Simulation Modeling of the Operation of the Toll Plaza with

Reversible Lanes

ALEXANDER TALAVIRYA1, MICHAEL LASKIN2

1Center of Econometrics and Business Analytics (CEBA),

St. Petersburg State University,

7/9 Universitetskaya nab., St. Petersburg, 199034,

RUSSIA

2Intelligent systems laboratory,

St. Petersburg Federal Research Center Russian Academy of Sciences,

14 Line, 39, St. Petersburg, 199178,

RUSSIA

Abstract: - The construction of toll roads depends on the available territory. The limited area often does not

allow the construction of a full-fledged toll plaza (hereinafter referred to as TP) with high capacity and many

lanes. In such cases, the configuration of TP is linked with the configuration of reversible lanes. Reversible

lanes carry traffic and help optimize traffic flow. The challenge is to choose the optimal configuration of a TP

that provides the highest capacity (traffic flow increases in both directions) and helps control operators’ errors

resulting in traffic congestion problems. The present study estimates TP with reversible lanes throughput

capacity in different configurations and traffic flow parameters. The study employs discrete-event simulation

modeling in the AnyLogic software environment. Our results show the optimal configuration of the reversible

lanes and explain what traffic flow parameters affect their capacity. The paper concludes with practical

recommendations on how to effectively apply simulation modeling to a TP operation and optimize it.

Key-Words: - discrete-event simulation, toll road, toll plaza, reversible toll plaza lanes, reversible lanes, toll

collection system, traffic congestion.

Received: March 13, 2024. Revised: July 6, 2024. Accepted: August 7, 2024. Published: September 23, 2024.

1 Introduction

The toll road construction in Russia has over a

15-year history. A large network of high-speed and

inner-city sections of toll roads has been developed.

Technical solutions for toll collection vary and

include adapting generally accepted standard

solutions to the transport, climatic, and socio-

geographical specifics of the regions. During this

time, Toll Plaza's engineering facilities (TP)

complexes have changed significantly. Despite the

development of free-flow toll collection technology,

road projects with the use of classical barrier TPs

continue to be widespread, which confirms the

relevance of this article.

This paper completes the authors' series of

studies on the throughput capacity of TP with

barrier-type tolling systems published by the authors

in 2020 – 2023 (the main results are collected in the

book, [1]). In those articles, authors have previously

reviewed several types of intra-city toll road TPs.

Our first simulation model has been created for the

TP at the exit from the intra-urban toll road. We

considered the specifics of traffic flows and user

behavior in this selected area. We have considered

different types of service time distributions and

estimated the parameters of the gamma laws of

service time distributions. We estimated the

emerging queue using the following parameters: the

number of vehicles in the queue, queue length,

waiting time of vehicles in the queue, and vehicle

flow density.

Similarly, we estimated throughput capacity,

possible risks of congestion, and its parameters for

the TP on the main course and exit from the intra-

city toll road in our second simulation model.

In our third simulation model, we considered a

separate case of the location of the TP on the exit

from the intra-urban toll road before the regulated

intersection. We estimated possible traffic situations

that led to traffic congestion problems. We studied

the throughput capacity of the TP and determined

the values of threshold traffic intensities affecting

the traffic situation. Our optimization experiments

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aimed at adjusting the phases of the traffic lights to

increase the speed of exit from the toll road. A

detailed summary of the research results from these

three studies is described and published in [1].

The types of TPs considered in our earlier

studies [1] had a fixed number of lanes. This fact

limits the number of possible configurations of the

toll collection system (hereinafter referred to as

TCS). In this paper, we consider a different type of

TP, a reversible-type barrier TP. This type of TP can

be used in cramped urban environments, and in the

regions where it is not possible to accommodate a

full-fledged TP due to land allocation constraints

(both in urban areas and outside the city on express

toll highways).

The objectives of this study are:

- To develop a simulation model (hereinafter

referred to as SM) of a TP with reversible

TCS;

- To estimate the capacity of a reversible TP

with different numbers of active lanes and

different configurations of the TCS;

- To estimate the share of electronic toll

collection (hereinafter referred to as ETC)

users that will allow traffic to pass through

the TP without congestion.

