Traffic Modeling and Control at Intelligent

Traﬀic Modeling and Control at Intelligent Intersections : Time Delay and Fuel Consumption Optimization Jinjian Li

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Jinjian Li. Traﬀic Modeling and Control at Intelligent Intersections : Time Delay and Fuel Consump- tion Optimization. Automatic Control Engineering. Université Bourgogne Franche-Comté, 2017. English. NNT : 2017UBFCA001. tel-01870543

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é c o l e d o c t o r a l e s c i e n c e s p o u r l ’ i n g é n i e u r e t m i c r o t e c h n i q u e s U N I V E R S I T É D E T E C HN O L OG I E B E LF OR T - M O N T B É L I A R D

Trafﬁc Modeling and Control at Autonomous Intersections :

Time Delay and Fuel Consumption Optimizations

JINJIAN LI

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é c o l e d o c t o r a l e s c i e n c e s p o u r l ’ i n g é n i e u r e t m i c r o t e c h n i q u e s U N I V E R S I T É D E T E C HN O L OG I E B E LF OR T - M O N T B É L I A R D

N◦ X X X

THÈSE présentée par

JINJIAN LI

pour obtenir le Grade de Docteur de l’Université de Technologie de Belfort-Montbéliard

Spécialité : Automatique

Trafﬁc Modeling and Control at Autonomous Intersections : Time Delay and

Fuel Consumption Optimizations

Unité de Recherche : L’Institut de Recherche sur les Transports, l’Energie et la Société (IRTES)

Soutenue publiquement le 7 Février 2017 devant le Jury composé de :

ABDELKHALAK EL-HAMI Rapporteur Professeur INSA, Rouen, France

MOHAMED BENREJEB Rapporteur Professeur ENIT, Tunis, Tunisie

PIERRE BORNE Examinateur Professeur EC-Lille, Lille, France

OLIVIER GRUNDER Examinateur Maître de Conférence UTBM, Belfort, France

ABDELLAH EL-MOUDNI Directeur Professeur UTBM, Belfort, France

MAHJOUB DRIDI Co-Directeur Maître de Conférence UTBM, Belfort, France

ACKNOWLEDGEMENT

I would like to give my sincere gratitude to my supervisors professor Abdellah EL MOUDNI and Associate professor Mahjoub DRIDI, for the continuous support of my Ph.D study and research in Lab IRTES-SET. Their patience, motivation, immense knowledge and their inspiring guidance during my thesis deserve the most appreciation and respect in my heart. It is really a great experience working with them. With their abundant research experience, they show me the method of becoming an independent researcher.

I would like to thank my committee members, professor Abdelkhalak EL-HAMI, professor Mohamed BENREJEB, professor Pierre BORNE, Associate professor Olivier GRUNDER. I also want to thank you for letting my defense be an enjoyable moment, and for your brilliant comments and suggestions which will help us to improve the thesis, thanks to you.

My acknowledgment is also given to the personnel in the laboratory of transportation system for their help during my study in university of technology of belfort- montbeliard.

I would further like to give my gratitude to the ﬁnancial support from the program of China Scholarship Council (CSC). I would like also to thank UTBM so that I could do my thesis in such comfortable and inspiring environment.

Finally, I wish to take this opportunity to express my appreciation and thanks to all my families and friends for their emotional supports and research help. They also encourage me to explore knowledge. With all the love and faith, tomorrow is going to be better.

LISTOF PUBLICATIONS

JOURNALS

1. Jinjian LI, Mahjoub DRIDI, Abdellah El Moudni. A Cooperative Trafﬁc Con- trol of Vehicle-Intersection (CTCVI) for the Reduction of Trafﬁc Delays and Fuel Consumption, Sensors (Basel, Switzerland), Vol.16-Issue 12 ( 2175), 2016. (IF=2.033, SCI).

2. Jinjian LI, Mahjoub DRIDI, Abdellah El Moudni. Cooperative Trafﬁc Control based on the Artiﬁcial Bee Colony. International Journal of Engineering Research and Applications, Vol.6-Issue 12, pp. 46-55, 2016.

CONFERENCES

1. Jinjian LI, Mahjoub DRIDI, Abdellah El Moudni. A dynamic cooperative traf- ﬁc control (DCTC) for the reduction of time delay. 3th International Confer- ence on Vehicle Technology and Intelligent Transport Systems, Porto, Por- tugal, April 2017. (accepted)

2. Jinjian LI, Mahjoub DRIDI, Abdellah El Moudni. A cooperative trafﬁc control for the vehicles in the intersection based on the Genetic Algorithm. 4th IEEE International Colloquium on Information Science and Technology, Tangier- Assilah, Morocco, October 2016, pp. 627-632.

