and give directions for future research (§6.6).

6.2 Macroscopic modelling of railway operations

6.2.1 Timed event graphs

Railway operations can be modelled at the macroscopic level by means of timed eventgraphs (TEG), as formally defined by Goverde (2007). A TEG is a representation of adiscrete-event dynamic system which consists of events, connected by processes thatare described by the minimum process times. The major difference from the graph-based model presented in the previous chapter is the pure macroscopic character of themodel.

Chapter 6. Rescheduling models for large networks 129

An individual train run is modelled as a series of events and processes that connectthem. Every node is an event, defined by the train number, the timetable point (station,stop on open track, junction), type (departure, arrival or through) and the scheduledevent time. A through event is the moment when a train passes the centre axis of atimetable point without stopping. Every running or dwell process is modelled by anarc, defined by the train number, type (run or dwell), start and completion event, andthe minimum process time.

Interactions between trains are modelled with headway and connection processes.Headway processes separate events of different trains that have identical, opposite,intersecting, merging or merging routes. The minimum headway time between twotrains is computed according to the blocking time theory (Hansen & Pachl, 2008). Allevents in a TEG take place on the platform tracks or centre axis of a timetable point.Since route conflicts may occur at signals that prevent a train from entering the oc-cupied or reserved block, a minimum headway time needs to be computed betweenevents in the station where conflicting outbound routes start and inbound routes end(minimum line headway). The connection processes separate the departure event of aconnecting train and arrival events of each feeder train by a minimum connection time.

An event in a TEG can occur only after all processes represented by incoming arcsof the corresponding node have been completed. Events in a TEG occur in a fixedsequence determined by the topology of the graph. The fixed structure of a timedevent graph is a major obstacle for the straightforward application in the field of real-time rescheduling since many dispatching decisions imply changes of relative order ofoccurrence among events. In this chapter, we overcome this limitation by converting aTEG to an alternative graph (Mascis & Pacciarelli, 2002).

6.2.2 Alternative graphs

An alternative graph (AG) is a representation of a job-shop scheduling model with ad-ditional operational constraints. On a mesoscopic level, the train rescheduling problemposed as a job-shop scheduling problem (D’Ariano, 2008) is to schedule a finite set ofjobs (trains), defined by fixed sequences of operations (train runs and dwellings) whichcannot be interrupted, on a finite set of resources (block sections or platform tracks)that can perform one operation at a time (no-store or blocking constraint). The objec-tive is to schedule all operations on the corresponding resources and to minimize thesecondary delay.

We extend this model to a macroscopic scale by aggregating multiple block sectionsinto open track segments and platform tracks into timetable points and use them asresources in macroscopic models. Therefore, the number of operations that can simul-taneously be handled by one resource, depends on the capacity of that resource.

Alternative graphs consist of nodes N, fixed arcs F , and pairs of alternative arcs A. Weadd the connection arcs C to this generic formulation as in Corman et al. (2012a). Weuse the following notation: M,O,T are sets of resources (machines), operations and


trains (jobs), respectively; i, j are indices of resources mi,m j ∈ M; r,s, are indices oftrains tr, ts ∈ T . We denote by xr

i the starting time and by pri the processing time of

operation ori ∈ O of train tr on resource mi. The headway time between the starting

times of operations of trains tr and ts on resource mi is denoted by hr,si . Ti is a set of

trains that use resource mi.

A node in the graph represents a single operation ori ∈O of job tr ∈ T , that is performed

on resource mi ∈M. Every node is described by the starting time xri of the correspond-

ing operation. Since one job consists of a predetermined sequence of operations, nodexr

i at the same time represents the completion time of the previous operation.

An arc (xri ,x

sj)∈{F∪A∪C}with weight pr

i represents the precedence relation betweenoperations or

i and osj given by the following equation.

xsj ≥ xr

i + pri , ∀i, j,r,s : mi,m j ∈M, tr, ts ∈ T (6.1)

Fixed arcs are used to model fixed precedence relations between operations that haveto be performed in a fixed relative order.

Alternative arcs are decision variables used to determine the relative order of oper-ations scheduled to be performed on the same resource. If operations or

i and osi are

scheduled to be performed on the same resource mi, then the relative order of opera-tions can be determined by selecting the appropriate alternative arc. The concept ofalternative arcs can be modelled with the binary control variable kr,s

i such that:

kr,si =

{1 if xr

i < xsi ,

0 otherwise∀i : mi ∈M, ∀r,s : tr, ts ∈ Ti, (6.2)

with the constraint that exactly one arc from each pair has to be selected:

kr,si + ks,r

i = 1, ∀i,r,s : mi ∈M, ts, tr ∈ Ti. (6.3)

In sections 6.2.4–6.2.4 we define different resource types, each of them with partic-ular properties in terms of capacity. For each resource mi with limited capacity, thestarting times of two operations or

i and osi depend on the value of the corresponding

decision variables kr,si and ks,r

i that define the relative order of operations. The con-straints that formalize this dependence are given separately for each resource type inthe corresponding section.

A selection of exactly one arc from each pair is called a complete selection. Theobjective is to select alternative arcs in a way that would minimize the waiting timeof all operations. A valid solution determines the precedence relations between eachtwo operations that are scheduled on the same resource. Two basic properties need tobe respected: (i) completeness (exactly one arc from each alternative pair is selected),(ii) consistency (it must not contain positive length cycles). A complete and consistent


selection yields the full schedule of all jobs. A possible interpretation of a completeselection of an alternative graph is a mode in a switching max-plus linear system (Vanden Boom & De Schutter, 2007).

Connections can be represented by a constraint between events of different trains. Ifthere is a scheduled connection between a feeder train ts and the connecting train trthen:

xri ≥ xs

j + cs,r, (6.4)

where xri is the starting time of the operation of train tr on resource mi (a departure

event when mi models an open track) and xsj is the starting time of the operation of

train ts on resource m j (an arrival event when m j models a station). The arc (xsj,x

ri )∈C

is weighted by cs,r, that represents the minimum connection time.

Scheduled starting and completion times of operations (timetable constraints) are in-corporated in an AG by means of dummy operations (nodes) 0 and n, with startingtimes x0 and xn. If operation or

i is scheduled to start at time dri , the fixed arc (x0,xr

i )

with weight dri (release time) is added to ensure that the operation cannot start before

its scheduled starting time.

In real operation, scheduled completion time αri (due date) of operation or

i may becomeinfeasible due to disturbances that can cause extension to the planned processing timepr

i (primary delays). This delay can propagate over successive operations of the traintr, thus making their due dates also infeasible. A modified due date can therefore bedefined by−max(αr

i ,τri ) where τr

i is the earliest possible completion time of operationor

i , considered isolated from interactions with all other operations not belonging to jobtr, that cannot be improved by any rescheduling action. A fixed arc with the weightequal to the modified due date is added to the graph from the node that representsthe completion time of the operation to node n. We define an unavoidable delay bymax(0,τr

i −αri ), a secondary delay by max(0,xr

i+1−max(αri ,τ

ri )) and a total delay as

the sum of the unavoidable and secondary delays.

D’Ariano (2008) showed that minimisation of the critical path between nodes 0 and nis equivalent to minimizing the maximum secondary delay over all operations. Thusthe objective function can be formally expressed with:

min xn− x0. (6.5)

The solution procedure (D’Ariano, Pacciarelli, & Pranzo, 2007) determines the startingtimes xr

i for every operation, and values of binary variables kr,si , that represent the orders

within each pair of trains tr, ts ∈ T scheduled to use the same resource mi. An exactsearch is performed in the solution space by means of a branch and bound algorithm.A good initial solution is found by a set of heuristics (first come first served, first leavefirst served, avoid most critical completion time). The solution procedure is truncated


after a time limit (in this work 5 min) is reached. We refer to Corman et al. (2014) andD’Ariano, Pacciarelli, and Pranzo (2007) for additional information on the solutionprocedure.

6.2.3 Conversion of timed event graphs to alternative graphs

The macroscopic modelling of railway traffic by means of alternative graphs is ex-plained with the terminology introduced in Chapter 2. Each timetable point and eachopen track segment is modelled by a resource. An individual train run is modelled asa sequence of operations. Every operation is attributed by the starting time, durationand the resource traversed by the train. A train run is represented with nodes and fixedarcs.

In order to describe how a TEG is converted to an AG, the difference in meanings ofnodes and arcs in these two graphs needs to be resolved. We keep the interpretationof nodes and arcs as in TEG and convert it to AG in the following manner. Fixed arcsrepresent operations (run or dwell). Weight of each fixed arc is equal to the minimumprocessing time of the corresponding operation. Every node is an event, i.e. arrival ordeparture (a through event is included by fixing the dwell time to 0), representing thestart of the operation denoted by the outgoing fixed arc and completion of the operationdenoted by the incoming fixed arc. Every departure after a scheduled stop is connectedto node 0 and every arrival to a station with a scheduled stop to node n, as explainedin the previous section. Having in mind that each operation in an AG is associatedto a particular resource, we dedicate an additional resource attribute to each event inthe corresponding TEG model. Arrival and through events are augmented with thetimetable point resource. On the other hand, the open track resource is added to eachdeparture event.

The advantage of using AG for macroscopic models is in modelling discrete decisionsthat manage interactions between trains. If two trains have operations that cannot besimultaneously performed on the same resource with constrained capacity, at least onepair of alternative arcs weighted by the minimum headway time between two oper-ations is added in order to specify the precedence relation between operations. Thenumber of alternative pairs and their start and end nodes depend on the resource type.The order of operations is determined by selecting the appropriate arc from the pair.This way, resolution of intra-track conflicts (conflicts between trains using the sameresource) can be appropriately modelled. However, inter-track conflicts on a macro-scopic level are modelled in a different manner since they represent conflicts betweenoperations taking place on different resources. Modelling of inter-track conflicts willbe explained in detail in Section 6.3.1.

Connections in the macroscopic AG models are fixed and modelled in the same wayas in timed event graphs. A connection arc is added between the node that modelsan arrival event of the feeder train and the node that models a departure event of theconnecting train with the weight equal to the minimum connection time.


6.2.4 Resources as building blocks of alternative graphs

Infrastructure elements can be modelled by using resources with different properties interms of capacity. This results in multiple models with different complexity and num-ber of operational constraints. Before presenting a detailed description of the macro-scopic models (Section 6.3), we first describe the essential meaning of each type ofresource.

Infinite capacity resources (ICR)

The simplest way of specifying a resource is by considering only the temporal dura-tion of the scheduled operation. This means that no further restriction is posed on trainorders and headways between trains. Therefore, these resources do not model interac-tions between trains and all trains can use them independently from each other. Thisresource type is used under the assumption that capacity is sufficient to accommodatedemand at all times, thus no conflict can occur and the only binding constraint is theprocessing time.