2 Literature Review

A large number of studies have assessed how well

toll road infrastructure functions. This fact

demonstrates the increasing research interest in how

to assess the quality of the TP management process.

Studies have explored various factors that impact

TP operation. The study [2], explored performance

indicators of the services provided at the TP in one

project in India. The results of this study, based on

exploring user perceptions, showed that factors such

as driver behavior, infrastructure and traffic

characteristics, trip characteristics, and the behavior

of the TP operators had a positive impact on the

quality of service at the TP. The importance of

driver behavior as a factor affecting the capacity of

the TP was explored in [1]. The application of ETC

as a means of improving the efficiency of the TP

operation is considered for toll road projects in

Taiwan [3], Korea [4], and India [5]. Separate

studies focused on the factors that affect the

efficiency of the traffic flow in a TP. The study [6]

explored the service time at the TP with the manual

toll payment method, using the example of the TP

project in India. The authors of the study [7]

explored the traffic flow for a two-lane toll road

with a TP and manual and automatic toll lanes.

Separately, it is necessary to mention the study [8],

devoted to the study of the traffic flow passing

through a TP as a hydrodynamic model, which is

able to describe its density and its evolution when

passing several TPs.

An important part of the tolling process is the

management of TCS configurations at the TP. The

study [9] introduced a control method based on the

configuration of TP lanes and variable speed limit

control. This study demonstrated, through

simulation experiments, an improvement in the

saving of traffic flow time through the TP and an

improvement in driving safety. A new methodology

for optimal toll management that combines recurrent

neural networks, mass service theory, and

metaheuristics was introduced in [10]. This

methodology was experimentally tested on real data

from a toll road project in Serbia.

The most acute problem related to the efficiency

of toll collection at the barrier-type TPs is the

problem of traffic congestion in the zone.

The main problem related to the efficiency of toll

collection at the barrier-type TPs is traffic

congestion. The study [11] employed a stochastic

model to explore congestion increase in the TP front

zone and how the number of toll lanes impacts it.

The study [12] investigated how congestion grows

in the TP exit zone, and developed a method of

combining the traffic flow patterns after the passage

of manual and automatic toll lanes. A queuing

model to estimate the profiles of waiting time and

queue length using closed-form equations was

presented in the study [13]. A quantitative

assessment of the total delay of the traffic flow of

vehicles passing through the TP zone, produced by

simulation modeling, was presented in studies, [14],

[15].

There are few works devoted to the study of

reversible TPs. There are only a few works devoted

to the study of reversible TPs. The most relevant

study is [16] as it explores different values of

forward and reverse traffic flow through the TP.

They concluded that the toll lanes for the direction

with lower intensity usually remain unused. The

traffic flows were estimated using the M/M/1

queuing model, [16]. They applied the reversible TP

concept and it led to the reduction of congestion and

the optimization of the parameters of the resulting

congestion. Further study of the reversible TP using

the simulation method will make it possible to

expand the set of used parameters involved in the

creation of the model, increasing the efficiency of

optimization processes of selecting the

configuration of the TCS at the TP.

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3 Simulation Model Construction of

the TP

In this section we consider supervisory controller

design to enforce boundedness, reversibility, and

liveness in a system modeled by a TP.

3.1 Technological Peculiarities of the TP

Let us consider the technological features of a

reversible TP. A reversible TP has one or more

central toll lanes that can collect tolls in both

directions of motorway traffic. Thus, the reversible

TP allows the number of lanes to be adjusted in

response to varying traffic volumes.

Reversible toll lanes, as well as stationary (non-

reversible) lanes, can operate in one or more toll

collection modes such as automatic (ETC), manual,

or mixed.

An example of a reversible TP lane arrangement

scheme is shown in Figure 1. This figure shows a

reversible TP that allows traffic to flow in two

directions. In one direction, the lanes pass through

lanes 1-6, while in the reverse direction, the lanes

pass through lanes 7-12.

