Simulation analysis:

Implementing a roundabout instead of junction with

traffic lights

Group 1 Paul Akinola

Alex Gutu

Ivana Huckova

Hasan Khan

Jozef Knaperek

Marek Kovalcik

Jakub Obetko

Simulation of Complex Computer Networks

Halmstad University

School of IDE

October 2013

Supervisor – Urban Bilstrup

2

Abstract

This paper deals with simulation of a roundabout. The goal is to find out if the roundabout

would be better solution instead of current intersection with traffic lights on Krisitan IVs väg.

This has been done by a computer simulation, where data were generated by random

functions with Poisson or uniform distributions. Pedestrian underpass was assumed instead of

classic zebra crossing in order to ease the complexity of the simulation. Upon examination of

the simulation we found out that estimates for efficiency of roundabout are much more better

than current intersection. These estimates support the idea that roundabout serves its purpose

and should be considered as a very good option when two or more roads under construction

are to be intersected.

3

Contents

Abstract ...................................................................................................................................... 2

1 Introduction ............................................................................................................................. 4

1.1 Methodology .................................................................................................................... 5

2 Problem formulation ............................................................................................................... 7

2.1 Reasons why roundabouts help reduce the likelihood and collisions .............................. 8

2.2 Roundabout Justification .................................................................................................. 9

2.3 Roundabout Rules and Regulations ............................................................................... 10

2.4 Benefits of roundabouts instead of traffic lights. ........................................................... 10

2.5 Objectives and variables ................................................................................................. 11

3 Data collection and analysis .................................................................................................. 13

4 Model development ............................................................................................................... 16

4.1 State diagrams ................................................................................................................ 16

4.2 Physical flowchart .......................................................................................................... 17

4.3 Model design .................................................................................................................. 18

4.4 Model implementation ................................................................................................... 19

5 Model verification and validation ......................................................................................... 20

6 Model experimentation and optimization ............................................................................. 21

7 Simulation results .................................................................................................................. 23

8 Conclusion ............................................................................................................................. 26

References ................................................................................................................................ 27

Appendix A .............................................................................................................................. 28

4

1 Introduction

In the favor of safety, the conflict between two competing traffic movements must be solved

by a traffic control rules and protocols that give one movement priority over the other [7].

When movement or road are busy or congested with traffic, the priority must be interchanged

in some manner or else this can lead to catastrophe or accident [1]. For high volume

roadways, traffic signals provide the most common traffic control regulation in big cities such

as Malmö, Göteborg and Stockholm because of the positive way in which the priority is

alternated. Countryside road is constantly controlled by stop signs [3].

The good road consists of markings and signs that regulate traffic such as vehicle and

human. Road denotes highways, streets, and squares [7]. Road markings such as longitudinal

marking are used as barrier liners and verge markings and as dividing lines between lanes and

transverse marking is used as stop lines, give way lines and pedestrian crossings and others

are lane arrow, symbol text and yellow marking. The Figure 1 below is a typical example of a

modern roundabout system that design to control the traffic jams at Scandinavian I Göteborg,

Sweden.

Figure 1 - An aerial view of a Scandinavian modern circle I Göteborg [13]

Other examples of the large traffic roundabout or circles can be found in Stockholm and

Malmö, while small one lane traffic roundabouts often exist in residential neighbourhoods

such as fig. 3 järnvägslede I Halmstad and Tjärby I Laholm. The roundabout can also

experience traffic jams that occur due to their unprofessional design or different methods exist

to regulate the traffic within a traffic circle. Our aims of proposing traffic circle is to control

the traffic jams during the rush hours at Laholmsvägen - Cristian - Östra Lyckan and it

therefore seem worth to investigate the impart of circle approaches instead of traffic control

system.

The research conducted in Europe, USA and Australia have refined the general

concept of a traffic circle into a form that has gained greater acceptance nationwide. The term

roundabout has generally been used in reference to this improved version and class of the

traffic circle [2], [3], [7].