Figure 6.1 shows how two trains tr and ts are modelled on infinite capacity resource(ICR) type resource mi. Each node represents the starting time of an operation on theresource (xr

i is a starting time of operation ori of train tr on resource mi). Arcs represent

the operation that started at their parent node and their weight is equal to the minimumprocessing time of operation (pr

i is the minimum processing time of operation ori ).

There are no arcs between operations associated with different trains in Figure 6.1,thus operations of both trains can be performed independently from each other. Theonly constraint that has to be respected when scheduling operations on this resourcetype is given by equation (6.1).

xri

xsi

pri

psi

xri+1

xsi+1

xri-1

xsi-1

pri-1

psi-1

Figure 6.1: Graph representation of resources with infinite capacity

Infinite capacity resource with headway (ICR+H)

If a resource is modelled as infinite capacity with headway, the number of operationsthat can simultaneously be processed is not restricted. However, the starting timesof two consecutive operations or

i and osi on the same resource mi are separated by a

time interval defined with headway hr,si . Trains are thus prevented to occupy the same

infrastructure element within a predefined headway time.

Introducing a minimum time separation between the starting times of two operations ona resource does not constrain completion times of operations, which are not constrained


by any headway. They can therefore occur simultaneously and not necessarily in thesame relative order in which they started. Figure 6.2 (left) depicts the alternative graphthat can be used to compute the starting time of both operations or

i and osi on resource

(machine) mi. Alternative arcs are shown with dashed lines with weights equal tothe minimum headway time between two operations of different trains on the sameresource. A possible selection is given on the right side of the figure. Note that inorder to independently observe the properties of this type of resources, neighboringresources mi−1 and mi+1 are modelled as non-constrained infinite capacity resources.

If we define by M2 ⊂ M a set of machines of type infinite capacity resource withheadway (ICR+H), the starting time of an operation scheduled on this resource can befully defined by equations (6.1)-(6.3) and the additional constraint, representing thechoice of train orders:

xri ≥ xs

i +hs,ri −L · kr,s

i , ∀i,r,s : mi ∈M2, tr, ts ∈ Ti, (6.6)

where L is a sufficiently large number (larger than the latest completion time of thelatest operation).

xri

xsi

pri-1

psi-1

his,r hir,s

xri+1

xsi+1

pri

psi

xri-1

xsi-1

xri

xsi

pri-1

psi-1

his,r

xri+1

xsi+1

pri

psi

xri-1

xsi-1

Figure 6.2: Graph representation of resources with infinite capacity and headway con-straint (left) and a possible selection (right)

Infinite capacity resources with FIFO property (ICR+FIFO)

This type of resource is an extension of the type infinite capacity with headway inthe sense that an additional headway constraint is imposed on the completion times ofoperations (Mascis et al., 2002). Note that capacity is limited only by the headway con-straints that separate the starting and completion times of two successive operations.The graph depicting two operations on resource mi of type infinite capacity resourcewith FIFO property (ICR+FIFO), is shown in the left part of Figure 6.3 (adjacent re-sources mi−1 and mi+1 are modelled as non-constrained infinite capacity resources).

In contrast to other resource types, two operations, performed on the same resource,are separated with two pairs of alternative arcs. Namely, alternative arc (xr

i ,xsi ) that

assigns precedence to start of operation ori is paired with arc (xs

i+1,xri+1) that gives

precedence to completion of operation osi . In the same way, alternative arc (xs

i ,xri ) is

paired with arc (xri+1,x

si+1) (arcs belonging to one pair are shown in the same color).

That way, both starting times and completion times of two operations are separated.


However, the increase in the number of arcs does not directly contribute to the increasein complexity since the selection of an arc from one pair implies the selection of anarc from the second pair, i.e. two pairs of alternative arcs represent only one decisionvariable (e.g. selection of arc (xs

i ,xri ) from the blue pair implies the selection of arc

(xsi+1,x

ri+1) from the red pair, as shown in the right part of Figure 6.3). Selection of

arcs (one from each pair) that would violate the first in first out (FIFO) constraint wouldresult in a positive length cycle, which is not permitted neither in a TEG (Goverde,2007) nor in an AG (D’Ariano, 2008).

xsi

pri-1

psi

hir,s

his,r

hi+1s,r

hi+1r,s

xri+1

xsi+1

xripri

psi-1xsi-1

xri-1

xsi

pri-1

psi

his,r

hi+1s,r

xri+1

xsi+1

xripri

psi-1xsi-1

xri-1

Figure 6.3: Graph representation of resources with infinite capacity and FIFO con-straint (left) and a possible selection (right)

If M3 ⊂ M is a set of machines of type ICR+FIFO, the starting time of an operationscheduled on those machines can fully be defined by constraints (6.1)-(6.3), (6.6) andthe additional constraints:

xri+1 ≥ xs

i+1 +hs,ri+1−L · kr,s

i+1, ∀i,r,s : mi ∈M3, tr, ts ∈ Ti (6.7)

kr,si = kr,s

i+1, ∀i,r,s : mi ∈M3, tr, ts ∈ Ti. (6.8)

Finite capacity resources (B)

The most restrictive resource type allows only one operation to be processed at thesame time. Figure 6.4 shows that an operation that is processed second, can be initiatedonly after the preceding operation has been completed and the required headway timehas passed.

xi,r

xi,s

pi,r

pi,s

hir,s

his,r

xi+1,r

xi+1,s

xi-1,r

xi-1,s

pi-1,r

pi-1,s

xi,r

xi,s

pi,r

pi,s

his,r

xi+1,r

xi+1,s

xi-1,r

xi-1,s

pi-1,r

pi-1,s

Figure 6.4: Graph representation of resources with finite capacity (left) and a possibleselection (right)


If we define by M4 ⊂M a set of machines of type B, the starting time of an operationscheduled on those resources can fully be defined by constraints (6.1)–(6.3) and theadditional constraint:

xri ≥ xs

i+1 +hs,ri −L · kr,s

i , ∀i,r,s : mi ∈M4, tr, ts ∈ Ti. (6.9)

6.2.5 Sequence-dependent setup times

Minimum headway times between two trains depend on blocking time diagrams ofboth trains (Hansen & Pachl, 2008). Figure 6.5 shows the AG of an example withthree trains: tr, ts, tq using resource mi (type IC+H) with starting times xr

i , xsi , xq

i ,respectively. In the standard AG model, all alternative arcs coming out of a node haveequal weights, which is suitable for mesoscopic modelling of railway traffic. However,in the macroscopic models, presented in this chapter, this formulation needed to beextended to allow different weights of outgoing alternative arcs from a node. Forexample, hq,r

i (headway between xqi and xr

i ) does not have to be equal to hq,si (headway

between xqi and xs

i ). In that manner, we are able to model minimum headways betweentrains according to the blocking time theory.

his,r

hir,s

xrixsi

xqi

hiq,s

his,q

hir,q

hiq,r

Figure 6.5: Example of sequence-dependent setup times

Kecman, Corman, D’Ariano, and Goverde (2012)presented the models without sequence-dependent setup times. In that approach, the weights of all outgoing headway arcs froma node are equal. They are computed as the maximum of all minimum headway timesbetween the event (modelled by the node) and the conflicting events. In the exam-ple from Figure 6.5, hq,r

i = hq,si = max(hq,r

i ,hq,si ), where hq,r

i , hq,si are weights of arcs

(xqi ,x

ri ) and (xq

i ,xsi ) without sequence-dependent setup times.

A precise modelling of train headways with complex sequence-dependent setup timescomplicates the setting from an algorithmic point of view (Corman, Goverde, & D’Ariano,2009), as discussed in detail in Section 6.5.2.


S1 S2St

S3

OT1 OT2

OT3

T1T2

T3

Figure 6.6: Layout of the illustrative example

6.3 Models examined

6.3.1 Macroscopic models

A description of the four rescheduling models for network-wide traffic managementwill be given in this section. The resources presented in the previous section willbe used to model different infrastructure elements. All macroscopic models assumeunidirectional traffic on double track lines. Bidirectional open track segments (singletrack line segments) are modelled with resource type B under the assumption of lowtraffic volumes over such segments. That approach is conservative because it limitsthe capacity of the line segment to one train at a time which in reality is not the casefor successive trains running in the same direction.

Macroscopic models will be described on an illustrative example shown in Figure 6.6.Infrastructure elements in the example are stations S1, S2 and S3, stop St and opentrack segments OT1, OT2 and OT3. Trains T1 and T2 run from S1 to S2 on open tracksegments OT1 and OT2. Train T1 has a scheduled stop at St. Train T3 runs from S3 toS1 on open track segment OT3. Routes of the three trains T1, T2 and T3 are presentedin Figure 6.6 with arrows of corresponding colours.

Since trains T1 and T2 use the same open track segments, all potential conflicts be-tween them can be characterized as intra-track conflicts. However, conflicts betweenthe inbound route of train T3 and the outbound routes of trains T1 and T2 at station S1are an example of inter-track conflicts.

Figures 6.7, 6.8, 6.10 and 6.11 present the alternative graphs for each described model.Every node is an operation of a train (defined by the colour) on the specified resource.Dummy nodes (0 and n) incorporate timetable constraints in the model.

Fixed arcs are presented in colours that correspond to train colours from Figure 6.6.They are marked by type of operation: run or dwell. Train departure is modelled as astart of operation on the open track resource and train arrival as a start of operation ona timetable point resource. The outgoing fixed arcs from node 0 are weighted by thescheduled departure times (SDT). The incoming fixed arcs to node n are weighted bymodified due dates (MDD) as explained in Section 6.2.2.


dwellS1 OT1 St S2

run rundwellOT2

dwellS1 OT1 St S2

run rundwellOT2

dwellS1

runOT3 S3

n0

SDTS1T1

SDTS1T2

SDTS3T3

MDDStT1

MDDS2T1

MDDS2T2

MDDS1T3

SDTStT1

Figure 6.7: Illustrative example - Model 1

Alternative arcs are shown in dashed lines. For the sake of clarity their weights (mini-mum headway times) are not shown in the figures.

Model 1

This is the simplest macroscopic model considered in this chapter. The AG of theillustrative example modelled by Model 1 is shown in Figure 6.7.

All timetable points are modelled as resources with infinite capacity and no constraints(Section 6.2.4). This black-box approach to modelling stations relies on the assump-tion that the capacity of each station is at all times sufficient to satisfy demand.

