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Capacity planning for railway systemsLeo Kroon Jan 17, 2002
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Conclusions
• Capacity planning at several levels• Relevant resources are:
¶ Infrastructure¶ Rolling stock¶ Personnel¶ . . .
• All relevant resources are scarce• Effective utilization of resources is required• OR models can provide useful support
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Dutch railway quantities
1.000.000 passengers per workday14.000.000.000 passenger kilometers per year5000 timetabled trains per workday
2800 kilometers of tracks380 stations
2650 wagons
3000 train drivers4000 conductors (and assistants)
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050
40
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UtHmlaWdGdCps NwkRtaRtnRtd VtnMda Gdg
21700
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14000
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2800
2000
2800
8800
9700
9700
0
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1700
Hourly Pattern for the track Rotterdam - Utrecht
2800
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4a4b
5a5b
7a7b
8a8b
Zl
Ah
Zl
Ah
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AhEhv Ehv
Zl
Ah
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Asd Asd
NmNmNmNm
Mt
Hdr Hdr
KolnRhn Rhn RhnRhn
Asd
Hlm Hlm
GvcGvc
Gvc GvcGn Es
0 504010 20 30 60
7500 75003500
5600
3500
2000 3000 2000 3000
500 900 1700
5900 5900100
0 504010 20 30 60
11a11b
12a12b
EhvNm Nm
HlmHlm
Mt
HdrHdr
Nm Nm
Gvc GvcGvc GvcGn EsRtd Rtd
1700500 20002000
3000800 3000900
RtdRtd
Rtd Rtd14000
Platform Occupation Chart
for
UtrechtCentral
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Japa
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nje
Dis-punctualiteit in procent
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Tarief in cent per rkm
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Utilization of the infrastructure (%)
Price per pkm in cents (Dfl)Dispunctuality (%)
Source: KoppelingDec 16, 2000
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Capacity aspects (infrastructure)
• Passengers vs. Cargo vs. Maintenance• Significant increase in demand is expected• Stations are a major bottle-neck• # Trains or # Passengers/Tons?• Utilization vs. Robustness
Different kinds of capacity (OptiRail)• Theoretical capacity• Practical capacity• Planned capacity
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Capacity aspects (infrastructure: tracks)
• # Parallel tracks• Heterogeneity of traffic• # Take-over facilities• Safety system (length of blocks)• Energy system (diesel/electric)• Rolling stock characteristics• Rolling stock capacity (per wagon/unit) • Environment (noise)• . . . .
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Capacity aspects (infrastructure: stations)
• # Platforms• # Parallel/simultaneous routes • Platform occupation times (length of return times)• # Shunting movements • # (Cross-platform) connections • Length of platforms• Rail-side vs. City-side• . . . .
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Traditional system
time
A B C D E F
5 trains
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Clustered
time
7 trains
A B C D E F
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A B C D E F
Take-over
time
9 trains
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Homogeneous system
time
A B C D E F
8 trains
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A B C D E F
2 tracks per direction
time
15 trains
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Capacity analysis and utilization
DONS/SIMONE: Feasibility and robustness(dependent on timetable)
Model Huisman: Network of queuing systems(independent of timetable)
OptiRail: Network flow model with discrete resources (independent of timetable)
B & B: Benutten & Bouwen (Utilize & Expand)
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Rolling stock
• In rush hours: Allocation of scarce capacity
• Outside rush hours: Efficiency
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Mat’64 with 2 or 4 wagons
Koploper with 3 or 4 wagons
Double decker with 3 or 4 wagons
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Capacity aspects (Rolling stock)
Increasing demand during last years Additional wagons (units) will be available soon
Rolling stock capacity mainly determined by - available # of wagons (units)- capacity per wagon (unit)- speed of the trains
Available operational rolling stock capacity = (rolling stock capacity) - (maintenance reservation)
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Capacity aspects (Rolling stock)
Required operational capacity mainly determined during the morning rush hours
Allocated capacity per trip => minimally required capacity - shortage
Allocated capacity per trip = # wagons (units) * capacity per wagon (unit)
Maximum train length <= minimum platform length
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Minimally required capacity per trip
• Based on counts by conductors
0
0.05
0.1
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0.25
0.3
0.35
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0.45
15%
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87 9
line 1
line 2
Eight o’clock cross section
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Rolling stock allocation model
Applied to 8 o’clock cross section of all stoptrainsImplemented in ILOG OPL Studio Solved by CPLEX 7.0 on PC (900 MHz, 256 Mb) # variables: 3700# constraints: 9600
Manual solution:Total shortages (2nd class) 4869# trains with shortages 75 (of 188)
Scenarios based on max. # types and subtypes per line:Best solution found: 3958# trains with shortages 71 (of 188)
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0 1Utilization
Wait
ing t
ime
Waiting time vs. Utilization
1cW
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Conclusions
• Capacity planning at several levels• Relevant resources are:
¶ Infrastructure¶ Rolling stock¶ Personnel¶ . . .
• All relevant resources are scarce• Effective utilization of resources is required• OR models can provide useful support
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Conference on Optimization in Public TransportMay 23, 2002, Erasmus University Rotterdam
http://www.few.eur.nl/few/research/ecopt/conference
Airline session:• Jacques Desrosiers GERAD and École des Hautes Études Commericales, Montréal• Gerrit Timmer; ORTEC Consultants and Free University Amsterdam
Railway session:• Paolo Toth; DEIS, University of Bologna, Italy• Leo Kroon; NS Reizigers and ECOPT, Erasmus University Rotterdam
Bus session:• Matteo Fischetti; DEI, University of Padua and Double-Click sas, Italy• Dennis Huisman; ECOPT, Erasmus University Rotterdam