5

1.1 Methodology

In this project we are focused on deciding, which type of crossing is more efficient for given

circumstances. We chose specific place and the specific type of crossing for applying our

experiments. In order to achieve some results we need to have a model of proposed solution.

It is possible to build physical model of crossing, but that is quite expensive solution for

school project. The best solution to build a model, in present, is to use cheap and effective

computation power in computers. We are going to use quantitative research method called

computer simulation.

Computer simulation is in present widely used method for quantitative research. It is

useful in mathematical modeling, physics, chemistry, biology, etc. Simulation means

execution of systems model with specific parameters. It can be used to explore and gain new

insights into new technology and to estimate the performance of systems, which are too

complex for analytical solutions.

Simulation model can be:

microscopic – model of behavior of each vehicle,

macroscopic – model of behavior of whole traffic system,

deterministic – use single estimates to represent the value of each variable,

stochastic – ranges of values for each variable are used.

There is a number of different simulation methods for traffic simulation available:

Monte Carlo method – one of the earliest methods,

Cellular Automata method – generates randomness from deterministic values,

Discrete event and continuous time simulation.

In our solution we will use discrete event simulation, which creates stochastic model.

Computer simulation in traffic analysis is widely used by most of the simulation projects

in that field. An example can be PVT VISSIM software [15], which is solution for intelligent

simulation of road traffic and traffic crossings. PVT VISSIM is worldwide used microscopic

simulation tool for modeling multimodal traffic flows and provides ideal conditions for

testing different traffic scenarios. This software can be used in following cases:

development planning – model and evaluate the effects of urban development concepts,

capacity analysis – model traffic flows and observe the performance,

public traffic simulation, pedestrian simulation, etc.

Just the first case is usable for our project as we either want to model and evaluate the effects

of our own crossing concept.

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Figure 2 - PVT VISSIM software

Figure 2 shows the simulation of traffic crossing in PTV VISSIM software. The software is

complex and can be used for wide scale of traffic simulations.

We can use this simulation tool to simulate our own concept of crossing. However, this

can be quite expensive, while the software is not freeware. To simulate our concept, we will

use self-made lower level simulation tool. This approach has advantage in the flexibility of

simulation tool. We are able to adjust tool’s parameters and options to precisely match our

simulation requirements. There are few drawbacks either, especially no visualization interface

and more work to do with implementing simulation tool.

7

2 Problem formulation

The project aims is to solve the current problems arising by traffic jams at Laholmsvägen -

Cristian - Östra Lyckan intersection, we will consider a traffic roundabout to be a two-way

circular road with two-way roads meeting the circle at T-junctions. Through this simulator, the

user will be able to get an insight of how traffic is organised, interact with each other. This

document presents technique for identifying appropriate roundabout sites and estimating

roundabout capacity and delay. The design principle is to install roundabout at Laholmsvägen

- Cristian - Östra Lyckan because the previous traffic control doesn’t seem to address the

traffic jams.

For examples, studies of over 100 intersections around the developing nation such as

the USA, Australia and Europe where traffic signals have been replaced with circular

roundabout to reduce the capacity of traffic jams on the roads [5], [6]. This really reduces

accident and waiting time that always caused by a traffic light. Roundabouts result in fewer

steps and lower traffic delays reducing vehicle emissions and fuel consumption. Installation of

roundabout at Laholmsvägen - Cristian - Östra Lyckan allows for landscaping, sculpture and

it eliminate the cluster associated with traffic control boxes, signals, poles and wires.

Figure 3 - Laholmsvägen Intersection

Figure 4 - Järnvägslede roundabout I Halmstad[13]

8

2.1 Reasons why roundabouts help reduce the likelihood and

collisions

I. Low travel speeds

Drivers must slow down and yield to traffic before entering a roundabout. Speeds in the

roundabout are between 15 and 20 miles/ hour. The very few collisions that occur at

roundabouts are typically minor and cause few injuries since they occur at such low speeds

[6], [10], [11].

II. No light to beat

Roundabouts are designed to promote a continuous, circular flow of traffic. Because traffic is

constantly flowing through the intersection, drivers don´t have the incentive to spread out to

try and “beat the light” like they might at a traditional intersection.