Fig. 1: An example of a reversible TP lane

arrangement scheme with 12 lanes

The direction of traffic flows is shown by lines

with arrows. As can be seen in Figure 1, lanes 1 and

8, 2 and 7 are reversible, where the lines have

arrows in two directions. Non-reversible lanes have

lines with arrows in only one direction. Thus,

between 4 and 6 lanes, lanes can operate in each

direction. In the case of four-lane operation, there

will be operation from lane 3 to lane 6 in one

direction, and from lane 9 to lane 12 in the opposite

direction. In the case of six lanes, there will be

operation from lane 1 to lane 6 in one direction, and

from lane 7 to lane 12 in the opposite direction.

The advantage of reversible TPs is that we can

regulate the number of functioning lanes in line with

the changes in the intensity of traffic flows, which

allows the most efficient use of the largest number

of lanes at pendulum intensity, which is possible

when carrying out various types of correspondence:

labor, recreational, and seasonal. Reversible TP

mode allows for more efficient use of engineering

and technical support of the TP and ensures

minimum downtime of the TP equipment.

Nevertheless, constructing a reversible TP has

one core limitation. The TP cannot function

effectively at a high intensity of traffic flow passing

through the TP in forward and reverse directions in

one period.

The above-mentioned technological peculiarities

of TP lead us to the problem of how to select the

optimal number of functioning toll lanes and to

configure the TCS for each direction of traffic at the

TP and thus ensure the maximum intensity of traffic

flow with the given parameters through the TP in

both directions.

3.2 Selecting the TP Configuration

To build the simulation model and conduct our

experiments, we selected a TP configuration

consisting of 18 physical toll lanes where 6 central

physical lanes are reversible. Thus, the modeled TP

has 24 logical toll lanes. The lane arrangement

scheme of the reversible TP of the simulation model

is shown in Figure 2.

Fig. 2: Reversible TP simulation model. Lanes

arrangement schemes

The direction of movement of vehicles is shown

by lines with arrows. As can be seen in Figure 2,

lanes 1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17, 18 are

reversible, and these lines have arrows in two

directions. Non-reversible lanes have lines with

arrows in only one direction. Thus, between 6 and

12 lanes can operate in each direction. In the case of

a six-lane operation, there will be operation from

lane 7 to lane 12 in one direction, and from lane 19

to lane 24 in the opposite direction. In the case of

twelve lanes, there will be operation from lane 1 to

lane 12 in one direction, and from lane 13 to lane 24

in the opposite direction.

3.3 Creation of the TP Simulation Model

To conduct simulation experiments, a simulation

model (SM) with 18 physical and 24 logical toll

lanes was developed. Of these, 6 central physical

lanes are reversible, which equals 12 logical lanes.

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Earlier in the book, the SM of the TP on the main

course of the intra-city toll road [1] with

18 physical lanes were radiated. The SM with this

number of physical lanes on the TP has shown

efficient operation with high throughput in both

intra-urban and motorway conditions.

Since the same configuration can be applied for

each direction of the TP, taking into account the

number and mode of operation of the toll lanes, it

will be sufficient to analyze the performance of the

TP in one direction of traffic.

Figure 3 and Figure 4 show the general view and

top view of the developed SM of the reversible TP.

Fig. 3: Simulation model of the reversible TP.

General view

Fig. 4: Simulation model of a reversible TP. Top

view.

As shown in Figure 3 and Figure 4, the

parameters of the simulation model of the reversible

TP correspond to the parameters and proportions of

the designed TP in terms of geometric dimensions,

enter and exit zones, as well as modes of operation.

This allows preliminary simulation calculations to

be carried out at the design survey and design

stages. Depending on the obtained parameters and

results of simulation modeling, design solutions can

be timely adjusted to improve the transport

characteristics of the TP.

If there are transport nodes in close proximity to

the TP that affect the traffic flow behavior in the TP

area, they can also be added to the SM.

The SM allows observing potential traffic in 3D

at different angles and spatial orientations of the

model. This improves the quality of visual

observations of the experiments and helps to

identify hidden features of traffic flows in the

simulated processes.