3. Jinjian LI, Mahjoub DRIDI, Abdellah El Moudni. Multi-vehicles green light optimal speed advisory based on the augmented lagrangian genetic algorithm. 17th International IEEE Conference on Intelligent Transportation Sys- tems (ITSC), Qingdao, 2014, pp. 2434-2439.

vii

CONTENTS

General Introduction1

1 Introduction of trafﬁc modeling and control methods5

1.1 Introduction of trafﬁc ...... 5

1.2 Trafﬁc control in the conventional systems ...... 6

1.2.1 Transport parameter ...... 6

1.2.1.1 Headway ...... 6

1.2.1.2 Flow of vehicles (Q) ...... 6

1.2.1.3 Density (D) ...... 8

1.2.1.4 Speed of vehicle ...... 8

1.2.1.5 Fundamental diagram of trafﬁc ...... 9

1.2.2 Trafﬁc Models ...... 10

1.2.2.1 Macroscopic trafﬁc model ...... 10

1.2.2.2 Microscopic trafﬁc model ...... 11

1.2.3 Conventional methods of trafﬁc control ...... 14

1.2.4 Some existing trafﬁc control systems ...... 16

1.3 Intelligent Transportation System ...... 18

1.3.1 Autonomous vehicle ...... 19

1.3.2 Global Positioning System (GPS) ...... 21

1.3.3 Wireless communication ...... 24

1.3.3.1 Communication of vehicle-to-infrastructure . . . . 26

1.3.3.2 Communication of Vehicle to Vehicle ...... 28

1.4 Conclusion and objectives of the thesis ...... 29

ix x CONTENTS

2 Dynamic modeling of transport networks 31

2.1 Introduction ...... 31

2.2 Structure of the studied transport network ...... 35

2.2.1 Generation of new vehicles ...... 36

2.2.2 Compatible and incompatible streams ...... 37

2.3 Objectives of control and safety constraints ...... 39

2.3.1 Objectives of control ...... 39

2.3.2 Safety constraints ...... 40

2.4 Mathematical model ...... 42

2.4.1 Movement of the vehicle ...... 44

2.4.1.1 Relationship between maximum speed and arrival time at the intersection ...... 44

2.4.1.2 Relationship between minimal passing time and initial speed of entering the intersection ...... 46

2.4.2 Fuel consumption model ...... 48

2.4.3 Choice of route for each vehicle in the intersection network 52

2.5 Conclusion ...... 56

3 Proposed control approaches 57

3.1 Introduction ...... 57

3.1.1 Some literature related to the exact methods ...... 57

3.1.2 Some literature related to the heuristic method ...... 60

3.2 Exact method — Dynamic Programming (DP) ...... 62

3.2.1 Recursion formula of DP ...... 62

3.2.2 Historical inﬂuence of each process of optimization based onDP...... 63

3.2.3 Initialization of DP ...... 65

3.2.4 Index of sub-problems ...... 66 CONTENTS xi

3.2.5 Optimization process for the passing sequence according to the DP ...... 68

3.3 Limitations of DP ...... 70

3.4 Approximate method — Artiﬁcial Bee Colony (ABC) ...... 72

3.4.1 Code of solution ...... 74

3.4.2 Operator of evolution ...... 75

3.4.3 Selection based on the roulette wheel ...... 77

3.4.4 Process of applying ABC to optimize the passing sequence 78

3.5 Conclusion ...... 79

4 Simulation and results 81

4.1 Introduction ...... 81

4.2 Simulation case in an isolated intersection ...... 81

4.2.1 Example of applying the Dynamic Programming in optimizing the passing sequence in detail ...... 82

4.2.1.1 Simulation results in the ﬁrst optimal process of DP 82

4.2.1.2 Method of coding the solution in the ﬁrst optimal process ...... 83

4.2.1.3 Some vehicles’ speed proﬁles in the ﬁrst optimal process of DP ...... 84

4.2.1.4 Results analysis ...... 86

4.2.1.5 Simulation performance under the different trafﬁc volumes ...... 87

4.2.2 Comparison between ABC and DP in an isolated intersection 89

4.3 Simulation case in a network of intersections ...... 92

4.3.1 Comparison with some works ...... 92

4.3.2 Comparison between ABC and DP in a network of intersections ...... 101

4.4 Conclusion ...... 104 xii CONTENTS

General Conclusion 105 GENERAL INTRODUCTION

The congestion in the traffic network is one of the most serious problems in the daily life. However it is difficulty and expensive to extend the infrastructure in some cities. Therefore a more reasonable solution is to improve the traffic control method based on the existent infrastructure on the road.

In the conventional systems, in general, the parameter are adapted based on the historical data or the information sent from the sensors to improve the throughput. But, vehicles can not receive the schedule of signals far away from the intersection because of the limit of vision. And the control center can not get the arrival information from the vehicles precisely in real-time. As a result, the efﬁciency is limited. However, with the improvement of technology of communication and autonomous cars, this problem can be improved with the Intelligent trafﬁc systems (ITS).

In the ITS, the communication between intersection and vehicles is two-way and real-time, by the connection of Vehicle-to-Infrastructure (V2I). As a result, each vehicle can be considered independently. The vehicles can send their arrival information before arriving at the intersection, based on which the control center can optimize right-of-way for the vehicles to pass the intersection more effectively. And the compatible streams can be combined dynamically during the control process instead of the ﬁxed combination as a phase, because the control center can get the precise and detailed information about the movement of vehicles, such as origin, destination, operation in the intersection (turn left, right or straight), type of vehicle, and so on. Moreover, it will be safer comparing with the conventional systems, due to the fact that the automatic vehicle is not allowed to pass the intersection without right-of-way.

After the schedule of signals is optimized in the intersection and sent to vehicles, each vehicle can adjust its speed in advance to avoid the useless acceleration and deceleration near the intersection to save the fuel consumption and to reduce the environmental pollution.

1 2 General Introduction

Therefore, the ITS can improve the traffic control efficiency and the standard of living by reducing the time delay and pollution, economizing the fuel consumption. In our work, a cooperative traffic control model is proposed.