III. One way travel

Roads entering a roundabout are gently curved to direct drivers into the intersection and help

them travel counterclockwise around the roundabout.

IV. Reduce delay and improve traffic flow

Roundabouts move traffic through an intersection more quickly and they promote a

continuous flow of traffic. Drivers don´t have to wait for a green light. To build traffic lights

means more environmental impact, the car is standing still and will then accelerate.

V. Less expensive

The cost difference between building a roundabout and a traffic signal is comparable, but

where long-term costs are considered, roundabouts eliminate hardware, maintenance and

electrical costs associated with traffic signals which can cost between 30000sek and 60000sek

per year.

VI. Capacity

Roundabouts are designed to make intersections safer and more efficient for drivers,

pedestrians and cyclists. Roundabouts are also designed to accommodate vehicles of all sizes

including emergency vehicles, buses, farm equipment and semi trucks with trailers.

During rush hour, roundabouts typically carry about 30-50% more vehicles than

similarly sized signalized intersections, because traffic is always moving. During normal

traffic conditions, roundabouts cause almost no delays, whereas a signalized intersection can

cause delays to side streets and left-turning traffic. Since traffic flows continuously,

roundabouts increase traffic capacity and eliminate waiting at stoplights [8], [9], [11], [12].

9

2.2 Roundabout Justification

In the USA, because of the positive way in which the priority is alternated. The low volume

roads are normally controlled by stop signs. “ The basic principle of a traffic circle is to

channelize the vehicle paths to disperse the conflicts that are contested at a conventional

intersection and resolve each one in an appropriate manner”. For example, Dupont circle in

Washington,DC employs a mixture of stop, yield and signal control in addition to weaving

and a grade separation to resolve all of the traffic jams that take place[4],[7].

Figure 5 - Basic Roundabout [7]

The following feature below is the interpretation of the figure. 4 above that explained the

common characteristic of the roundabout:

The traffics entering a circle on all approaches are required to yield to vehicles within

the circulating roadway [2].

A vehicle entering as a subordinate vehicle immediately becomes a priority vehicle

until it exits the roundabout. Some traffic circles are designed with weaving areas to

resolve conflicts between movements [6].

The speed at which a vehicle is able to negotiate the circulating roadway is controlled

by the location of the central island with respect to the alignment of the right entry

curb. For examples

10

Some circles provide a straight path for major traffics while some small movements do not

achieve adequate deflection for speed control because of the small central island diameter

[2],[9].

2.3 Roundabout Rules and Regulations

No parking is allowed on the circulating roadway, parking manoeuvres prevent the

roundabout from operating in a manner consistent with its design.

No pedestrian activities take place on the central island i.e. pedestrians are not

intended to cross the circulating roadway. Some larger traffic circles provide for pedestrian

crossing to, and activities on the central island.

All vehicles circulate counterclockwise, passing to the right of the central island [14].

2.4 Benefits of roundabouts instead of traffic lights.

Improve Safety

Studies have shown that roundabouts are safer than traditional stop sign. Roundabouts

reduced injury crashes by 75 percent at intersections where stop signs or signals were

previously used for traffic control.

Studies by the HIS and Federal Highway Administration have shown that roundabouts

typically achieve:

A 37 percent reduction in overall collisions

A 75 percent reduction in injury collisions

A 90 percent reduction in a pedestrian collision [12]

Figure 6 - comparism between Intersection and Roundabout [12]

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Figure 7 - Reduction in Collisions [12]

2.5 Objectives and variables

The main objective of this study is to answer following questions by the computer simulation

of the roundabout:

Will the roundabout provide more effective traffic flow when compared to the current

situation?

Can the average overall time of crossing the junction be minimized using roundabout?

Can the maximum overall time of crossing the junction be minimized using

roundabout?

This study will use the method of computer simulation to obtain all necessary data to answer

these question with following variables and measures defined:

Decision variables:

The diameter of the roundabout – the actual size of the roundabout will affect the

overall time that a car spends by crossing the junction. It is important to balance the

trade-off between the number of cars in the roundabout in one time and the distance a

car has to traverse.