Open track segments that connect stations are modelled with resource ICR+H (Section6.2.4). A pair of alternative arcs is added to ensure the time separation between start-ing times of two successive operations on the same open track resource (departures).However, headways between arrivals are not considered in this model and the order ofarrivals is not implied by the order of departures.

Moreover, inter-track conflicts are not included as a constraint in this model which hasa great level of idealization and its use can only be justified with low complexity andshort computation time. Operational constraints considered in this model satisfy therequirements for modelling homogeneous traffic (all trains have equal speeds) on theline. In that case, trains are separated in time at the departure points and the modelassumes fixed running times, thus arrival headways become redundant if trains havethe same running time.

Model 2

We extend the previous model by considering arrival headway time and sequence ofarrivals to a timetable point from the same open track segment. That is achieved bymodelling open track segments with resource type ICR+FIFO (Figure 6.8). This abil-ity to model intra-track conflicts between trains with different speeds on the line resultsin the increased size of AG, since the number of alternative arcs used to model train


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interactions on open track segments has doubled when compared with Model 1. How-ever, the complexity of this model is not directly influenced by the increase of the sizeof the graph as shown in Section 6.2.4.

Model 3

None of the previously presented macroscopic models is able to capture potential inter-track conflicts. Since the two potentially conflicting operations are performed on dif-ferent resources (different open track segments), capacity constraints associated with asingle resource are not able to model these conflicts.

In order to overcome this, we introduce an additional finite capacity resource with pro-cessing time 0. This resource does not have any physical interpretation (we thereforerefer to it as a virtual resource) and its purpose is to separate in time events leading tointer-track conflicts.

If two trains with conflicting routes through a timetable point arrive to (depart from)the timetable point using different open track segments, we add the virtual resource tothe path of each train. An inbound route is represented by an arrival event (the resourceis added between the open track and the timetable point) and an outbound route with adeparture event (the resource is added between the timetable point and the open trackresource). Having an additional resource results in the additional operation (thereforealso a node in the AG) with processing time 0. A pair of alternative arcs is then addedbetween every two nodes that represent events leading to an inter-track conflict, inorder to regulate the precedence relation between the two events.

Figure 6.6 shows an example of potential inter-track conflicts between train T3 andtrains T1 and T2 at station S1. Figure 6.9 shows the resulting incompatibility graph.Events that can lead to conflict and can thus not occur within a specified headway timeare connected by undirected arcs (red for inter-track and black for intra-track conflicts).

The alternative graph for this illustrative example is shown in Figure 6.10. Alternativearcs between virtual resources D1, D2 and A3 are added according to the incompati-bility graph (Figure 6.9), where red pairs represent inter-track conflicts and black pairs


represent intra-track conflicts. For example, a possible inter-track conflict in station S1between T2 and T3 is modelled in the following way. If T2 departs first, T3 can arrive(operation A3 can start) only after T2 has departed (operation D2 has been completed,i.e. operation at resource OT2 of train T2 has started) and corresponding headway timehas passed. Similarly, if T3 arrives first, T2 can depart (operation D2 can start) onlyafter operation at station S1 of train T3 has started and the minimum headway time haspassed. Since the time separation of trains running on the same open track segmentis ensured by the selection of the alternative arcs related to the open track resource,there is no need to separate virtual resources representing D1 and D2 by additionalalternative arcs.

D1

D2 A3

Figure 6.9: Incompatibility graph of illustrative example

Model 4

In this model, we partition the set of timetable points to stations, where overtaking ispossible and stops on open tracks (or other timetable points), with no additional tracksto accommodate overtaking. The important property of the latter group is that theircapacity allows only one operation (dwelling or through ride) at a time per direction.

Stations are modelled with resources type ICR like in the previously described models.Stops are modelled with two resources of type B, one per direction. That way, due tothe properties of this resource type (Section 6.2.4), timetable points where overtaking is

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not possible cannot be occupied by more than one train per direction at the same time.Overtaking is in this model enabled only in stations with sufficient number of tracksand appropriate layout. The alternative graph of the illustrative example is presentedin Figure 6.11.

6.3.2 Mesoscopic model

The mesoscopic model of D’Ariano (2008) is used to evaluate the performance of eachmacroscopic model studied here. This model has been validated and tested on numer-ous case studies. The model incorporates all operational constraints of railway trafficand provides accurate estimations of train movements at the level of block sections andsignals.

6.3.3 Overview of the five models

Table 6.1 summarizes operational constraints which are taken into account in the pre-sented models. A gradual increase in number of considered operational constraintsin the presented sequence from Model 1 to the mesoscopic model (Meso) is visible.Depending on the network and traffic properties such as: capacity of stations, possibil-ities for occurrence of inter-track conflicts and heterogeneity of traffic, the appropriatemodelling approach can be applied.

Another important criterion for selecting the most appropriate model is the size of theresulting graph and the computation time needed to obtain a solution of good qual-ity. The performance of each model in terms of this criterion depends mainly on thenetwork size and the number of trains (as shown in the following sections).

6.4 Test case A: corridor Utrecht - Den BoschComprehensive evaluation of the macroscopic models relies on comparison with themesoscopic model, which requires detailed infrastructure data on the level of blocksections, signals and valid rolling-stock dynamics.


Table 6.1: Operational constraints in models

Model Stations Stops Inter Intra Departurecapacity capacity track conflicts track conflicts headway

Model1 - - - - XModel2 - - - X XModel3 - - X X XModel4 - X X X XMeso X X X X X

6.4.1 Test case settings

All models have been applied to one hour of a timetable for the busy double-trackline between Utrecht (Ut) and Den Bosch (Ht) in the Netherlands. We also consider abranch that leads to station Den Bosch Oost (Hto) and merges with the main corridorin Diezebrug junction (Htda). Track layout of the corridor is presented in Figure 6.12.

Utrecht

Den Bosch Geldermalsen

Zaltbommel LunettenHoutenCulemborg

Diezebrug junct.

Den Boschoost

Figure 6.12: Layout of infrastructure and main stations Sporenplan (2014)

The macroscopic infrastructure layout with all timetable points (stations, stops andjunctions) is presented in the lower part of Figure 6.13. Big circles represent largestations where overtaking is possible (since Ht and Ut are area limits in this study,overtaking can be performed only in Geldermalsen), small circles represent stops onopen track and the red circle in Htda specifies that inter-track route conflicts are possi-ble.

In the periodic hourly timetable (Figure 6.13) there are four pairs (one per direction) ofintercity trains that run between Utrecht and Den Bosch without stopping in intermedi-ate stations. There are also two pairs of regional trains that stop in Zaltbommel (Zbm),Geldermalsen (Gdm), Culemborg (Cl), Houten (Htn), Utrecht Lunetten (Utl) and twopairs between Ut and Gdm (also stop in Cl, Htn, Utl). Trains operating between DenBosch and Htda (junction with a branch toward Nijmegen–Nm) in Figure 6.13 are twopairs of intercity trains and two pairs of regional trains running on the service betweenNijmegen and Den Bosch.


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The scheduled departure and arrival times are given in the timetable for each station.The minimum dwell time is 120 s in large stations Ut, Gdm and Ht and 60 s in stops.

All minimum running times in the macroscopic models are computed by a standardapproach of simulating each train run using the mesoscopic model and summing upminimum running times over the corresponding block sections. Kettner et al. (2003)and Schlechte et al. (2011) used a similar concept.

The minimum headway times are in the mesoscopic model computed according toso-called ’departure on yellow’ concept of blocking time theory (Hansen & Pachl,2008), i.e., a train is allowed to depart as soon as the previous train has released thefirst block section. This reflects the behaviour of local traffic controllers in disturbedconditions. The logic of blocking time theory is implemented in the mesoscopic model.Therefore, interactions between trains along the open track segments are regulated withhigh precision (i.e., a block section can never be occupied by more than one train).

On the other hand, macroscopic rescheduling models need to mimic the behaviourof network traffic controllers and aim to produce a new operational and conflict-freetimetable with minimum deviation from the published timetable. We impose a minimalheadway for open track segments at departure (in all macroscopic models) and arrivalevents (Model 2, 3 and 4). We use the standard approach to compute minimum head-way times by compressing the blocking time diagrams (Hansen & Pachl, 2008). Forcomputing arrival headways and inter-track headways, a two-block separation princi-ple of blocking time theory for conflict-free running was used.


6.4.2 Comprehensive evaluation

The five models were applied to the corridor test case. The solution procedure de-scribed in Section 6.2.2 was used to minimize secondary delay in all models. Thecomplete equivalence of all models is achieved in terms of departure and arrival timesof trains, when they were applied without delays.

In the following subsections the quality of solutions obtained by the macroscopic mod-els will be evaluated by comparisons with the mesoscopic model (reference model).The smaller the differences, in terms of relative orders of trains, between the solutionsobtained using the mesoscopic model and those obtained using a macroscopic model,the better is the performance of the macroscopic model under evaluation. Comparisonsbetween the objective values will be performed only among the macroscopic modelsdue to the different way of computing the minimum headway times in the mesoscopicmodel.

A comprehensive evaluation of the models was performed over 200 delay instances.All trains from the timetable shown in Figure 6.13 are delayed in each instance accord-ing to the Weibull distributions as in Corman et al. (2012b). The maximum primarydelay is 326.80 s and the average primary delay is 30.15 s (both values are averageover all instances). All experiments are performed on a computer with Intel Core i5-520M/2.4 GHz processor and 4 GB memory.

Quantitative analysis

In the quantitative part of evaluation, presented in Table 6.2, the size of the resultingAG for each model is given in number of nodes, number of fixed arcs and number ofalternative pairs (Columns 2–4). We also present the average computation time (CTF)to obtain the first solution using initial heuristics and average computation time (CTB)to compute the best solution or prove optimality for the initial solution (Columns 5–6).Moreover, average (ASD) and maximum (MSD) values of secondary delay over allinstances are presented for each model (Columns 7–8).

Table 6.2: Quantitative assessment of the 5 models

Model Nodes Fixed Alt. CTF CTB ASD MSDarcs pairs (s) (s) (s) (s)

Model1 394 505 558 < 1 < 1 4.17 84.16Model2 394 505 1116 < 1 < 1 6.14 112.00Model3 410 521 1164 < 1 < 1 7.50 118.00Model4 410 521 1636 < 1 < 1 11.05 182.00Meso 1018 1155 2312 < 1 1.20 5.88 119.56

As expected, the size of the graph increases together with the number of operationalconstraints considered in each model. There is a large difference in terms of rationumber of nodes/number of alternative pairs, between Model 1 and the mesoscopic


model on the one side, and Models 2, 3 and 4 on the other. That can be explained bythe fact that Models 2, 3 and 4 employ ICR+FIFO resource type for modelling opentrack segments. Therefore, those models need twice as many pairs of alternative arcsto model train runs along open tracks compared to Model 1 (see Section 6.2.4).