PLANOFTHETHESIS

In this thesis, there are four chapters in total as follows.

Chapter 1 introduces the state-of-the-art about trafﬁc model and control methods in the conventional systems and the Intelligent Transportation System. After that, the objective of the thesis is proposed to build a cooperative trafﬁc control model.

Chapter 2 presents a cooperative modeling to solve a problem of reducing traffic delays and decreasing fuel consumption simultaneously in a network of intersections without traffic lights, where the implement of cooperation between vehicles and intersection is based on the communication of Vehicle-to-Infrastructure (V2I). This resolution of the problem contains two main steps. The first step concerns the itinerary which means a list of the intersections chosen by vehicles to arrive at their destination from their origins. Based on the principle of minimal trip distance, each vehicle chooses its itinerary dynamically based on the traffic load in the adjacent intersections. The second step is related to the following cooperative processes which allow the vehicles to pass through each intersection more rapidly and economically: on one hand, according to the real-time information sent by vehicles via V2I in the edge of the communication zone, each intersection applies Dynamic Programming (DP) or Artificial Bee Colony (ABC) to cooperatively optimize the sequence with minimal time delay. As a result, the vehicles can pass the intersection faster; on the other hand, after receiving this sequence, each vehicle optimizes the speed profile before the intersection by an exhaustive search to get the minimal fuel consumption.

Chapter 3 shows the studies of applying the DP and ABC to optimize the passing sequence for vehicles to pass the intersection. For the DP, the passing sequence is decomposed by deleting the last vehicle. Then the total time delay for a passing sequence equals to the sum of time delay between its sub-problem and the last vehicle. Although the DP can always ﬁnd the optimal solution in theory, it takes long time and large space of sub-problems to get the best solution. Therefore, the ABC is applied to ﬁnd a near best solution more quickly. 3

Finally, the chapter 4 illustrates the simulations to show the performance of the proposed method. The results are analyzed and compared with other papers to present the performance of the cooperative control model.

INTRODUCTION OF TRAFFIC MODELING ANDCONTROLMETHODS

1.1/I NTRODUCTION OF TRAFFIC

The first traffic signal control system has been used in London in 1868. This system applies manually the operated semaphores to prevent accidents by al- ternately assigning the right-of-way to vehicles. Currently, this system is greatly improved due to the increase of vehicles. In the United States, there are over 272,000 traffic signal systems, which operate on the roads throughout each year. These systems play an important role in the safety of traffic network. However, people spend more and more time on the road, and the intersection is one of the worst places causing traffic congestion. Therefore, researchers are trying to update the equipment of traffic control or to adjust the time-table of signal lights to improve the efficiency of traffic. As a result, the following benefits can be achieved:

• Proving the high efﬁciency of movement to people in everyday life.

• Reducing the time delay and increasing the trafﬁc volume at intersections.

• Improving safety in mobility by decreasing the frequency and severity of accidents.

• The economy of fuel consumption and the protection of the environment.

In this chapter, there are two main parts. In the ﬁrst part, we focus on the conventional methods, such as the general description of the trafﬁc control and research

5 6CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS concerned. In the second part, the history of the Intelligent Trafﬁc System (ITS) is presented, which is based on the technology development of the wireless connection.

1.2/T RAFFIC CONTROL IN THE CONVENTIONAL SYS-

TEMS

1.2.1/T RANSPORT PARAMETER

In general, there are two essential components in the traffic system: the mobiles and the infrastructure. The infrastructure is all the elements that provide the foundation for traffic, such as, roads, bridges, lines and electrical systems. The mobiles are the objects that run on the infrastructure of roads. Generally, mobiles are the rolling cars. Pedestrians are not the mobile because it is assumed that their movements are determined by the mobile. We will present the variables to measure and analyze the traffic.

1.2.1.1/H EADWAY

This part introduces the headway (tInter). It is deﬁned as the interval of time when two successive vehicles pass over the same point of observation, as shown in Fig. 1.1. This time is imposed on all successive vehicles because of road safety.

1.2.1.2/F LOWOFVEHICLES (Q)

This variable represents the distribution of vehicles in the range. Generally, we m calculate the average ﬂow Q for the interval[t1, t2]. On one hand, it can be measured as the number of vehicles passing the same point of observation X for the interval [t1, t2], as shown by Eq. (1.1) and Fig. 1.2.

m N(t1, t2, X) Q (t1, t2, X) = (1.1) t2 − t1 1.2. TRAFFIC CONTROL IN THE CONVENTIONAL SYSTEMS 7

point of observation vehicle 2 vehicle 1

time t1 tinter=t2-t1 point of observation vehicle 2 vehicle 1

time t2

Figure 1.1: Headway

wherein the term N(t1, t2, X) is the number of vehicles passing the point X during the interval [t2 − t1].

point of observation (X)

vehicle 1

t1 Time

point of observation (X) N(t1, t2, X)=4

vehicle 5 vehicle 4 vehicle 3 vehicle 2 vehicle 1

t2 Time

Figure 1.2: Flow of vehicles

On the other hand, it can be represented by the inverse of average inter-vehicle 8CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS

m interval tInter.

m 1 Q = m (1.2) tinter m t2 − t1 tinter = (1.3) N(t1, t2, X)

1.2.1.3/D ENSITY (D)

This variable refers to the spatial distribution of the vehicles. In general, the average density is calculated Dm and there are two methods. The ﬁrst method, there are vehicles that are in an area bounded by two points of observation (X1, X2) at time t, as shown by Eq. 1.4 and Fig 1.3.

m N(X1, X2, t) D (X1, X2, t) = (1.4) X2 − X1 where the term N (X1, X2, t) is the number of vehicles that are in the section of the road between two points (X1, X2) at time t.