The TP zone is connected to the main road

sections with 2 lanes located upstream and

downstream. There are no additional transportation

nodes before or after the TP.

3.4 Estimation of Capacity Limits of the

Reversible TP

The developed SM of the reversible TP allows

taking into account the following parameters:

1. Traffic intensity on the TP;

2. Traffic composition;

3. Distribution of vehicles by payment mode;

4. Number of toll lanes in operation;

5. Modes of operation of the lanes;

6. Automatic lane service time;

7. Manual lane service time;

8. Additional parameters (user behavior).

A detailed description of the SM parameters is

outlined within the study, [1].

In order to conduct simulation experiments for

this type of TP, the values of SM parameters № 2, 3,

6, 7, 8 were fixed, corresponding to the parameters

of TP operation on the main course of a toll road

outside a large urban agglomeration (distribution of

vehicles by class: Car - 75%, Lorry - 5%, Truck -

20%; share of ETC users: 70%; impact of user

behavior: 5%). The choice of the 70% ETC usage

share is based on the assumption that the TP under

study is located in a suburban area, outside the

urban agglomeration within a radius of ≥ 200 km

from its center, which corresponds to real examples

of this type of TPs. If the assumption of closer or

farther away from the city is adopted, the parameter

of the share of ETC use will increase or decrease

accordingly, which may affect the results of the

study and will require additional analysis.

To solve the set research problems, we assumed

that for both directions, traffic flow would have the

same values. Accordingly, the values of parameters

№ 1, 4, and 5, were changed during the simulation

experiments.

The configuration of the TP is set by the number

of toll lanes and their operation mode. The

developed SM allows to consideration of all

possible configurations both at minimum and

maximum possible number of operating lanes in one

direction of motorway traffic. The SM also takes

into account that the TP should operate with a

minimum of two manual lanes to ensure

uninterrupted acceptance of cash and bank cards by

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users and to provide redundancy in case of failure of

one of the lanes.

Table 1, Table 2, Table 3, Table 4, Table 5,

Table 6 and Table 7 summarize all reversible TP

configurations in one direction of the motorway.

These configurations may differ in the number of

lanes and the ratio of manual to ETC lanes. The

tables show possible configurations with

corresponding numbers, for which the number of

manual and ETC lanes (in the "Number of lanes"

rows) and lane numbers (in the "Lane №." rows) are

shown. The lane numbers in the "Lane №" column

correspond to the lane numbers in Figure 2.

