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.
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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].
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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.
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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]
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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.
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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.
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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.
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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
1
2
3
4
5
6
7
8
9
10
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67
Nu
mb
er
of
cars
[p
cs]
Inter-arrival time [s]
Histogram of traffic
East to North
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Am
ou
nt
of
cars
[%
]
Inter-arrival time [s]
Distribution of traffic
East to North
29
0
2
4
6
8
10
12
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Nu
mb
er
of
cars
Inter-arrival time [s]
Histogram of traffic
East to West
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Am
ou
nt
of
cars
[%
]
Inter-arrival time [s]
Distribution of traffic
East to West
30
0
0.5
1
1.5
2
2.5 1
7
13
19
25
31
37
43
49
55
61
67
73
79
85
91
97
10
3
10
9
11
5
12
1
12
7
13
3
13
9
14
5
Nu
mb
er
of
cars
Inter-arrival time [s]
Histogram of traffic
South to West
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
Am
ou
nt
of
cars
[%
]
Inter-arrival time [s]
Distribution of traffic
South to West
31
0
0.5
1
1.5
2
2.5
3
3.5
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
Nu
mb
er
of
cars
Inter-arrival time [s]
Histogram of traffic
South to North
0
0.02
0.04
0.06
0.08
0.1
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
Am
ou
nt
of
cars
[%
]
Inter-arrival time [s]
Distribution of traffic
South to North
0
2
4
6
8
10
12
14
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55
Nu
mb
er
of
cars
Inter-arrival time [s]
Histogram of traffic
South to East
32
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Am
ou
nt
of
cars
[%
]
Inter-arrival time [s]
Distribution of traffic
South to East
0
0.2
0.4
0.6
0.8
1
1.2
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 82
Nu
mb
er
of
cars
Interarrival time [s]
WEST to NORTH
WEST to NORTH
33
0
2
4
6
8
10
12
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47
Nu
mb
er
of
cars
Interarrival time [s]
Histogram of traffic
WEST to EAST
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45
Nu
mb
er
of
cars
[%
]
Interarrival time [s]
Distribution of traffic
WEST to EAST
34
0
0.5
1
1.5
2
2.5
3
3.5
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
Nu
mb
er
of
cars
Interarrival time [s]
Histogram of traffic
WEST to SOUTH
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70
Nu
mb
er
of
cars
[%
]
Interarrival time [s]
Distribution of traffic
WEST to SOUTH
35
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10 33 100
Nu
mb
er
of
cars
Interarrival time [s]
Histogram of traffic
NORTH to WEST
0
0.5
1
1.5
2
2.5
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61
Nu
mb
er
of
cars
Interarrival time [s]
Histogram of traffic
NORTH to SOUTH
36
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67
Nu
mb
er
of
cars
[%
]
Interarrival time [s]
Distribution of traffic
NORTH to SOUTH
0
0.2
0.4
0.6
0.8
1
1.2
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
Nu
mb
er
of
cars
Interarrival time [s]
Histogram of traffic
NORTH to EAST