N(X1, X2, t)=5 vehicle 5 vehicle 4 vehicle 3 vehicle 2 vehicle 1

Distance

X1 X2

Figure 1.3: Density

In the second method, the density can be described by the average spacing of the vehicle sm.

1 Qm = (1.5) sm X − X sm = 2 1 (1.6) N(X1, X2, t)

1.2.1.4/S PEEDOFVEHICLE

The instantaneous vehicle speed v(t) instantly shows the way with which the car drives on the road at time t. After recording all instant speeds on a route, we can 1.2. TRAFFIC CONTROL IN THE CONVENTIONAL SYSTEMS 9 trace the speed profile of the car and this profile is very useful in analyzing the quality of traffic and fuel consumption.

The average vehicle’s speed Vm describes the average movement of the vehicle during the interval T. It is measured by the following formulation:

RT v(t) dt Vm = 0 (1.7) T

1.2.1.5/F UNDAMENTAL DIAGRAM OF TRAFFIC

It refers to the relationship between flow rate and the density of vehicles. It can be applied to predict traffic capacity. This diagram is shown in Fig. 1.4 [1]. When density increases before the point DC, throughput increases correspondingly. Be- cause there are more vehicles on the roads and all vehicles can run with a high speed. But when the density increases after point DC, the flow rate decreases, because of congestion.

Debit Vmax max Q

dc Density

Figure 1.4: Fundamental diagram of trafﬁc 10CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS

1.2.2/T RAFFIC MODELS

The traffic models are basically divided into two types: macroscopic and microscopic. The macroscopic traffic models are applied to describe the characteristics of traffic at intersections. These models capture the overall or average traffic characteristics. But the microscopic traffic models search the movement of each vehicle respectively. These models allow the people to monitor all retail vehicles. Both models are very active in research and can study the phenomena of traffic (e.g. traffic jams).

1.2.2.1/M ACROSCOPIC TRAFFIC MODEL

The first macroscopic model named the Lighthill Whitham Richards (LWR), which was created by the authors Lighthill and Whitham [2] in 1950. This model neglects the dimension of the vehicle and defines traffic as a compressible fluid. Conse- quently, it presents the traffic system overall or average characteristics instead of specific character of a vehicle. The formulation of this model is given by the following equations:

ρt(x, t) + (ρ(x, t)V(ρ(x, t))x = 0 (1.8)

A more recent model is the Aw-Rascle (AR) model [3]. The AR model tries to move away from a model based on a ﬂuid, such as the LWR model. The authors believe that the macroscopic models are very old and are very involved in ﬂuid dynamics. The AR model is described by the following wording:

ρt + (ρv)x = 0 (1.9)

(v + P(ρ))t + v(v + P(ρ))x = 0 (1.10)

The ﬁnal model is referenced Zhang model [4] (named after its creator H. Michael Zhang). This model is completely different from ﬂuid behavior. Zhang model applies a second equation derived from a microscopic model, which establishes 1.2. TRAFFIC CONTROL IN THE CONVENTIONAL SYSTEMS 11 a link macro - micro. The model is given by the following equations:

ρt + (ρv)x = 0 (1.11) 0 vt + vvx + ρV (ρ)vx = 0 (1.12)

There are advantages and disadvantages at the same time applying the macroscopic model to analyze trafﬁc. The main advantage of macroscopic models is that they are relatively "simple" to calculate relative to microscopic models. The macroscopic models have fewer parameters than their microscopic counterparts. For example, in the model equations, the number of required parameters is not large. The disadvantage of a macroscopic model is the loss in the details of vehicle movement that can be modeled in microscopic models.

1.2.2.2/M ICROSCOPIC TRAFFIC MODEL

Microscopic models attempt to model the movements of individual vehicles on the tracks. Generally, they are functions of the position, velocity and acceleration of vehicles. Microscopic models are created by using ordinary differential equations. Each vehicle has its own equation. The behavior of these models is usually headed by a leading vehicle models and it is called " car following". The Figure 1.5 shows how microscopic models label the number of vehicles in the car following situation. Vehicle n+2 Vehicle n+1 Vehicle n vn+2 vn+1 vn

n+2 n+1 tinter tinter

Figure 1.5: Car following

Microscopic models have been developed to try to imitate the way that a human reacts in trafﬁc situations. They contain three different lines of statements to describe the driving types typically encountered.

1. The ﬁrst rule of driving is the free state. This situation occurs in a low density 12CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS

of vehicles and all private vehicles can accelerate to their desired speeds. No leading vehicle is present to inﬂuence the position, speed or acceleration of the other vehicles.

2. The second driving state is the state of car following. This condition is often encountered in everyday trafﬁc, when there is the average density on the road. In this state, the speed and acceleration of a vehicle are largely determined by his previous vehicle. Each driver tries to maintain a reasonable interval of space or time between himself and the leading vehicle.

3. The ﬁnal driving state is the braking state. This condition is sometimes referred to an intervention of the emergency. This state becomes active when the current vehicle is currently approaching a stopped or signiﬁcantly slower vehicle. The driver will attempt to stop by using varying degrees of braking force to avoid the collision with the object in front of him.