Table 1. One-way reversible TP configurations with

6 lanes in one direction

Table 2. One-way reversible TP configurations with

7 lanes in one direction

Table 3. One-way reversible TP configurations with

8 lanes in one direction

Table 4. One-way reversible TP configurations with

9 lanes in one direction

Table 5. One-way reversible TP configurations with

10 lanes in one direction

Table 6. One-way reversible TP configurations with

11 lanes in one direction

Manual

lanes

ETC lanes

Number

of lanes

2 4

Lane № 11-12 7-10

Number

of lanes

3 3

Lane № 10-12 7-9

Configurations

Configuration 1

Configuration 2

Manual

lanes

ETC lanes

Number

of lanes

2 5

Lane № 11-12 6-10

Number

of lanes

3 4

Lane № 10-12 6-9

Configurations

Configuration 1

Configuration 2

Manual

lanes

ETC lanes

Number

of lanes

2 6

Lane № 11-12 5-10

Number

of lanes

3 5

Lane № 10-12 5-9

Number

of lanes

4 4

Lane № 9-12 5-8

Configurations

Configuration 1

Configuration 2

Configuration 3

Manual

lanes

ETC lanes

Number

of lanes

2 7

Lane № 11-12 4-10

Number

of lanes

3 6

Lane № 10-12 4-9

Number

of lanes

4 5

Lane № 9-12 4-8

Configuration 2

Configuration 3

Configurations

Configuration 1

Manual

lanes

ETC lanes

Number

of lanes

2 8

Lane № 11-12 3-10

Number

of lanes

3 7

Lane № 10-12 3-9

Number

of lanes

4 6

Lane № 9-12 3-8

Number

of lanes

5 5

Lane № 8-12 3-7

Configuration 1

Configuration 2

Configuration 3

Configuration 4

Configurations

Manual

lanes

ETC lanes

Number

of lanes

2 9

Lane № 11-12 2-10

Number

of lanes

3 8

Lane № 10-12 2-9

Number

of lanes

4 7

Lane № 9-12 2-8

Number

of lanes

5 6

Lane № 8-12 2-7

Configurations

Configuration 1

Configuration 2

Configuration 3

Configuration 4

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Table 7. One-way reversible TP configurations with

12 lanes in one direction

As shown in Table 1, Table 2, Table 3, Table 4,

Table 5, Table 6 and Table 7, the reversible TP can

operate in a range of 6 to 12 toll lanes, with the

number of manual lanes ranging from 2 to 6 units

and the number of automatic lanes ranging from 3 to

12 units.

To evaluate the capacity limits of a reversible TP

with different numbers of active lanes and different

configurations of the TP, 23 groups of experiments

were conducted to identify the threshold traffic flow

intensity at which congestion starts to form on the

TP. This intensity can be considered as the threshold

intensity for the configuration of the TP and the

corresponding set of recorded SM parameters. Each

group of experiments included the analysis of the

operation of the TP configuration at increasing

traffic flow intensity in the range from 250

vehicles/h to 3500 vehicles/h, with a step of 10

vehicles/h. The duration of observations for each

experiment was 1 hour.

The results of the experiments to evaluate the

ultimate capacity of the reversible TP are presented

in Table 8.

In the TP configuration column, the "ETC"

indicates the number of automatic lanes, and the

"M" indicates the number of manual toll lanes.

As shown in Table 2, the threshold intensity for

each TP configuration ranged from 710 to 1070

vehicles/h.

Our experimental results show that when the

share of ETC users in the flow is not high enough,

congestion forms at the TPs due to the accumulation

of queues at the manual toll lanes. An example of

queuing at manual toll lanes is shown in Figure 5

and Figure 6.

Table 8. Experimental results for estimating the

ultimate throughput of the reversible TP

Fig. 5: Formation of congestion on manual toll lanes

of a reversible TP. General view

Fig. 6: Formation of congestion on manual toll lanes

of a reversible TP. Top view

Manual

lanes

ETC lanes

Number

of lanes

210

Lane № 11-12 1-10

Number

of lanes

3 9

Lane № 10-12 1-9

Number

of lanes

4 8

Lane № 9-12 1-8

Number

of lanes

5 7

Lane № 8-12 1-7

Number

of lanes

6 6

Lane № 7-12 1-6

Configurations

Configuration 1

Configuration 2

Configuration 3

Configuration 4

Configuration 5

Experiment

group №

Number

of lanes

TP configuration

Threshold

intensity

23 12 6 ETC; 6 M 1070

12 7 ETC; 5 M 1010

21 12 8 ETC; 4 M 930

20 12 9 ETC; 3 M 830

12 10 ETC; 2 M 780

18 11 6 ETC; 5 M 980

17 11 7 ETC; 4 M 910

11 8 ETC; 3 M 840

15 11 9 ETC; 2 M 750

14 10 5 ETC; 5 M 970

10 6 ETC; 4 M 860

12 10 7 ETC; 3 M 830

11 10 8 ETC; 2 M 750

9 5 ETC; 4 M 950

9 9 6 ETC; 3 M 820

8 9 7 ETC; 2 M 710

8 4 ETC; 4 M 860

6 8 5 ETC; 3 M 800

5 8 6 ETC; 2 M 700

7 4 ETC; 3 M 810

3 7 5 ETC; 2 M 710

2 6 3 ETC; 3 M 800

1 6 4 ETC; 2 M 710

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In addition, we conducted 5 groups of

experiments to evaluate the influence of the

parameter of ETC users' share on congestion

formation in front of the reversible TP. For the

experiment, the configuration of the TP with the

maximum (12 units) number of functioning lanes

was selected, 10 of which operate in ETC mode and

2 – in manual mode. The results are shown in Table

9. When developing an SM of the TP, two target

indicators are key: the length of the queue formed

and the waiting time in the queue. To calculate the

time of queue length and waiting time in the queue,

classical methods of mass service theory can be

applied, taking into account the peculiarities of the

modeled TP. The derivation of the necessary

formulas, the applied mathematical apparatus, and

numerical methods are described in detail by the

authors of this paper in [1].