For applications on this relatively small test case all five models show excellent per-formance in terms of computation time to obtain the first as well as the best solution.For the macroscopic models, the solution is produced almost instantaneously (around0.1 s for the best solution in Model 4), whereas the size of the mesoscopic modelcauses a slightly longer computation time to prove the optimal solution. For this set ofinstances, the optimal solution was always found for all models.

The last two columns of Table 6.2 show that the average and maximum secondary delayincrease along with the number of operational constraints taken into account in eachmacroscopic model, meaning that the more realistic models are able to capture moreinteractions between trains and therefore compute more realistic delay propagation(the mesoscopic model is not considered in this analysis due to different computationof minimum headway times).

Comparison of train reordering actions

Reordering trains (changing the order of departures) is a common dispatching actionfor reducing delay propagation. In this section, we will investigate how close are thesolutions of macroscopic models to the solution of the reference mesoscopic model interms of orders of departures. The analysis has been carried out on trains running fromDen Bosch towards Utrecht. There are three checkpoints where the relative order oftrains is determined: through runs in Htda, departure from Gdm and arrival in Ut. Bychecking the orders of through runs in Htda we are able to estimate the effect of consid-ering inter-track conflicts that are possible to occur in the junction Htda. According tothe published timetable, intercity trains are scheduled to overtake slower regional trainsin Gdm. Therefore, checkpoints in Gdm and Ut are used to verify if some macroscopicmodels provide solutions with a different point of overtaking (which in reality is infea-sible). The first three rows of Table 6.3 give the percentage of train sequences (for eachmacroscopic model) that are different from the corresponding sequences produced bythe mesoscopic model, in each check point on the 200 instances. The last row ofthe table shows the percentage of different sequences aggregated over all three checkpoints.

In almost all instances, the solutions of the four macroscopic models suggest identi-cal sequences of departures from Htda as the mesoscopic model. In this checkpoint,differences in operational constraints among models, only to small extent affect theresulting relative order of trains.

By comparing the percentage of different sequences of departures from Gdm and ar-rivals to Ut for each model, it is visible that in a large number of instances, Models 1,2 and 3 allow overtaking between Gdm and Ut (the number of differences at arrival toUt is much smaller than the number of differences at departure from Gdm). In Model


Table 6.3: Difference in orders between the mesoscopic and each macroscopic model.Direction Ht→ Ut

Model 1 Model 2 Model 3 Model 4Through run Htda (%) 1.0 1.0 0.5 0.0Departure from Gdm (%) 33.5 20.0 20.0 2.0Arrival to Ut (%) 4.5 4.0 4.0 2.0Average (%) 13.0 8.3 8.2 1.3

4, the percentage of different sequences is the same in both check points which impliesthat the relative order of trains that depart from Gdm is maintained until Ut. Therefore,we can conclude that Model 4 showed the best performance in terms of feasibility ofsolutions.

This comparison of aggregated differences shows that Model 4 gives solutions closestto the accurate mesoscopic model compared to other macroscopic models. Only 1.3%departure sequences are different on the three checkpoints. Other macroscopic modelsshow greater deviation from solutions provided by the mesoscopic model. This devi-ation percentage is again correlated to the number of operational constraints includedin the models.

6.5 Test case B: Dutch national railway network

The primary purpose of this section is to test the applicability of the macroscopic mod-els presented in Section 6.3 for the management of large and busy networks. Figure6.14 shows the test case of the Dutch national network that represents one of the busiestrailway networks in the world with more than 700 passenger trains per hour operatingduring peak hours.

6.5.1 Description of the tested instances

Input data for the macroscopic models of traffic on the Dutch national network is ob-tained from the macroscopic timetabling tool DONS (Hooghiemstra, 1996), that is ableto generate a periodic hourly timetable on the national level with all scheduled eventtimes in all timetable points (departures and arrivals) and scheduled process times (run-ning and dwell times, connection times and headways) rounded to full minutes. Slacktimes and time reserves are not included in the DONS constraints database, which isused to build the timed event graph. Scheduled headway times are normally used fortimetabling purposes. However, in real-time traffic management, trains are separatedby minimum headway times. Due to unavailability of exact blocking times, the proce-dure of computing minimum headways, explained in Section 6.4 could not be applied.Instead, the norms given in the Dutch network statement (ProRail, 2013) were used.

In order to reduce the size of the problem without losing validity we have computedall strongly connected components in the graph as explained in Goverde (2007). If a


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Figure 6.14: Dutch railway network considered (in black), with main stations

primary delay occurs within a strongly connected component, it cannot propagate toother strongly connected components. Therefore, each strongly connected componentof a TEG corresponds to an autonomous model. The strongly connected componentconsidered in this example comprises the largest part of the Dutch national hourlytimetable and takes into account all trains operating on the lines depicted by black solidlines in Figure 6.14. Thick solid lines represent double and multiple-track segments,whereas the thin solid lines stand for single-track segments.

Table 6.4 reports specific information on the network-wide test case. We take intoaccount all intercity, regional and freight trains (reserved slots).

6.5.2 Comprehensive evaluation

The four macroscopic models have been tested on 200 delay instances in which alltrains were delayed according to Weibull distribution, similar as in Section 6.4.2. Themaximum primary delay is 18.22 min and the average primary delay is 1.41 min (bothvalues are average over all instances).

Table 6.5 reports average results for the network-wide instances on each macroscopic


Table 6.4: Characteristics of the network-wide test case

Instance property NumberStations 298Other timetable points 294Unidirectional open track segments 1119Bidirectional open track segments 324Trains 679Connections 84

model (Column 1): the number of nodes, fixed arcs and alternative pairs (Columns 2–4), the average computation time (CTF) to obtain the first solution using initial heuris-tics (Column 5), average computation time (CTB) to compute the best solution or proveoptimality for the initial solution over all instances (Column 6) and the average (ASD)and maximum (MSD) secondary delays (Columns 7–8). All values in Columns 5–8are average over 200 instances.

Table 6.5: Quantitative assessment of the macroscopic models on test case B

Mode Nodes Fixed Alt. CTF CTB ASD MSDarcs pairs (s) (s) (min) (min)

Model1 17490 20591 16494 9.89 10.04 0.21 4.75Model2 17490 20591 32380 50.79 50.85 0.25 5.17Model3 18968 22069 33956 52.95 53.22 0.29 6.09Model4 18968 22069 42750 89.43 89.57 0.34 6.72

Model 4, the most realistic macroscopic model, captures the largest amount of sec-ondary delays compared to the other macroscopic models. The more precise infor-mation comes with a cost in the alternative graph size and in the computation time ofsolution algorithms.

For Models 1–3, the instances were solvable with the standard setting reported in Sec-tion 6.2.2. For Model 4, the increased complexity defined a set, comprising 32% of theinstances, that are harder to be solved. A solution for those instances could be foundonly by considering additional initial heuristics, as in Corman et al. (2014). However,10% of all instances of Model 4 needed more than 5 minutes to be solved.

The branch and bound algorithm proves optimality for 90%, 84%, 82% and 80% ofinstances of Models 1–4, respectively. For the remaining instances the branch andbound algorithm is not able to compute the optimal solution within the given timelimit of computation.

Finally, the computational cost of implementing sequence-dependent setup times inour models is analysed. There is an increase of 15% (on average over all models) interms of computation time, compared to the case without sequence-dependent setup


times, where conservative, larger minimum headway times were considered (Kecmanet al., 2012). Comparing the results and especially the different feasibility rates in thetwo studies, it appears that the instances tackled in the current work are more challeng-ing. They require longer computation times and the percentage of feasible solutionsis smaller. A possible reason for the identified differences is that the headways con-sidered in the case with sequence-dependent setup times are shorter. The two optionsof alternative ordering of trains are therefore more similar to each other, thus trainsare competing more closely for priority, and there is a higher chance to have multipleoperations requesting the same resource at the same time. In other words, the resultingschedule is more compact, and computing a good quality solution is more challenging.

6.5.3 Network-wide effects of reducing delay propagation

In order to demonstrate the effect of minimization of secondary delays on the nationalnetwork, we compare the delay propagation that arises if the relative order of events(departures and arrivals of all trains) remains as scheduled in the timetable, with thesecondary delays that occur as a result of the solution procedure on Model 4. Themaximum primary delay for a typical instance is 16 min and the average primary delayis 1.24 min. The total secondary delay accumulated in all stations is 3093 min when theorder of events is fixed and 1611 min if secondary delays are minimized by applyingthe solution procedure (Section 6.2.2) on Model 4.

Figure 6.15 presents the maximum secondary delays in major stations in the Nether-lands with fixed order of events (left) and after modifying the order of events as pro-posed by the optimal solution (right). Without rescheduling actions, the maximumsecondary delays are the largest in the busiest part of the network around Amsterdam(Asd) and Utrecht (Ut), as well as in Leiden (Ledn), Apeldoorn (Apd) and Tilburg(Tb). Secondary delays still occur after optimization in the busiest part of the networkbut the network-wide effect of rescheduling actions is clearly visible compared to theleft part of Figure 6.15.

6.6 Conclusions and outlook

The potential further growth of both passenger and freight flows in already busy rail-way networks in western Europe will mostly have to be accommodated over the ex-isting railway infrastructure. This will lead to an increase of capacity utilization, thusreducing reliability and punctuality of railway services. Improvements in traffic man-agement and control have to be made in order to prevent a decrease of traffic reliability.In that context, this contribution leads to an improvement of global delay propagationin case of disturbances.

This chapter presented four models of railway traffic flows at a macroscopic level. Thetrade-off between the level of detail included in each model and the number of con-sidered operational constraints was examined in terms of minimization of secondary


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Figure 6.15: Maximum secondary delays without (left) and with (right) rescheduling

delay and computation time. A comprehensive evaluation was performed on two real-world case studies. We were able to handle very large instances such as the Dutchnational network within short time (less than 90 seconds) even with the most com-plex macroscopic model, which had the best performance with respect to feasibility ofsolutions.

A major contribution of the work presented in this chapter is a modification to themesoscopic alternative graph railway rescheduling model of D’Ariano (2008). Themacroscopic capacity constraints were implemented by choosing the appropriate re-source type for each infrastructure element. By maintaining the structure of the al-ternative graph models, efficient solution procedures developed by D’Ariano, Paccia-relli, and Pranzo (2007) and Corman et al. (2014) became applicable for for solvingrescheduling problems on a network-wide level. Moreover, the transformation of themesoscopic constraints to the macroscopic level was performed with respect to feasi-bility of the resulting models. This was achieved by applying the concept of sequence-dependent setup times for implementing the realistic minimum headway time valuesfor each considered train sequence.