The most basic model is the microscopic Gibb model [4]. Developed in the year 1970, this model uses the states of driving to model the trafﬁc ﬂuid and is given by the following equation:

x˙n(t) − x˙n−1(t) x¨n(t) = C (1.13) xn(t) − xn−1(t)

th the symbol xn(t) is the location of the n vehicle and the symbol xn−1(t) is the location of the (n − 1)th vehicle (the previous car of the nth vehicle). This equation th shows that the current acceleration of the n vehicle x¨n(t) is determined by the speed and the position of the previous car (n − 1)th. The variable C is a sensitive parameter.

A drawback of the model above is that some parameters are unrealistic. For example, they can allow unrealistic braking behavior beyond the capacity of physical vehicles. Consequently, modern models trying to solve these problems by using multiple sensitivity settings or other methods.

A current model is the intelligent driver model (IDM) [5]. This model was developed by the authors Treiber, Hennecke Helbing to improve previous models, and was published in 2000. This model contains a strategy of accelerating and braking to cover the three states of conduct above. The IDM model is given by the 1.2. TRAFFIC CONTROL IN THE CONVENTIONAL SYSTEMS 13 following equations:

∗ v δ s (v, 4v) 2 v˙IDM(s, v, 4v) = a[1 − ( ) − ( ) ] (1.14) v0 s ∗ v 4 v s (v, 4v) = s0 + vT + √ (1.15) 2 ab where the term s∗(v, 4v) is given in Eq. (1.15).

The free state dominates the equation 1.15 when s is very large, which makes the term negligible interaction. Then the free status of movement is given as the following equation:

v δ v˙ f ree(v) = a[1 − ( ) ] (1.16) v0 where when the variable v approaches the variable v0 the term v˙ f ree(v) approaches zero. It implies that the driver decreases gradually the acceleration as it approaches its desired speed v0. The term braking or interaction of the equation 1.15 dominates the state of following and braking. The braking term is given by the following equations:

s∗ v˙ (s, v, 4v) = −a( )2 (1.17) brake s ∗ v 4 v s (v, 4v) = s0 + vT + √ (1.18) 2 ab where the term vT dominates in normal driving. The vehicle attempts to maintain √ a special interval T in monitoring other vehicles. The term v 4 v/2 ab dominates when the vehicle approaches an object at a very high speed. Consequently, the vehicle brakes in the b limit but exceed the value of b if necessary to avoid a collision.

As macroscopic models, there are advantages and disadvantages at the same time by applying the microscopic models to analyze the trafﬁc. A major advantage of microscopic models is the ability to individually study the movement of the vehicle. In addition, the macroscopic parameters, e.g. the ﬂow rate and density, can also be studied in the microscopic models. The big disadvantage of microscopic models is that an ordinary differential equation is required for each vehicle. Accordingly, the calculation of equations of microscopic models costs a lot of time in large systems. It asks for the high power of modern computers to make it 14CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS practical. This is probably why the microscopic models are not used in the year 1950. As the power of computers increased and prices declined, the advantage of simple calculations in the macroscopic model has become less important.

1.2.3/C ONVENTIONAL METHODS OF TRAFFIC CONTROL

In order to describe a trafﬁc control system, there are a few key terms that should be presented ﬁrst [6]:

• Adaptive signal control: In a trafﬁc network, the signal control at downstream intersections based on the detected information of the vehicles from the points located in the upstream intersections.

• Approach: a group of stream having the same direction. Some different functions at the intersection are assigned to these streams as turn left, cross and turn right.

• Capacity: the maximum number of passing vehicles at the intersection, under certain given conditions.

• Cycle: one complete sequence of signal in a phase, such as red, green and yellow.

• The cycle: the time required in a complete sequence of signal.

• Detector: a device on the road to detect the presence of a vehicle.

• Green time: a period of green signal on certain roads where vehicles are allowed to cross the intersection.

• Maximum or minimum green time: the maximum or minimum green time in a cycle.

• Red time: the duration of the red signal in a cycle.

• The interval of time: the minimum time between two successive vehicles passing the same point on the track.

• Phase: period of the signal. Each phase is assigned to one or more independent movements. 1.2. TRAFFIC CONTROL IN THE CONVENTIONAL SYSTEMS 15

• The phase sequence: the order of a set of different phases.

• Travel time: a total time spent by vehicles to pass a given distance.

There are three kinds of trafﬁc control methods: the non-induced control, the semi-induced control and the fully induced order.

The non-induced control is a process of the signal control, where the parameters are preset and ﬁxed during the period, based on historical data. It is very suitable for the intersection where trafﬁc demand are consistent in every day, such as intersections in areas of the city center. Therefore, by applying this system to the control, the following advantages can be achieved:

• Efﬁcient cooperation between adjacent intersections. Because all parameters can be set in advance, for example, the beginning and ending of the green time at adjacent intersections.

• No detector in this system. Therefore, this system can be immunized against the problems caused by the failure of the sensor.

• Economy. It does not take much cost and training to install and maintain the system. So this system is cheaper.

However, there are shortcomings in the system. It can not compensate for un- expected changes that occur in the volume of traffic. And it is ineffective to the intersection where the traffic is random. An example of this system is the study of the Traffic Network Study Tool (TRANSYT) [7].