Speed of the car – the speed has to be appropriate in regard to the size of the

roundabout. The security concern has to be taken into consideration.

Size of the car (slot) – the size of each slot for a car can also influence the overall

diameter of the roundabout. Additionally, smaller slots mean smaller space between

the cars which also decreases security.

Uncontrolled variables:

The traffic pattern – the rate and amount of cars traversing the junction is considered

to be random. The generator for the simulator will use actual values gathered by

observing the real traffic patterns in the junction.

12

Constraints:

Maximum diameter of the roundabout – the diameter of the roundabout is limited,

since the area of the junction is surrounded by buildings. We do not assume that

demolition of buildings is reasonable approach to this study.

Maximum speed of car – the speed of cars is limited even before the junction by

traffic signs and rules. Also the speed of the car in the roundabout is limited by

physical laws.

Maximum size of the car – Although cars can have very different proportions, it

cannot be larger than certain size. Therefore we can assume that all cars will have

delimited length.

Measures:

The average overall time spend by waiting in the queue and traversing the roundabout

– the main measure to define the effectiveness of our solution will be the time a car

has to spend since entering the lane until exiting the roundabout. This measure can be

compared to the same time spent in the current crossing which was obtained by

analyzing and measuring actual data from the junction.

The maximum time spend by waiting in the queue and traversing the roundabout – the

secondary measure will indicate the worst possible case of a car traversing the

roundabout. This value can be also compared to the actual values from the current

situation.

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3 Data collection and analysis

Parameters to be considered for data collection in this stage will be

1. The amount of cars drive through during peak and off-peak hour (per lane)

2. Inter-arrival time of cars (per lane)

3. The amount of time a driver has to wait to cross the road (per lane)

Data can be collected by observing the crossing in different hours physically in this case. To

have a probabilistic idea we can do some statistical math also. Such as Halmstad has 62750

inhabitants and Laholm has 6,150 inhabitants, among them how many percentage moves

across for work, study. Moreover one of the Halmstad popular business park which is called

Eurostop is on the west side of Halmstad. How many people average go there daily. From all

of these data we can have a probabilistic idea how many cars can pass through that crossing.

The data collection was provided by recording the traffic of the analyzed crossing.

Created recordings were analyzed to gather information about the inter-arrival time of cars,

waiting time for the green light and the overall number of cars entering the crossing. Each of

these parameters had to be analyzed per lane since different lanes in the crossing have

different load.

The waiting time for the green light can be used as measure of performance of the

crossing. Higher values of the waiting time mean higher load of the crossing. The main goal

of this project is to propose a solution to minimize these values and thereby solve the current

problems. Since the roundabout does not have any signal lights the waiting time can be

considered as the time required for entering the crossing. Then, it can be easily compared with

the results of the simulation. The effectiveness of proposed solution can be verified by this

comparison.

Information about the inter-arriving time is crucial for creating the data generator for

our simulation. The simulator will gain more exact results when real traffic data will be used

and therefore these results can be compared to the current situation.

The information about overall number of cars entering the crossing is also important

for the traffic generator since the roundabout will have only two lanes in each direction. The

actual crossing has two, three or even four lanes in different direction. The traffic load in these

lanes will have to be merged into two lanes provided by the roundabout.

Number of histograms (one per each lane) was created from the analyzed data to

supply the traffic generator. One example of such a histogram is in Figure 8. The x-axis

represents the inter-arrival time of cars and the y-axis represents actual number of cars per

each inter-arrival time.

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Figure 8 – Histogram of traffic

Further processing of these data was necessary in order to use them as an input for the traffic

generator. Each histogram had to have a specific statistical function assigned. Since there is

no exact method to get the function of a graph, we had to analyze various distribution

functions and their parameters to get the most accurate and most similar graph from the

distribution function. We tried to get the best possible graphs by changing the parameters of

various functions and comparing the results to the required one.