The presented models are applicable for a decision support system for network traf-fic control. The potential for model improvements is in studying other traffic distur-bances and dispatching measures, such as global rerouting. This chapter presentedan MILP formulation of the macroscopic rescheduling problem. A large number ofefficient commercial software packages exist that provide great flexibility for select-ing the objective function. This would enable to examine different passenger oriented


objectives, possibly dependent on the magnitude of disruption. However, D’Ariano,D’Ariano, Sama, and Pacciarelli (2013) presented a study that compared the solutionquality and computation time required by a commercial software and the branch &bound algorithm (D’Ariano, Pacciarelli, & Pranzo, 2007). The commercial softwareunderperformed in both aspects for large instances. Therefore, this direction for futureresearch requires a reduction of problem size in a preprocessing step before applyinga commercial software.


Chapter 7

Conclusions

7.1 Summary of the main findings and contributions

The work presented in this thesis was dedicated to developing the components andbuilding blocks of a model-predictive controller for railway traffic management. Model-predictive control can be used to plug in the tools for traffic control that assume fullknowledge of the future to an online environment. The main components of model-predictive control: monitoring, short-term prediction and optimisation are translated inthe context of real-time management of railway traffic.

These challenging problems from the current traffic control practice have been tackledby numerous contributions from the professional, academic and scientific community.A review of the existing approaches revealed two clear gaps that determined the mainresearch objectives set for this research. The first objective was to develop a system thatmonitors train traffic and predicts its future evolution. The monitoring system needsto keep track of the traffic state. That includes monitoring of train positions, runningtimes, actual delays, headways and route conflicts. Based on the current traffic state inthe network, the evolution of the future traffic state within a certain time horizon needsto be predicted.

The second research objective focused on creating a real-time rescheduling model thatcan produce (near) optimal schedules on the network level. The aim was to create aglobal traffic model that takes into account all interdependencies between trains in thenetwork. Given the predicted traffic state at the end of the rescheduling computationprocedure, the model should provide a solution that minimises the deviation from thereference plan within a short computation time.

This chapter gives a summary of the main findings, and scientific and practical contri-butions of this research. Recommendations for the future research are given in Section7.2.

153


7.1.1 Monitoring and traffic state prediction

The purpose of this research objective was to develop a monitoring and short-termprediction system that can be embedded in an MPC loop, as well as used independentlyto support traffic controllers in supervising and managing traffic in their part of thenetwork. The availability of high-quality traffic realisation data from the Dutch traindescriber system TROTS motivated a data-driven approach. The general idea was toanalyse and quantify the impact that current traffic conditions may have on the processtimes. The future process times were predicted using the actual traffic state informationfrom the monitoring system. In order to include interdependencies between trainsin the predictions, a model was developed that captures the operational constraintsof railway traffic and identifies all route and connection conflicts. The model wascalibrated in real time using process time estimates derived with respect to the actualtraffic conditions. A fast critical path algorithm predicts all event times within theprediction horizon.

Process mining train describer data

The first step in the development of the system for monitoring and traffic state pre-diction was to develop a data mining algorithm that can quickly extract occupancytimes of infrastructure elements, recover train paths and identify route conflicts fromthe train describer log file. The work resulted in a process mining tool implemented inan object-oriented environment applicable for quick processing of large data archivesand real-time data streams. The analysis of the system architecture and data structureof TROTS archives revealed several drawbacks for applications in process discoveryand performance analysis on open track sections. Consequently, several preprocessingsteps have been developed that enable traffic monitoring on open tracks and not justin station areas. Moreover, signal messages have been coupled to section and trainmessages to enable the analysis of train runs on the level of block sections.

The algorithm discovers and keeps track of processes such as train runs on the levelof block sections, dwell times, and headway times between all trains at every infras-tructure element. Moreover, the tool continuously monitors the actual delays, and therealised running and dwell times of all trains. The accuracy of the arrival and departuretime measurements is significantly improved compared to the measurements obtainedby the method currently in use in the Netherlands. The resulting data structure is con-venient for statistical analysis and model calibration in this and other research projects.Hindered train runs are identified and can be filtered out to calibrate the models withconflict-free running times. Finally, the algorithms have been implemented in a toolequipped with a visualisation component that simplifies the analysis of realised or ac-tual traffic conditions.

The applicability of the tool is strongly dependent on the data structure and formatof train describer log archives. The level of information captured by a train describersystem varies depending on the particular infrastructure manager. However, processmining is a generic method that can be applied for discovering processes and extracting

Chapter 7. Conclusions 155

information. In the process mining tool presented in this thesis, a three-level model isimplemented which enables extracting information about processes on a micro-, meso-and macroscopic level.

Predictive modelling of process times

The second step in the development of the monitoring and traffic state prediction sys-tem is to develop predictive models that can derive robust estimates of process times,depending on the current traffic conditions. The process time estimates can be usedfor calibrating traffic prediction models. Having in mind the system requirement fora traffic model that needs to identify and model route conflicts, the estimates of run-ning times were derived on the mesoscopic block section level. The application oftransparent statistical learning methods, such as robust linear regression and tree-basednon-linear methods, resulted in several insights about running times. Domain knowl-edge and hypotheses related to railway traffic were used to define a set of predictorsfor process time estimation. Two approaches were presented. First, a single globalpredictive model was developed that discovers dependency of process times on a set ofpredictors. The second approach relies on a separate model for each train line, blocksection and station.

A set of predictors for running times was determined based on the three months of traindescriber event data from two traffic control areas in the Netherlands. Both linear andtree-based methods reveal a weak dependence of running times on departure delays.Furthermore, the small variation of running times is explained to a great extent bythe block length and position with respect to the previous and following scheduledstops. Observations for a particular train line and block section confirmed that no cleardistinction can be made between the running times of delayed and punctual trains. Theheadway time passed since the preceding train run turned out to have an impact ontrain running time even for conflict-free train runs.

The predictive modelling of dwell times required close attention due to the high varia-tion of dwell times observed in the training data set. The arrival delay and scheduleddwell time turned out to be the strongest predictors of dwell times especially in largestations. A statistical analysis of dwell times of a particular train line revealed that thedwell times of delayed trains are responsive to peak-hour variations. Moreover, theanalysis of coefficients and intercept after applying robust linear regression revealedthe magnitude of the inevitable error that occurs when the dwell times are estimatedusing only train describer data. A high percentage of variance of dwell times can beexplained using the developed predictive models. However, the difficulty to predictthe dwell times of local trains still represents the major source of inaccuracy for theprediction model. For more accurate estimates, other data sources than train describers(e.g. on-board units) need to be used.

A high predictive power of the presented models was established by cross-validatingthe models and applying them on an independent test set. Robust linear regressiongave insight into the predictive quality of each individual explanatory variable but the


accuracy of this model is still insufficient for real-time applications. The tree-basedmethods managed to capture the non-linear relationship between the response and ex-planatory variables. The prediction accuracy was significantly increased especially af-ter applying the random forests method. The large set of available data was exploitedto derive the local models that on average outperform the global model in terms ofaccuracy. The limitation of this approach is that a test set needs to be related to thesame infrastructure area and train lines as the training set.

Real-time prediction of train event times

The final step for developing the monitoring and traffic state prediction system wasto create a traffic model. The model is built and updated based on the traffic controlactions and current train positions reported by the train describer system. The modeltopology reflects all capacity and synchronisation interdependencies between trains.The calibration is performed in real time with the robust estimators of process times.With each update of train positions, an efficient prediction algorithm visits all arcs inthe graph, retrieves their weights depending on the actual traffic condition, and predictsthe realisation times of all signal and station events within the prediction horizon. Themesoscopic character of the graph allows identification of all route and connectionconflicts.

An improvement of the prediction model was achieved by accurate modelling of thetrain dynamics for the trains hindered by route conflicts. The process mining toolwas used to filter out all route conflicts from the training data set. The time lossdue to braking, running at lower speed, waiting in front of the signal at danger, andre-acceleration was determined. Moreover, a robust statistical model established andquantified a strong correlation between the time loss and conflict duration. For everypredicted route conflict, the corresponding running times of the hindered trains canbe adjusted to take into account the expected time loss. The tool has been furtherextended with an online adaptive component that keeps track of the realised runningtimes of trains in real time. The trains with running times that deviate from their ro-bust estimates in a certain pattern are identified and downstream estimates are adaptedto reduce the expected prediction error. This can be used to identify malfunctioningtrains, peculiar driving styles or trains that significantly differ from the trains used inthe training set, with respect to dynamic properties.

The prediction accuracy was validated against data from the test set. Prediction hori-zons of different lengths were examined and a significant decrease of prediction errorswas revealed for horizons shorter than 30 minutes. An average prediction error smallerthan one minute was obtained even for a prediction horizon of two hours. This is asignificant improvement compared to the current practice or the approaches describedin the literature.

The applicability and the quality of results of the presented approach depend signifi-cantly on the availability and quality of data for model calibration as well as the fre-quency and spacial resolution of train position updates. For practical applications a


high quality data sources that provide frequent and accurate updates on train positionsare required. At the moment, the presented results after the application of the methodon the Dutch train describer event data indicate a direct applicability of the proposedapproach in practice on the Dutch national network.

7.1.2 Network-wide traffic rescheduling

The second research objective in this thesis was directed at real-time rescheduling forlarge networks with dense traffic and many interdependencies between trains. Opera-tional constraints of railway traffic were translated to the macroscopic level where theonly events are arrivals and departures in stations. The traffic was modelled by meansof alternative graphs which enabled the implementation of dispatching actions in themodel. Four macroscopic models were created, each with a different number of oper-ational constraints included. The impact of including an additional constraint on themodel complexity and feasibility of produced solutions was analysed.

The models were validated using an accurate mesoscopic model on a case study ofa single corridor. The feasibility of solutions produced by the macroscopic modelsturned out to be strongly correlated with the number of included operational con-straints. More realistic models produced a larger number of solutions that were equiv-alent to the reference obtained by using the detailed model. A large case study of onepeak-hour of the Dutch national timetable was used to demonstrate the applicabilityof the models for real-time applications with respect to the computation time requiredto produce a solution. Tackling a problem of such size would be infeasible with theexisting mesoscopic model. The expected positive correlation between the number ofconsidered constraints and the computation time was confirmed. Even the most com-plex considered macroscopic model was able to produce optimal solutions in less than90 seconds which shows its suitability for practical applications.