The semi-induced command is a traffic control that applies only detections on the secondary road in an intersection. In other words, there is no detections on the main road. In this type of operation, the control center focuses on the highest traffic roads (highway or not prompted road) and gives more green time for those. The right of way is given to the small road on the basis of the appeal of the detectors. This control system is very suitable for the intersection in the arterial street, where there is a large volume of traffic in the main road and a small demand in the lane. Therefore, the following advantages can be obtained by applying this control system:

• It is very easy for this system to be applied effectively in a coordinated trafﬁc control system. 16CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS

• It can reduce the delay for trafﬁc in the great highway.

• The failure detectors do not affect the main road, as there are no sensors on these roads.

However, there are certain disadvantages in this control system. First, a exces- sive delay of trafﬁc can be caused by the continuous call from the secondary road. Second, some detectors should be installed in the small road, which costs a lot of money and maintenance. Finally, this system needs more training than non-induced order.

The fully-induced control means that all streams are encouraged in the intersections. In other words, there are detectors in all trafﬁc patterns. Therefore, this control system is very suitable for intersections where trafﬁc volumes are largely random and change throughout the day. And it is very easy for this system to realize the coordinated control in a road network. Therefore, there are several advantages obtained through this control system:

• The trafﬁc delays can be greatly reduced by a more sensible structure to the different volumes of trafﬁc.

• The information that is obtained by sensors can help the control center to exploit the green time resource.

• Some phases without the call for service can be skipped to save the green time. Then, this time can be assigned to another phase to improve the efﬁciency of circulation.

However, the disadvantage of this system is very clear. It takes a lot of detectors, which cost a lot of money. And it takes a long time and a lot of people to maintain this system [8].

1.2.4/S OME EXISTING TRAFFIC CONTROL SYSTEMS

There are many well-known existing traffic control systems. The paper [7] proposed by the author DIRobertson presents a Traffic Network Study Tool (TRAN- SYT), which is a software applied worldwide for the optimal control of the flow in a road network. It was invented by the laboratory of transport and the road in the 1.2. TRAFFIC CONTROL IN THE CONVENTIONAL SYSTEMS 17

UK in 1960. It simulates the movement of vehicles on the basis of traffic flows or historical data. In order to respond to local conditions, it applies the dispersion of platoons. The TRANSYT is often applied by highway engineers to manage the signal plans in the traffic control system.

The paper [8] proposed by the author RA.Vincent introduce the Microprocessor Optimised Vehicle Actuation (MOVA), which overcomes the problems in the traditional control. It is more sensitive to the real-time traffic conditions, as a result, it can significantly increase the capacity at the intersection. There are two modes of operation in the MOVA based on road conditions: uncongested (Free-flow condition) and congested. In the previous mode, the MOVA works in the mode of maximum capacity in order to optimize the total flow for each intersection. In the congested mode, the goal is to move all vehicles that wait before the red light through the intersection in one cycle.

The paper [9] shows the Sydney Coordinated Adaptive Traffic (SCAT), which is based in Sydney, Australia, to solve the problem of traffic congestion caused by increasingly heavy traffic movement. The SCAT is fully adaptable to the actual demand of traffic through the communication network. Therefore, the SCAT of- fers a significant improvement in the efficiency of traffic at a very low cost. A case of actual test shows that the SCAT can save 35-39 % of travel time in peak periods within the time fixed control optimized cooperative traffic. We can obtain benefits not only in reducing the delay time, but also in decreasing accidents and air pollution.

The paper [10] proposed by PB.Hunt authors describes the Split Cycle Offset Op- timization Technique (SCOOT). The SCOOT is a tool for the management and control of the city traffic to reduce the growing problem of traffic congestion. The SCOOT is an adaptive system because it automatically answers the demand for real-time traffic sensors embedded in the network of urban traffic. There is evi- dence that the SCOOT is a world leader in the control of urban traffic by reducing the time delay in an average of 20 % and providing some high-level management, such as priority bus detection incidents and so on.

The paper [11] proposed by V.Mauro authors describes an adaptive traffic signal control system — Urban Traffic Optimization by Integrated Automation (UTOPIA). This traffic control method applies the optimal management strategies to control city traffic. The UTOPIA can address the control problems in a very complex traffic 18CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS networks and can provide the priority control, such as transport and the police car, taking into account historical data, real-time traffic demand and events predicted. The objective of the system is to reduce the circulation time in all urban traffic networks. Therefore, we can get a smoother flow, save energy, reduce emissions and improve traffic safety.

The paper [12] proposed by the author NHGartner has a trafﬁc control method — the Optimised for Adaptive Control Policies (OPAC), which is a signal trafﬁc control method. It can realize the demand for real-time response by applying the associated computing strategy. It has the following four characteristics:

• Earning a very good result which is close to the theoretical optimum.

• Needs of the information from the on-line sensors in the upstream link.

• Application on the basis of existing microprocessors.

• Excellence in decentralized control of the network by the formation of the block structure.

The performance of the proposed method is tested in the NETSIM simulation model.