In complex cases, for example, when building a

simulation model that includes several

transportation objects, such as a TP and a regulated

traffic light object directly following the TP,

machine learning (ML) methods as an application of

artificial intelligence (AI) can be used. An example

of such an object is considered in detail by the

authors in [1].

Table 9. Estimation of the fraction of ETC that

allows vehicles to pass through the TP without

causing congestion. Experimental results

As it can be seen from Table 8 and Table 9, with

70% ETC share, at any configuration of the

reversible TP, a stable congestion is formed at a

flow rate of 1500 vehicles/h and higher. Table 3

shows that increasing the ETC share to 75-80% does

not solve the problem of congestion formation at

flow rates of 1500 vehicles/h and above. At ETC

share equal to 85%, stable congestion is formed at

flow rates of 3500 vehicles/h and above. Only at

values of 90-95% of ETC share, traffic congestion

will not occur for the considered configuration of

the reversible TP. This means that the remaining 5-

10% of vehicles in the flow are not equipped with

ETC on-board units and are not enough to form

congestion due to queuing on the manual lanes

shown in Figure 5 and Figure 6.

4 Conclusion

The reversible TP simulation model considered in

this study shows that the ways to increase capacity

for one direction of traffic flow are:

- Increasing the number of functioning lanes;

- Changing the configuration of the TP by

changing the combination of ETC and

manual toll lanes;

- Increasing the proportion of ETC users in the

traffic flow.

It should be noted that in order to assess the risks

of a toll road and the TPs located on it, it is

advisable to apply an individual SM for each

charging point, taking into account the peculiarities

of its geographical location, remoteness from urban

agglomerations, the composition of traffic at the

facility, the regularity of user correspondence, as

well as the impact of the surrounding transport,

logistics, and social infrastructure. When the TP is

located in pronounced industrial and logical areas of

the city, as well as in the border zones between the

city and the region, in order to analyze the capacity

of the TP, an additional assessment of traffic

intensity in different conditions, taking into account

the daily, weekly and seasonal irregularity of the

flow, may be required.

Further work on the development of the SM of

the reversible TP, which is beyond the scope of the

described study, should focus on identifying the

parameter set to improve its accuracy, as well as

analyzing and identifying the following

dependencies that affect toll plaza capacity:

- TP configurations and ETC user shares;

- TP configurations and the "Tag failure"

parameter;

- TP configurations and traffic composition.

Further research direction for us is to study the

ratio of flow density and flow speed on free flow

sections of toll roads because as follows from the

results of [17], the decrease in flow speed due to the

increase in flow density can also lead to the

formation of congestion at the TP.

Acknowledgement:

The research was carried out at the expense of the

Russian Science Foundation grant No 20-18-00365,

https://rscf.ru/project/23-18-45035/.

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27 12 10 ETC; 2 M 250 1690 3500 85%

26 12 10 ETC; 2 M 250 1040 1500 80%

25 12 10 ETC; 2 M 250 880 1500 75%

12 10 ETC; 2 M 250 780 1500 70%

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors equally contributed to the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

The research was carried out at the expense of the

Russian Science Foundation grant No 20-18-00365,

https://rscf.ru/project/23-18-45035/

Conflict of Interest

The authors have no conflicts of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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WSEAS TRANSACTIONS on SYSTEMS

DOI: 10.37394/23202.2024.23.24

Alexander Talavirya, Michael Laskin

E-ISSN: 2224-2678

222

Volume 23, 2024