In the context of online application and integration with the predictive model, thereare several constraints for the presented macroscopic rescheduling models. The arcweights in the models were fixed and the model assumes full knowledge of future trainmovements during the prediction horizon. Therefore, the process time estimates areindependent of the actual traffic condition. However, different solutions may causedifferent values of delays and headway times which in the current models has no im-pact on the process times. This limitation is related to the solution procedure used tocompute the optimal schedule that does not support dynamic arc weight computation.

The solution procedure (D’Ariano, Pacciarelli, & Pranzo, 2007) minimises the max-imum consecutive delay. However, the objectives for rescheduling in the context ofnetwork-wide traffic control may differ depending on the magnitude of disruption andthe condition of traffic on the network. In this thesis an alternative MILP formulationof the macroscopic alternative graph model was given that enables applications of thegeneric MILP solvers and heuristics that provide greater flexibility in choosing the ap-propriate objective function. This enables implementation of the passenger oriented


objectives that minimise the passenger delay rather than minimising the maximumsecondary train delays.

7.2 Recommendations for future work

In this section we present three general directions for future work on models for pre-dictive railway traffic management. The first direction should be focused on a furtherimprovement of the presented models. Secondly, we analyse a possible research direc-tion towards the integration of the models. Finally, the challenges and opportunitiesfor practical implementation are discussed.

A possible improvement of the developed system for monitoring and traffic state pre-diction mostly depends on the availability of data from sources other than train de-scriber systems. The data-driven approach for real-time prediction of train trafficturned out to produce stable and accurate predictions of train event times. A furtherimprovement of the model accuracy is envisaged through a more detailed modelling ofdwell times. Additional data on the station design and train length are required in orderto determine the exact stopping position of each train. This can result in a significantreduction of the error for registering the exact arrival and departure times. Moreover,detailed train event recorder data could enable accurate modelling of separate subpro-cesses of dwell times. Finally, the recent trend of migration from passenger tickets tosmart cards in the Netherlands Railways opens a possibility for computing estimates ofthe number of passengers even in real time, provided that almost all passengers use thelatter (Van der Huurk, Kroon, Maroti, & Vervest, 2012). The use of accurate passengercounts may result in increased accuracy of dwell time estimation.

Further work on improving the presented macroscopic models for real-time reschedul-ing in large networks should be dedicated to speeding-up the solution procedure. Apotential method to increase the computation speed is to investigate the performanceof advanced metaheuristics that quickly provide feasible solutions of good quality al-beit with no guarantee of optimality. Furthermore, the presented MILP formulationenables the application of commercial software packages that offer great flexibility forchoosing the objective function. However, in order to exploit the benefits of flexibilityof commercial software, the problem size needs to be reduced. A possible algorithmicway to to that is by reducing the problem size in a preprocessing step. A heuristiccan be developed that may reduce the graph size by limiting the number of alternativereordering options to the most probable set. A similar approach, based on stochasticmodelling, has been implemented by Acuna-Agost et al. (2011) on a mesoscopic level.

An important aspect for the future research on this topic is the integration of the pre-sented models. The impact of uncertainty on the feasibility of solutions producedby a rescheduling system could be significantly decreased by means of a more com-prehensive prediction system, similar to the one presented in this thesis. One wayfor integrating the models into an online process would be by plugging them into amodel-predictive control loop. In an laboratory environment this requires the use of


a microscopic simulation tool that would simulate the real-time operation and enablethe implementation of the rescheduling decisions. Another possible direction is to cre-ate a single integrated system that supports a dynamic, time-dependent computation ofprocess times in the optimisation phase.

Integration of the monitoring and traffic state prediction with an advanced driver advi-sory system is also a possible direction for future work. Accurate predictions of routeconflicts could be used to compute optimal train trajectories that would prevent a con-flict or minimise its consequences related to the waiting time and energy consumption.An interesting challenge in this aspect would be to investigate the mutual impact of thetwo systems. In particular, it is important to analyse how the future predictions are af-fected by the driver advisory system. The reaction of the driver and compliance to thegiven advice need to be considered in a closed-loop regime between the two systems.

Finally, we focus on the practical implementation of the described models. The mon-itoring and traffic state prediction systems have been developed based on the data for-mat of the train describer system TROTS. This system is currently in use for trackingtrain positions across the Netherlands by the infrastructure manager ProRail and pro-vides data of sufficient quality. Thus the presented tools are practically applicable ina straightforward procedure by plugging the system to a live data stream. Moreover,having in mind the constant increase of the quality and availability of the traffic data inmany railway companies, there are promising prospects for the general applicability ofthe data-driven approach for monitoring and traffic state prediction on other networks.

The potential practical application of the rescheduling model depends on the infras-tructure managers which are still reluctant to applying computer aided reschedulingsystems even as a decision support to traffic controllers. The presented models couldprovide fast and reliable support for network traffic controllers for example at the net-work control centre such as the OCCR in the Netherlands. It contains a centralisedinformation system that can provide live data feed to the rescheduling system and dis-tribute the solutions to the corresponding local centres that need to implement them.A technical requirement for application of the presented models is the availability of acontinuous and accurate estimate of the traffic state over the whole network that couldserve as an input for the rescheduling process. That implies the necessity to integratethe monitoring and prediction systems from the multiple local traffic control centres.It is highly recommended to implement an advanced monitoring and traffic predictionsystem, such as the one presented in this thesis, to the live data feed in order to ob-tain reliable predictions of route-conflicts, arrival times, and have a valid input to arescheduling system.


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Acronyms

AG alternative graph.

ARI Automatische Rijweginstelling.

CSV comma separated values.

DAG directed acyclic graph.

DCSC Delft Centre for Systems and Control.

DFS depth-first search.

DONS Design of Network Schedules.

DUT Delft University of Technology.

FCFS first come first served.

FIFO first in first out.

GPS Global Positioning System.

GSM-R Global System for Mobile Communications-Railway.

GUI graphical user interface.

ICR infinite capacity resource.

ICR+FIFO infinite capacity resource with FIFO property.

ICR+H infinite capacity resource with headway.

ILP integer linear programming.

IM infrastructure manager.

LTS least trimmed squares.

MAE mean absolute error.

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MILP mixed integer linear programming.

MPC model-predictive control.

MSE mean squared error.

NS Netherlands Railways.

OCCR Operational Control Centre Rail.

OOB out of bag.

PESP periodic event scheduling problem.

PRL Procesleiding.

RCS Rail Control System.

ROMA Railway traffic Optimization by Means of Alternative Graphs.

RSE residual standard error.

RSS residual sum of squares.

STEG Styrning av Tag genom Elektronisk Graf.

T&P Department of Transport and Planning.

TEG timed event graph.

TNV Treinnummer Volgsysteem.

TOC train operating company.

TROTS Train Tracking and Observation System.

TSS total sum of squares.

VKL Verkeersleiding.

Summary

This thesis is focused on predictive management of railway traffic in real time. Themain research topics include: (1) monitoring and real-time traffic prediction and (2)rescheduling in large and heavily utilised networks.

Railway traffic control is typically hierarchically structured into a local and a global(network) level. Local traffic control (signallers and/or dispatchers) has the task toperform all safety related actions, set routes for trains, predict and solve conflicts, andmanage processes that take place on the designated part of infrastructure. A train typi-cally crosses multiple traffic control areas. The global level (regional or network con-trollers) comprises the supervision of the state of traffic on the network level, detectionof deviations from the timetable, resolution of conflicts affecting the overall networkperformance, handling failures and events that may have big impact on performanceindicators, etc.

Signallers in general do not have any intelligent decision support system to estimate theexpected running times. Delay propagation could be prevented or reduced if the trafficwas managed proactively, i.e., if controllers had a reliable prediction of a route andconnection conflict with a possibility to prevent it. The current practice in operationalcontrol of disruptions and delays still relies predominantly on the predetermined rulesand experience and skills of personnel. Neither local nor network traffic controllershave an efficient supporting tool to make dispatching decisions, predict their effect andevaluate them.

A possible way to model and optimize railway traffic control is through a closed-loopcontrol approach, called model-predictive control (MPC). This thesis presents an MPCframework and railway traffic control models that can be integrated in the closed con-trol loop. Trains are operated according to a timetable and a daily process plan. Due toinevitable disturbances and deviations from the planned schedule, train runs need to becontinuously monitored. Monitoring provides the actual traffic state that can be usedto predict the future evolution of traffic on the network. A predictive traffic model isthus required to continuously provide the local control level with the information aboutthe expected traffic conditions. It can further be used to evaluate the impact of trafficcontrol actions. In case of longer disruptions that may affect the traffic in a wider area,network traffic controllers can use the prediction model to optimise traffic on the net-work, compute network-optimal timetable updates and transmit them as a reference to

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the local level. That way all traffic control actions on the local level will match withthe network-optimal traffic state.

Monitoring and traffic state prediction

A way to overcome the drawbacks of the current practice and the existing tools formonitoring and short-term traffic prediction emerged with the availability of historicaltraffic realisation data. This thesis shows how a real-time stream of raw train describerdata from the Dutch TROTS system can be processed in a way that extracts the actualtraffic condition in the network: train positions, accurate estimates of current delaysand realised running and dwell times. Moreover, archives of event logs are used tolearn how trains behave depending on the traffic conditions. The variability of pro-cess times is explained by isolating the factors with high impact on the correspondingprocess time. Estimates of future process times depend on the current or predictedvalues of explanatory variables. Therefore, predictions incorporate the empirically de-termined variation of process times due to e.g. driving style, passenger behaviour orpeak hours. The final step for developing the monitoring and traffic state predictionsystem was to create a traffic model. The model is built and updated based on thetraffic control actions and current train positions reported by the train describer sys-tem. The model topology reflects all capacity and synchronisation interdependenciesbetween trains. The calibration is performed in real time with the robust estimates ofprocess times.

The monitoring tool is based on the process mining algorithm that discovers and keepstrack of processes such as train runs on the level of block sections, dwell times, andheadway times between all trains at every infrastructure element. Moreover, the toolcontinuously monitors the actual delays, and the realised running and dwell times ofall trains. The accuracy of the arrival and departure time measurements is significantlyimproved compared to the current practice. The resulting data structure is convenientfor statistical analysis, calibration and validation against real-life data in this and otherresearch projects. Hindered train runs are identified and can be filtered out to calibratethe models with conflict-free running times. Finally, the algorithms have been imple-mented in a tool equipped with a graphical user interface and a visualisation componentthat simplifies the analysis of the realised or actual traffic conditions.