1.3/I NTELLIGENT TRANSPORTATION SYSTEM

The Intelligent Trafﬁc System (ITS) is an application that integrates electronics, computer communication technologies and management strategies. Conse- quently, this system can provide information to travelers, improve transport safety and the driving experience, maximize the use of existing transport infrastructure, reduce risks in the transport, relieve congestion, improve the transport efﬁciency and reduce air pollution. 1.3. INTELLIGENT TRANSPORTATION SYSTEM 19

Figure 1.6: Intelligent Trafﬁc System

1.3.1/A UTONOMOUSVEHICLE

An autonomous vehicle is a car that is able to sense its environment, to decide the route that takes them to their destination, to drive without human intervention [13]. In other words, we can say that autonomous vehicles are smart cars that use a variety of sensors, computer processors and cards to drive automatically. Cars with this technology have their own advantages. We can have high environmental beneﬁts such as improved fuel economy [14, 15]. By optimizing auto-roads, the necessary number of vehicles can be reduced up to 15 % [14–17]. The Platoon driving would save up to 20-30 % of fuel consumption [18]. These cars can also reduce accidents and deaths on the road which are the eighth highest cause of death worldwide in 2013 [19], reduce stress [20], decrease the need of parking space at a up to 25 % [21], reduce an average of 38 hours of travel time by person per year, and save the US economy 1.3 billion per year [22]. 20CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS

Figure 1.7: Autonomous Vehicles

There are a lot of autonomous vehicles that have already been applied in many car brands such as BMW, Mercedes-Benz and Google. The National High- way Trafﬁc Safety Administration (NHTSA) has classiﬁed the autonomous vehicle technology into 4 different levels [23]:

• Level 1: the speciﬁc control function. This includes the speciﬁc functions of automatic control, such as cruise control, guidance on the way and automatic parallel parking. Drivers are fully engaged in vehicle control and are responsible for the vehicle.

• Level 2: combined automation function. This point locates in the automation functions, such as adaptive cruise control. Drivers are responsible for monitoring the ﬂoor and should be available to control all the time. But the driver may be released from the operation of the vehicle under certain conditions.

• Level 3: limited automation. Drivers can transfer all vehicle functions under certain conditions and the vehicle can monitor changes in the road, except the conditions which need manual operation. Consequently, there is no 1.3. INTELLIGENT TRANSPORTATION SYSTEM 21

need for the driver to monitor constantly the road conditions.

• Level 4: full automation. Vehicles can perform all the functions of the control and monitoring road conditions for an entire trip without human intervention. There are many car manufacturers that have begun testing the prototypes, but it demands a long way to go to reach a level where we can absolutely trust the autonomous vehicles. The Google company has set a target that it will launch its commercial autonomous vehicle in 2018. The autonomous vehicles will have a huge impact on society and change the way with which we travel.

1.3.2/G LOBAL POSITIONING SYSTEM (GPS)

Figure 1.8: Global Positioning System (GPS)

The Global Positioning System is a satellite navigation system that provides location and time information in all weather conditions. There are 24 satellites that are orbiting the earth about 12,000 miles above the surface and make two complete 22CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS orbits every 24 hours. The GPS satellites continuously transmit digital radio signals that contain data on the satellite locations and the exact time to the receivers connected to the land. The satellites are equipped with atomic clock which is accurate within a billionth of a second. Based on this information, the receivers know how long it takes for the signal to reach the receiver on the ground. As each signal travels at the speed of light, the longer it takes for the receiver to obtain the signal, the farthest satellite is. Getting how far away a satellite is, the receiver knows that he is somewhere on the surface of an imaginary sphere centered on the satellite. By using three satellites, GPS can calculate the longitude and latitude of the receiver based on where the three spheres intersect. By using four satellites, GPS can also determine altitude. GPS is operated by the US Depart- ment of Defense (DOD). It was originally called Navigation System with Timing and Ranging (NAVSTAR). According to the different location accuracy, GPS can be divided in different levels.

• The Standard Positioning Service (SPS). Civilian users are allowed access to a broadcast code in 1 MHz which modulates a signal to FLI (1575.42 MHz). With the recent innovations receiver, this rate provides a measure- ment accuracy of the distance about 0.5 m. However, the biggest errors are slowly varying due to ionospheric refraction and selective availability (SA). SA is the largest source of error and is intentionally introduced by the Ministry of Defense for the reasons of national security. With SA, the SPS provides 100 m horizontal accuracy.

• The Standard Positioning Service (PPS). Users are granted access to a code of 10 MHz, which modulates the signal FL1 (1575.42 MHz) and fL2 (1227.60 MHz). This higher rate gives higher precision distance measure- ment and greater protection against multi-paths. Moreover, the PPS receivers use measurements at two frequencies to reduce the effect of ionospheric refraction, and the PPS users do not suffer from selective availability (SA). For these reasons, PPS provides a horizontal accuracy of about 20 m.

• The Differential Global Positioning System (DGPS). DGPS is a GPS receiver with high quality and an antenna to a known location. This reference station is a scalar correction for each GPS satellite in view. The correction is broadcast to all GPS satellite in view, but its validity decreases with time and the distance between the satellite and the reference station. If the cor- 1.3. INTELLIGENT TRANSPORTATION SYSTEM 23

rection is delivered within 10 seconds and the user is located 1000 km, the accuracy is between 2 and 10 m. Alternatively, reference station networks may be used to form a correction vector for each satellite. The validity of this correction also decreases with time, but does not decrease as rapidly as the distance. DGPS can provide an accuracy of 5 m on continental areas.

Generally, the ﬁrst level of GPS is for the civil application. The other levels are for military or special application. This GPS system is practiced in civil life widely [24–26]. It is also very useful in intelligent transport systems [27–31].