None of the found functions could satisfy the “long-tail” characteristic of our

histograms. Due to this complication we took the mean value of each graph as the most

important parameter and we used it within created distribution functions. Each function

represents the distribution of traffic from the statistical point of view, although these functions

do not exactly represent the collected data.

Eventually two distribution functions were used: Poisson distribution function and

uniform distribution function according to actual data.

The example of the distribution function created is shown in Figure 9.

15

Figure 9 – Distribution of traffic

Distribution functions and their parameters differ for each lane since the load and inter-arrival

time of cars are different. Therefore, distribution function for each lane was assigned its

specific parameter to reflect the actual values. The assignment of function and its parameters

for each lane is shown in Table 1.

Distribution

function Parameter Value λ DIRECTION

Lane 1 POISSON 9,125 EAST to NORTH

Lane 2 POISSON 9,319 EAST to WEST

Lane 3 UNIFORM <2,82> EAST to SOUTH

Lane 4 POISSON 36,417 SOUTH to WEST

Lane 5 POISSON 19,208 SOUTH to NORTH

Lane 6 UNIFORM <7,83> WEST to NORTH

Lane 7 POISSON 8,42 WEST to EAST

Lane 8 POISSON 9,039 SOUTH to EAST

Lane 9 UNIFORM <33,100> NORTH to WEST

Lane 10 PoISSON 24,11 NORTH to SOUTH

Lane 11 UNIFORM <10,71> NORTH to EAST

Lane 12 POISSON 20,72 WEST to SOUTH

Table 1 – Assignment of function and parameters

The graphs of traffic inter-arrival time distributions for all of the lanes are included in

Appendix A.

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4 Model development

4.1 State diagrams

In order to describe the state change approach it is necessary to define additional endogenous

variable classification state variable and introduce the concept of an event. The state variable

representing the current state of a discrete-time system (i.e. digital system) is x(n), where n is

the discrete point at which the system is being evaluated. In our scenario we have states like

when car arrives and wait in the queue, entering the crossing/roundabout etc. We have two

state diagrams, roundabout and crossing. A useful approach for the state change approach is

to represent this as an event graph. Events are represented as nodes and progression from

event to event as arrows

Event list for a roundabout:

1. Car arrives

2. Que choice

3. Waiting for its turn

4. Enter in roundabout

5. Exit the roundabout.

Figure 10 - State diagram for roundabout

Event list for a crossing:

1. Car arrives

2. Que choice

3. Waiting for green signal

4. Enter in crossing

5. Check for another cars in crossing.

6. Exit the crossing

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Figure 11 – State diagram for crossing

4.2 Physical flowchart

Physical flow approach is one of the ways to develop the model. It identifies the physical

entities for which processing or transformation constitutes the main purpose of the system.

These entities are then tracked through the system, noting points of processing and branching

decision rules that determine their route. In our scenario Car and roundabout is two physical

entities, which we will track through the process. The process starts from choosing queue and

finish by getting out of roundabout. Tracking the entity in between these, a physical flow chart

can be defined.

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Figure 12 – Physical flowchart

4.3 Model design

The roundabout is modeled as a system of two circles made of car slots. Every slot represents

one car position in the outer or inner circle and thus can either be empty or contain one car at

a given instant of time. Cars spend some constant time in every slot on the way (depending on

the size of the slot and the speed of cars – both being decision variables). Slots are taken one

by one from the first one positioned at the ingress exit untill the last one at the egress exit, for

particular car.

All cars going right or straight always take the path through the outer circle while cars

going left use the inner circle. Cars doing U-turn would have taken the inner circle also, but

we're not considering these due to the lack of information about their incomming rate in the

current system.

When entering the roundabout cars have to yield to the traffic already circulating

inside the junction. In our situation that means a car will only take the first slot if there's no

car going from the left, trying to get it also. In order to join the inner circle both slots being

first in each circle must be free.

The whole model is depicted in Figure 13. Slots marked red serve as ingress while

blue ones are egress.