The running times are estimated based on the correlation and dependence on explana-tory variables. Both linear and tree-based methods reveal a weak dependence of run-ning times on departure delays. Furthermore, the small variation of running times wasexplained to a great extent by the block length and position with respect to the previ-ous and following scheduled stops. Observations for a particular train line and blocksection confirmed that no clear distinction can be made between the running times ofdelayed and punctual trains. The headway time passed since the preceding train runturned out to have an impact on train running times even for conflict-free train runs.

The predictive modelling of dwell times required close attention due to the high varia-tion of dwell times observed in the training data set. The arrival delay and scheduled

Summary 181

dwell time turned out to be the strongest predictors of dwell times especially in largestations. The statistical analysis of dwell times of a particular train line revealed thatthe dwell times of delayed trains are responsive to peak-hour variations. Moreover, theanalysis of coefficients and intercept after applying robust linear regression revealedthe magnitude of the inevitable error that occurs when the dwell times are estimatedusing only train describer data. A high percentage of variance of dwell times can beexplained using the developed predictive models. However, the difficulty to predictthe dwell times of local trains still represents the major source of inaccuracy for theprediction model. For more accurate estimates, other data sources than train describers(e.g. on-board units) need to be used.

A graph-based traffic model has been developed that accurately represents operationalconstraints of railway traffic. With each update of train positions, an efficient pre-diction algorithm visits all arcs in the graph, retrieves their weights depending on theactual traffic condition, and predicts the realisation times of all signal and station eventswithin the prediction horizon. The high level of detail in the model allows the iden-tification of all route and connection conflicts. The prediction accuracy was validatedagainst the actual realisation data from the test set. The prediction horizons of differ-ent lengths were examined and a significant decrease of prediction errors was revealedfor horizons shorter than 30 minutes. An average prediction error smaller than oneminute was obtained even for the prediction horizon of two hours. That is a signifi-cant improvement compared to the current practice or the approaches described in theliterature. A further improvement of the prediction accuracy was achieved by accu-rate modelling of the train dynamics for the trains hindered by route conflicts. If aroute conflict is predicted, the corresponding running times of the hindered train canbe adjusted to take into account the expected time loss. The tool has been furtherextended with an online adaptive component that keeps track of the realised runningtimes of trains in real time. The trains with running times that deviate from their ro-bust estimates in a certain pattern are identified and downstream estimates are adaptedto reduce the expected prediction error. This can be used to identify malfunctioningtrains, peculiar driving styles or trains that significantly differ from the trains used inthe training set, with respect to dynamic properties.

Macroscopic models for network-wide rescheduling

The second research objective in this thesis is to develop a decision support system fornetwork traffic controllers that can be integrated in an MPC loop. The system is basedon a macroscopic rescheduling model that can be applied for optimal control of trafficin large and heavily utilised networks. Alternative graphs are used as a modelling toolfor traffic rescheduling. This requires a definition of different resource types to modelthe macroscopic constraints of railway traffic. A series of models, each with a differentlevel of granularity, is presented with the purpose to search for a compromise betweenprecise modelling of railway capacity constraints and a reasonable time to computethe alternative solutions for the large scale railway traffic management instances. Asuitable choice of the granularity of the macroscopic model is determined that reflects


the balance between limiting the problem complexity and maintaining the feasibilityof produced solutions.

The macroscopic models are validated using an accurate detailed model on a casestudy of a single corridor. Furthermore, a large case study of one peak-hour of theDutch national timetable is used to demonstrate the applicability of the models for real-time applications with respect to the computation time required to produce a solution.The expected positive correlation between the number of considered constraints andthe computation time was confirmed. However, even the most complex consideredmodel was able to produce optimal solutions in less than 90 seconds which shows itssuitability for practical applications.

Samenvatting

Dit proefschrift richt zich op voorspellend railverkeersmanagement. De belangrijksteonderzoeksthema’s zijn: (1) monitoring en real-time voorspelling van het treinverkeeren (2) de herplanning bij vertragingen in grootschalige en zwaar belaste netwerken.

Railverkeersleiding is meestal hierarchisch gestructureerd in een lokaal en een globaal(netwerk) niveau. De lokale verkeersleiding (treindienstleiders) heeft de taak om alleveiligheid gerelateerde acties uit te voeren, rijwegen voor treinen in te stellen, conflic-ten te voorspelen en op te lossen, en processen die plaats vinden op het aangegeven deelvan de infrastructuur te beheersen. Een trein overspant meestal meerdere verkeerslei-dinggebieden. Het globale verkeersleidingniveau (regionale en netwerkverkeerleiders)omvat het toezicht op de toestand van het verkeer op netwerkniveau, de detectie vanafwijkingen van de dienstregeling, het oplossen van conflicten, en de afhandeling vanstoringen en gebeurtenissen die grote invloed op het railvervoer hebben.

Treindienstleiders hebben in het algemeen geen intelligent beslissingsondersteunendsysteem beschikbaar om de verwachte rijtijden van treinen in te schatten. Vertragings-voortplanting zou voorkomen of verminderd kunnen worden als het verkeer proactiefwerd beheerd, d.w.z., als verkeerleiders een betrouwbare voorspelling zouden heb-ben van conflicterende treinbewegingen en daarbij de mogelijkheid om het conflict tevoorkomen. De huidige praktijk in de operationele beheersing van storingen en vertra-gingen is nog steeds voornamelijk gebaseerd op vooraf bepaalde regels en de ervaringen vaardigheden van het personeel. Noch lokale noch netwerkverkeersleiders hebbeneen efficient ondersteunend hulpmiddel om de bijstuurmaatregelen uit te voeren, huneffect te voorspellen en deze te evalueren.

Een mogelijke manier om de verkeersmanagement te modelleren en optimaliseren isdoor middel van een gesloten-lus besturingssysteem, de zogenaamde model-gebaseerdevoorspellende regelaar (MPC, model-based predictive control). Dit proefschrift pre-senteert een MPC kader en verkeersmanagementmodellen die in een gesloten lus kun-nen worden geıntegreerd. Treinen worden bediend volgens een tijdschema en een da-gelijks proces plan. Door onvermijdelijke storingen en afwijkingen van het geplandetijdschema moeten de treinritten voortdurend worden bewaakt. De monitoring levertde actuele verkeerstoestand die gebruikt kan worden om de toekomstige ontwikkelingvan het treinverkeer op het netwerk te voorspellen. Een voorspellend verkeersmodelis dus noodzakelijk om het lokaal besturingsniveau continu de informatie te leveren

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over de verwachte verkeerssituatie. Het kan verder gebruikt worden om de impactvan mogelijke beslissingen van de verkeersleiding te evalueren. Bij langere storin-gen die het verkeer in een grotere regio beınvloeden, kan de netwerkverkeersleidinghet voorspellingsmodel gebruiken om het verkeer op het netwerk te optimaliseren, denetwerk-optimale dienstregeling te actualiseren, en deze als nieuw plan naar het lo-kale niveau te sturen. Op die manier zullen alle acties van treindienstleiders op lokaalniveau overeenkomen met de netwerk-optimale toestand.

Monitoring en voorspelling verkeerstoestand

Een manier om de beperkingen van de huidige praktijk en bestaande tools voor moni-toring en verkeersvoorspelling te overbruggen wordt mogelijk door de beschikbaarheidvan historische verkeersgegevens. Dit proefschrift laat zien hoe een real-time stroomvan onbewerkte gegevens uit het Nederlandse treinnummervolgsysteem TROTS ver-werkt kan worden om de actuele verkeerstoestand in het netwerk te tonen: actueletreinposities, nauwkeurige schattingen van de actuele vertragingen en de gerealiseerderij- en halteertijden. Bovendien worden de archieven van logbestanden van gebeur-tenissen gebruikt om te leren hoe treinen zich afhankelijk van de verkeerssituatie ge-dragen. De variabiliteit van procestijden wordt verklaard door factoren met een hogeimpact op het desbetreffende procestijd te isoleren. Schattingen van toekomstige pro-cestijden zijn afhankelijk van de huidige of voorspelde waarden van verklarende va-riabelen. Daarvoor bevatten voorspellingen de empirisch bepaalde variatie van pro-cestijden als gevolg van bijvoorbeeld rijstijl, reizigersgedrag of spitstijden. De laatstestap voor de ontwikkeling van het monitoring en verkeersvoorspellingssysteem is hetcreeren van een verkeersmodel. Het model wordt gebouwd en bijgewerkt op basisvan de bijstuurmaatregelen van de verkeersleiding en de actuele positie van de treinendie door het treinnummervolgsysteem gemeld worden. De modeltopologie weerspie-gelt alle onderlinge capaciteit- en synchronisatie afhankelijkheden tussen treinen. Dekalibratie wordt uitgevoerd in real-time met robuuste schattingen van procestijden.

Het monitoring instrument is gebaseerd op een process mining algoritme dat de pro-cestijden zoals rijtijd op het niveau van bloksecties, halteertijden op stations, en op-volgtijden tussen treinen op alle infrastructuurelementen, opzoekt en bijhoudt. Bo-vendien controleert het instrument continu de werkelijke vertragingen en de gereali-seerde rij- en halteertijden van alle treinen. De nauwkeurigheid van de metingen vande aankomst- en vertrektijd is aanzienlijk verbeterd ten opzichte van de huidige prak-tijk. De resulterende datastructuur is handig voor statistische analyse, kalibratie en va-lidatie van real-life data in deze en andere onderzoeksprojecten. Gehinderde treinrittenworden geıdentificeerd en kunnen gefilterd worden om de modellen met conflictvrijerijtijden te kalibreren. Ten slotte zijn de algoritmes geımplementeerd in een Matlabtool, uitgerust met een grafische gebruikersinterface en een visualisatie component,dat de analyse van de gerealiseerde verkeerssituatie vereenvoudigt.

De rijtijden zijn geschat op basis van de correlatie en de afhankelijkheden van de ver-klarende variabelen voor een specifieke casus. Zowel lineaire als beslisboom-gebaseerdemethoden tonen voor rijtijden een zwakke afhankelijkheid van vertrekvertragingen. De

Samenvatting 185

kleine variatie in rijtijden wordt grotendeels verklaard door de bloklengten en de posi-tie ten opzichte van de vorige en volgende geplande haltes. Observaties van een speci-fieke treinserie en bloksectie bevestigen dat er geen duidelijk onderscheid gemaakt kanworden tussen de rijtijden van vertraagde en van stipte treinen. De opvolgtijd vanaf devorige treinrit blijkt impact op de treinrijtijd te hebben, zelfs voor conflictvrije treinrit-ten.