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Figure 13 – Roundabout model

4.4 Model implementation

The simulator application was written in Python programming language, with the use of

simulation library called SimPy. Behavior of every car is implemented as library entity called

Process. Roundabout object contains two circular buffers of Resources. Resource is a special

type of object in SimPy library, having its capacity (1 in our case) and a queue of Processes

requesting it. The Resource is given to the processes in the order they've requested it with the

exception of requests of higher priority comming from cars already inside the roundabout.

Simulation clock is advanced on next-event basis. Events are fired as cars are

generated (based on random distributions calculated) and also as slots are being taken or

released. Simulation is run for long enough time (24 hours in our tests) and statistics are

calculated at the end. Average and maximum times are printed and histogram of total times is

created also.

To see detailed output of the simulation tracing all the steps of every car, DEBUG

mode can be turned on in the program settings. Likewise, all decision variables can be

assigned arbitrary values in the settings section.

The final version of the program was thoroughly tested by the team members and it

has shown to be operational and bug-free. From observed behavior it seems to provide a good

estimate of real system.

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5 Model verification and validation

The source code of the program was analyzed in detail during the verification of our

simulation model. The analysis was provided by people who did not participate in the

implementation part of this work to provide independent and objective results. The program

was verified and no serious problems were found.

Another step in the model verification was performed when the simulation started.

With given diameter of the roundabout and speed of the cars we approximately calculated the

average time of crossing for one car. This calculation was compared to the results of the

simulator. This way we could determine whether the calculations in the simulation model are

accurate, although they were only an estimated values (since we calculated with even

distribution for car direction).

During the validation of the model we used the conceptual model of the system. We

agreed on which aspects should be included in the simulation model and also what will be the

output of the model. Among the included aspects was the theoretical probabilistic distribution

function of arriving cars, and no pedestrians on the road. The output of the model should be

calculated average time the car spends from choosing the lane until exiting the roundabout.

21

6 Model experimentation and optimization

In order to determine the performance of roundabout, we need to experiment with variables of

our simulation model. We are going to change following decision variables:

the diameter of the roundabout,

speed of a car,

car slot size.

Our performance variable is time spend by car waiting in the queue (average and maximum).

The best performance is then defined as lowest average and maximum time spend for a car in

the queue. We are going to simulate the crossing with following sets of parameters:

Roundabout diameter: 30, 35, 40 m.

Car slot size: 4, 5 m.

Car speed: 20, 25, 30, 35, 40 km/h.

We will do combination of all parameters so we need to run at least 30 simulations. However

the results can be predictable, because best performance will be probably given by the

combination of highest car speed and lowest roundabout diameter if we use the same inter-

arrival distribution functions within all simulations.

We need also to consider the constraints, especially the roundabout diameter. According to

measures made using Google Maps®, we can tell what is the maximum roundabout diameter

can be about 40 meters. The measuring is shown in Figure 14.

Figure 14 - Measuring the crossing diameter using Google Maps®

We can see that the measured distance 39 meters, however we are sure that it is possible to fit

the 40 meter diameter roundabout there, we just need to cut a bit from the footpath. Footpaths

will be in either way solved by the underpass.

22

Next constraint we need to think about is the maximum car speed in dependency to radius of

the half circle. It can be physically proven, that the centrifugal force rises with the speed of

object (in this case car) during the circular motion (on roundabout). Therefore, the speed

needs to be adapted according to physical laws. However, we are not able to do the

experiments to determine the maximum speed on the roundabout with specific diameter,

because we do not have testing car. We can just determine theoretical constraint for this

parameter, which is 40 km/h in our opinion.

23

7 Simulation results

We have performed multiple simulations with different parameters, as we have discussed in

section Model optimization and experiments. To find optimal solution, we are able to change

the decision variables of our simulation model: the roundabout diameter, car slot size and car

speed on roundabout. Each simulation ran for 24 simulation hours, which is enough to collect

sample so big, that we can estimate the accurate average of performance measures. Results of

our experiments are summarized in Table 2.