Het voorspellingsmodel voor halteertijden vereist grote aandacht vanwege de hoge va-riatie van halteertijden waargenomen in de training dataset. De aankomstvertragingen geplande halteertijd bleken de sterkste voorspellers van halteertijden te zijn, vooralin grote stations. De statistische analyse van de halteertijden van een bepaalde treintoonden dat de halteertijden van vertraagde treinen reageren op de spitsurenvariaties.De analyse van de geschatte coefficienten van robuuste lineaire regressie toonde deomvang van de onvermijdelijke fout die optreedt wanneer de halteertijden alleen metgegevens van het treinnummervolgsysteem geschat worden. Een hoog percentage vanhalteertijdvariatie kan verklaard worden met de ontwikkelde voorspellende modellen.De moeilijkheid om de halteertijden van lokale treinen te voorspellen vormt nog steedsde belangrijkste bron van onnauwkeurigheid voor het voorspellingsmodel. Voor meernauwkeurige schattingen zouden andere gegevensbronnen dan het treinnummervolg-systeem (bv. on-board units) moeten worden gebruikt.

Een graaf-gebaseerd verkeersmodel is ontwikkeld dat nauwkeurig operationele beper-kingen van het spoorverkeer vertegenwoordigt. Met elke update van de positie van detreinen doorzoekt een efficiente voorspellingsalgoritme alle takken in de graaf, bepaalthet gewicht afhankelijk van de actuele verkeerstoestand en voorspelt de realisatietijdenvan alle sein- en spoorsectiegebeurtenissen binnen de voorspelde tijdhorizon. Het hogedetailniveau van het model maakt de identificatie van alle conflicten op rijwegen enaansluitingen mogelijk. De nauwkeurigheid van de voorspellingen werd gevalideerdtegen de daadwerkelijk gerealiseerde gegevens uit de test set. De voorspellingshori-zon voor verschillende lengtes werden onderzocht en een significante daling van devoorspellingsfouten werd aangetoond voor ene horizon korter dan 30 minuten. Zelfsvoor de voorspellingsperiode van twee uren werd een gemiddelde voorspellingsfoutkleiner dan een minuut verkregen. Dit is een aanzienlijke verbetering ten opzichte vande huidige praktijk of de methoden beschreven in wetenschappelijke literatuur.

Een verdere verbetering van de nauwkeurigheid werd bereikt door accurate model-lering van de dynamiek van de treinen, die gehinderd worden door rijwegconflicten.Als een rijwegconflict wordt voorspeld, kan de rijtijd van de gehinderde trein wordenaangepast om rekening te houden met het verwachte tijdverlies. Het model is ver-der uitgebreid met een online adaptieve component die de gerealiseerde rijtijden vantreinen in real-time bijhoudt. De treinen met rijtijden die afwijken van hun robuusteschattingen in een bepaald patroon worden geıdentificeerd en schattingen stroomaf-waarts worden aangepast om de verwachte voorspellingsfout te verminderen. Dit kangebruikt worden voor identificatie van defecte treinen, eigenaardige rijstijl, of anderetreinen die aanzienlijk verschillen van de treinen in de training set met betrekking tot


de dynamische eigenschappen.

Macroscopische modellen voor herplanning in grootschalige netwerken

Het tweede doel van het onderzoek in dit proefschrift is de ontwikkeling van een be-slissingsondersteunend systeem voor de netwerkverkeersleiding dat in een MPC-lusgentegreerd kan worden. Het systeem is gebaseerd op een macroscopisch railverkeers-model dat toegepast kan worden voor een optimale besturing van het treinverkeer ingrote en zwaar belaste netwerken. Alternative graphs worden gebruikt voor de mo-dellering voor de herplanning van het treinverkeer. Verschillende macroscopische mo-dellen, elk met een verschillend niveau van fijnheid, zijn onderzocht met het doel eencompromis te zoeken tussen nauwkeurige modellering van infrastructurele capaciteits-beperkingen enerzijds en een redelijke rekentijd voor het oplossen van grootschaligeverkeersmanagement situaties anderzijds. Een geschikte keuze van de fijnheid van hetmacroscopische model weerspiegelt het evenwicht tussen de probleemcomplexiteit ende haalbaarheid van geproduceerde oplossingen.

De macroscopische modellen zijn gevalideerd met behulp van een gedetailleerd modelvan een casus van een grote corridor. Daarnaast is een grote casus van een spitsuurvan de Nederlandse nationale dienstregeling gebruikt om de toepasbaarheid van demodellen voor real-time landelijke toepassingen te demonstreren met betrekking totde rekentijd nodig om een oplossing te genereren. De verwachte positieve correlatietussen het aantal beschouwde beperkingen en de rekentijd werd bevestigd. Zelfs hetbeschouwde meest complexe model was in staat om optimale oplossingen te produce-ren in minder dan 90 seconden. Dit toont de geschiktheid van het ontwikkelde modelvoor praktische toepassingen.

About the author

Pavle Kecman was born in Belgrade, Serbia in 1982. Hestudied traffic and transport engineering at the Universityof Belgrade where he obtained his M.Sc. degree in trans-portation engineering in 2008. After spending two years asa research and teaching assistant at the Faculty of Trans-port and Traffic Engineering in Belgrade, in June 2010 hejoined the Department of Transport and Planning, DelftUniversity of Technology, as a Ph.D. candidate. He wasworking on a research project: “Model-predictive rail-way traffic management” sponsored by the Dutch Technol-ogy Foundation STW. After completing his Ph.D. thesis inJune 2014, he started the postdoctoral research as a part of

EU project Capacity4Rail at the Department of Science and Technology, LinkopingUniversity, Sweden. His research interests include railway operations and applicationof data mining and operations research to traffic and transport related problems.

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TRAIL Thesis Series

The TRAIL Thesis Series is a series of the Netherlands TRAIL Research School ontransport, infrastructure and logistics. The following list contains the most recent dis-sertations in the TRAIL Thesis Series. For a complete overview of more than 100 titlessee the TRAIL website: www.rsTRAIL.nl.

Kecman, P., Models for Predictive Railway Traffic Management, T2014/5, October2014, TRAIL Thesis Series, the Netherlands

Davarynejad, M., Deploying Evolutionary Metaheuristics for Global Optimization,T2014/4, June 2014, TRAIL Thesis Series, the Netherlands

Li, J., Characteristics of Chinese Driver Behavior, T2014/3, June 2014, TRAIL ThesisSeries, the Netherlands

Mouter, N., Cost-Benefit Analysis in Practice: A study of the way Cost-Benefit Analysisis perceived by key actors in the Dutch appraisal practice for spatial-infrastructureprojects, T2014/2, June 2014, TRAIL Thesis Series, the Netherlands

Ohazulike, A., Road Pricing mechanism: A game theoretic and multi-level approach,T2014/1, January 2014, TRAIL Thesis Series, the Netherlands

Cranenburgh, S. van, Vacation Travel Behaviour in a Very Different Future, T2013/12,November 2013, TRAIL Thesis Series, the Netherlands

Samsura, D.A.A., Games and the City: Applying game-theoretical approaches to landand property development analysis, T2013/11, November 2013, TRAIL Thesis Series,the Netherlands

Huijts, N., Sustainable Energy Technology Acceptance: A psychological perspective,T2013/10, September 2013, TRAIL Thesis Series, the Netherlands

Zhang, Mo, A Freight Transport Model for Integrated Network, Service, and PolicyDesign, T2013/9, August 2013, TRAIL Thesis Series, the Netherlands

Wijnen, R., Decision Support for Collaborative Airport Planning, T2013/8, April2013, TRAIL Thesis Series, the Netherlands

Wageningen-Kessels, F.L.M. van, Multi-Class Continuum Traffic Flow Models: Anal-ysis and simulation methods, T2013/7, March 2013, TRAIL Thesis Series, the Nether-lands

189


Taneja, P., The Flexible Port, T2013/6, March 2013, TRAIL Thesis Series, the Nether-lands

Yuan, Y., Lagrangian Multi-Class Traffic State Estimation, T2013/5, March 2013,TRAIL Thesis Series, the Netherlands

Schreiter, Th., Vehicle-Class Specific Control of Freeway Traffic, T2013/4, March2013, TRAIL Thesis Series, the Netherlands

Zaerpour, N., Efficient Management of Compact Storage Systems, T2013/3, February2013, TRAIL Thesis Series, the Netherlands

Huibregtse, O.L., Robust Model-Based Optimization of Evacuation Guidance, T2013/2,February 2013, TRAIL Thesis Series, the Netherlands

Fortuijn, L.G.H., Turborotonde en turboplein: ontwerp, capaciteit en veiligheid, T2013/1,January 2013, TRAIL Thesis Series, the Netherlands

Gharehgozli, A.H., Developing New Methods for Efficient Container Stacking Opera-tions, T2012/7, November 2012, TRAIL Thesis Series, the Netherlands

Duin, R. van, Logistics Concept Development in Multi-Actor Environments: Align-ing stakeholders for successful development of public/private logistics systems by in-creased awareness of multi-actor objectives and perceptions, T2012/6, October 2012,TRAIL Thesis Series, the Netherlands

Dicke-Ogenia, M., Psychological Aspects of Travel Information Presentation: A psy-chological and ergonomic view on travellers response to travel information, T2012/5,October 2012, TRAIL Thesis Series, the Netherlands

Wismans, L.J.J., Towards Sustainable Dynamic Traffic Management, T2012/4, Septem-ber 2012, TRAIL Thesis Series, the Netherlands

Hoogendoorn, R.G., Swiftly before the World Collapses: Empirics and Modeling ofLongitudinal Driving Behavior under Adverse Conditions, T2012/3, July 2012, TRAILThesis Series, the Netherlands

Carmona Benitez, R., The Design of a Large Scale Airline Network, T2012/2, June2012, TRAIL Thesis Series, the Netherlands

Schaap, T.W., Driving Behaviour in Unexpected Situations: A study into the effectsof drivers compensation behaviour to safety-critical situations and the effects of men-tal workload, event urgency and task prioritization, T2012/1, February 2012, TRAILThesis Series, the Netherlands

Muizelaar, T.J., Non-recurrent Traffic Situations and Traffic Information: Determiningpreferences and effects on route choice, T2011/16, December 2011, TRAIL ThesisSeries, the Netherlands

Cantarelli, C.C., Cost Overruns in Large-Scale Transportation Infrastructure Projects:A theoretical and empirical exploration for the Netherlands and Worldwide, T2011/15,November 2011, TRAIL Thesis Series, the Netherlands

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Models for Predictive Railway Traffic Management

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