Number of

experiment

Roundabout

diameter [m]

Car slot

size [m]

Car speed

[km/h]

Average

waiting +

traversing

time [s]

Maximum waiting

+ traversing time

[s]

1 30 4 20 6,13 12,96

2 30 4 25 4,89 10,39

3 30 4 30 4,08 8,47

4 30 4 35 3,48 7,39

5 30 4 40 3,06 6,39

6 30 5 20 6,12 13,85

7 30 5 25 4,88 11,00

8 30 5 30 4,07 9,02

9 30 5 35 3,47 7,61

10 30 5 40 3,04 6,68

11 35 4 20 7,39 15,10

12 35 4 25 5,91 12,24

13 35 4 30 4,91 9,97

14 35 4 35 4,22 8,60

15 35 4 40 3,68 7,52

16 35 5 20 7,31 13,99

17 35 5 25 5,83 10,82

18 35 5 30 4,85 9,00

19 35 5 35 4,17 7,51

20 35 5 40 3,63 6,61

21 40 4 20 8,63 17,65

22 40 4 25 6,90 13,72

23 40 4 30 5,74 11,48

24 40 4 35 4,92 9,84

25 40 4 40 4,31 8,57

26 40 5 20 7,69 16,47

27 40 5 25 6,13 12,92

28 40 5 30 5,10 10,79

29 40 5 35 4,38 9,46

30 40 5 40 3,82 8,00

Table 2 - Experiments results

The results represent the overall average and overall maximum calculated from times

measured for each car. That means that it is average for whole crossing (roundabout),

independent of the output direction of incoming cars.

All of our experiments were performed correctly, however we need to select some

representative pattern from them in order to compare it with current status. As we have

mentioned in section Model optimization and experiments, the results behavior is as expected.

24

The lower roundabout diameter and higher speed results in lower average and maximum

waiting and crossing time. It is logical, because when we traverse the roundabout which has

30 meters in diameter and our speed is 40 km/h, we will cross it faster (3,04 s in average) than

when we need to cross the 40 meter roundabout and our speed is the same (3,82 s in average).

The car slot size has also its impact on results. We have experimented only with two car slot

sizes: 4 and 5 m. However, the 4 meter car slot size may not be enough for some bigger cars.

Average car length is approximately 4,12 m, so 5 m car slot size is better to use. Size of the

slot also includes the distance between cars, which have to be obeyed. If the car has 4,12 m

and car slot size is 5 m in length, the distance between cars is more than 0,8 m, which is more

than enough for safe driving in 40 km/h. The bigger the slot, the less cars can be in

roundabout at one time (for fixed roundabout diameter) and therefore, the more cars need to

wait for their turn. Bigger slot size increases the waiting time.

The speed on roundabout has also to be limited, so that the car will stay on the road. We have

theoretically estimated this speed to maximum 40 km/h, however the lower the diameter of

roundabout is, the lower the speed has to be.

When we consider all of these constraints, we can select following experiments from our

experiments table:

Experiment 8: 30 m diameter, 5 m car slot, 30 km/h speed.

Experiment 19: 35 m diameter, 5 m car slot, 35 km/h speed.

Experiment 30: 40 m diameter, 5 m car slot, 40 km/h speed.

Selected experiments and their results are again summarized in Table 3.

Number of

experiment

Roundabout

diameter [m]

Car slot size

[m]

Car speed

[km/h]

Average waiting

+ traversing time

[s]

Maximum

waiting +

traversing

time [s]

8 30 5 30 4,07 9,02

19 35 5 35 4,17 7,51

30 40 5 40 3,82 8,00

Table 3 - Selected representative results

Output of the table shows that the maximum minimalization of average waiting + traversing

time was achieved in experiment 30, where the biggest roundabout with highest speed was

simulated. The maximum waiting + traversing time was higher than in experiment 19. In this

case, we will focus on the average time, because maximum time could be caused by

occurrence of some almost impossible phenomenon during the simulation. The most optimal

configuration is with the maximum minimalization of average waiting + crossing time and

that was achieved in experiment 30: 3,82 s.

Further we need to compare the calculated simulation optimal result of roundabout crossing

with the current light crossing performance. Using our collected data, we have calculated the

same performance measures for the current light crossing. The results are in Table 4.

Crossing type Average waiting + traverse

time [s] Maximum waiting + traverse time [s]

Light crossing 23,85 58,85

Table 4 - Performance measures for light crossing

25

The average waiting + traverse time of light crossing is almost 8 times higher than the value

of this parameter in optimal configuration of roundabout crossing. We can say that roundabout

is way more effective solution in this case. The differences in the waiting times could be

caused by:

Long interval of red light in one direction when talking about light crossing.

The cars can block each other when they enter the light crossing – they need to obey the right-

hand rule and also the preference of oncoming vehicle rule.

The exit from the crossing is not fluent, because of pedestrian interaction.

In our simulation studies, we assume that pedestrian crossing will be solved by underpass, and

therefore, they are not influencing our waiting and crossing time. The advantage of this

solution is that there is always fluent exit from the crossing and cars do not need to wait to

exit blocking other cars in the same lane. The long interval of red light is also not the issue of

roundabout. The car can enter the roundabout, when the slot to enter is free and there is no

danger of collision.

To sum up, we can tell that roundabout is more efficient solution than the light crossing, when

the performance is given by the average waiting and traversing time.

26

8 Conclusion

This paper was dealing with simulation of a roundabout. We had to identify the proper

decision and uncontrolled variables as well as measures for subsequent evaluation in order to

accomplish this task. The next task was to collect the suitable data for further analysis. The

collected data were processed and used in decision process where random functions with

Poisson or uniform distributions were identified. These random functions were utilized in

traffic generation which resembled the traffic pattern of current intersection with traffic lights.

Once everything prepared, the actual model development took place. The roundabout was

modeled as a system of two circles made of car slots where each slot could either be empty or

contain one car at a given instant of time. After the implementation of this model, series of

examinations were conducted under which several variables were optimized for the sake of

better roundabout's performance. From the simulation's results, the most optimal scenario was

chosen as suitable sample for comparison with the current intersection. The result is

interesting, the average waiting + traverse time of optimal configuration of roundabout is

almost eight shorter than crossing with traffic lights. From these estimates, we can conclude

that deployment of roundabouts was the right thing to do and should be considered in future

road projects whenever possible, including the reconstruction of the observed intersection.

27

References

[1] Federal Highway Administration, Standard Highway Signs. As referenced in Florida

[2] Department of Transportation's Plans Preparation Manual.

[3] R.J. Troutbeck (1993). Capacity and Design of Traffic Circles in Australia.

Transportation Research Record 1398, TRB, National Research Council, Washington

D.C.

[4] Ourston L, and Doctors P. (1994). Roundabout Design Guidelines, California.

[5] W. Brilon and M. Vandehey, Roundabouts|The State of the Art in Germany, Inst.

Transp. Eng. J. 68 (1998), 48-54.

[6] M. Hossain, Capacity Estimation of Traffic Circles under Mixed Tra c Conditions using

Micro-Simulation Technique, Transport. Res. Part A 33 (1999),47-61.

[7] http://www.dot.state.fl.us/trafficoperations/doc_library/pdf/roundabout_guide8_07.pdf

[8] http://www.korkort.se/rondell/

[9] http://www.vtpi.org/calming.pdf

[10] http://www.streetsblog.org/2011/04/26/to-get-safer-streets-traffic-lights-and-stop-signs-

arent-the-answer/

[11] http://www.wsdot.wa.gov/safety/roundabouts/benefits.htm

[12] http://www.nevadadot.com/safety/roundabout/benefits.aspx

[13] eniro.se

[14] http://ncsu.edu/project/nsaudiovideo/pdf/roundabout.pdf

[15] http://vision-traffic.ptvgroup.com/en-uk/products/ptv-vissim/use-cases/

28

Appendix A

0

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8

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1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67

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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41

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30

0

0.5

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2.5 1

7

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31

0

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1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79

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Distribution of traffic

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0

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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41

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WEST to NORTH

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Distribution of traffic

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34

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35

0

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36

0

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NORTH to SOUTH

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1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79

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Interarrival time [s]

Histogram of traffic

NORTH to EAST