The GPS technology can help reduce the number of accidental crossovers on the road, which can make great strides in improving road safety. Transit lines can use the GPS to better track their bus services and improve performance in time. GPS technology can also facilitate the rapid response of emergency vehicles on the scene of accidents. In addition, the GPS can improve landing capacity at airports. It is clear that the applications of GPS technology can increase safety, reduce congestion and improve efﬁciency. GPS has become a powerful technology for transport. In the following, three applications are presented in detail:

• The operation ﬂeet. The main advantage of this applications is that it allows you to send the nearest vehicle to a shipping point, in view of fuel economy and time. This can be used both for the operation of commercial vehicles and the management of the emergency vehicle.

• Automatic Vehicle Location (AVL). The AVL system follows the positions of a ﬂeet of vehicles in a particular area and reports the information to a host via a communication infrastructure. The GPS system is more appropriate, because the required accuracy is in the order of centimeters. In this system, the communication system transmits the actual location at host server. The transmission contains a packet position report data, which includes the latitude and longitude of the vehicle obtained with the aid of a GPS receiver installed in the mobile vehicle.

• Dynamic navigation system. It uses real time trafﬁc information to help users traveling on the roads. This technique is also known as dynamic guide of way. At any time during the journey, the vehicle must be traveling on a segment contained in the planned route. The road follows the position of the vehicle in this segment to determine when to take appropriate policy 24CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS

measures. These actions communicate with the driver through the display units. The display information can be in terms of a series of voice to warn the driver with the approaching maneuvers.

1.3.3/W IRELESS COMMUNICATION

The wireless communication is deﬁned as the transfer of information between two or more objects that are not connected by an electrical conductor. There are several types of wireless communications.

Figure 1.9: Wireless communication

Wireless Access in Vehicular Environment (WAVE) The process of IEEE 802.11p WAVE comes from Dedicated Short Range Communications (DSRC) in the United States [32–35]. In 1999, the "Federal Communications Commis- sion (FCC)" in the United States has allocated the frequency (75MHz-5.9 GHz) to be used exclusively for communications vehicle-to-vehicle (V2V) and vehicle- to-infrastructure (V2I). The main objective is to enable public safety applications that can save lives and improve circulation. Private services are also allowed in 1.3. INTELLIGENT TRANSPORTATION SYSTEM 25 order to spread the costs of deployment and promote the rapid development and adoption of DSRC applications and technologies. The band of DSRC is a free spectrum, but under license. It is free because the FCC does not charge a fee for the use of spectrum. Yet it must not be confused with the unlicensed bands at 900 MHz, 2.4 GHz and 5 GHz which are also free in use. These unlicensed bands, which are increasingly populated with WiFi, Bluetooth and other devices, not place restrictions on technologies other than certain transmission and coexis- tence rules. The band DSRC, on other hand, is more restricted in terms of uses and technologies.

Bluetooth: Bluetooth technology is a wireless communication technology that is simple, secure, and can be found almost everywhere [36–44]. You can find the billions of devices, such as mobile phones, computers and medical devices. It is designed to replace cables for connecting devices, maintaining security at high levels. Automotive applications of Bluetooth technology began with Hands Free Profile for mobile phones in [45, 46]. The development is coordinated by the Car Working Group (CWG) and has been ongoing since 2000. The key features of Bluetooth technology are that the power and the cost is low. The Bluetooth specification defines a uniform structure for a wide range of devices to connect and communicate with each other. When two Bluetooth devices connect to each other. The structure and global acceptance of Bluetooth technology means that any Bluetooth enabled device, almost anywhere in the world can connect to other Bluetooth devices that are located near each other.

WIFI: Wireless Fidelity (WiFi) or Wireless Local Network (WLAN). These communication systems are based on 802.11 standards of the Institute of Electrical and Electronics Engineers [47–52]. The 802.11 family is composed of a number of modulation techniques that use the same basic protocol. The most popular protocols are those defined by the 802.11b and 802.11g protocols, which are amendments to the original standard. The protocol 802.11-1997 was the first wireless networking standard in the family, but the 802.11b was the first widely accepted. Other standards in the family (c-f, h, j) are service amendments and extensions or corrections to previous specifications.

Mobile networks: The most widespread mobile network technology is GSM (Global System for Mobile communication) [53–57]. GSM was designed primarily for voice telephony, but a range of support services has been deﬁned, allowing switched data connections circuits up to 9600 bit/s. Although GSM is primarily 26CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS designed for operation in the 900 MHz band, it was also adapted quickly to 1800 MHz. The introduction of GSM in North America means a further adaptation to bands 800 and 1900 MHz. For years, there are more frequency bands in the GSM to meet market demands.

Short range radio: It means an older technology that is widespread in the case of public transport [58–61]. They are installed with a short-range radio transmitter that operates on a lower ISM band (such as 433 MHz). It can broadcast an iden- tiﬁer that can be received by the tag of road trafﬁc control systems, and therefore the public transport vehicles may be given priority in intersections or edges.

1.3.3.1/C OMMUNICATION OF VEHICLE-TO-INFRASTRUCTURE

Vehicle to Infrastructure (V2I) is the wireless exchange of critical operational and safety data between vehicles and infrastructure, primarily intended to avoid or mitigate the accidents of motor vehicles, but also to enable a wide range of other safety measures and mobility [62–71]. The V2I communications apply to all types of vehicles and all roads, and transform infrastructure equipment into "intelligent infrastructure". They include algorithms that use data exchanged between vehicles and infrastructure components to perform calculations that take into account situations in advance the high risk, the resulting alerts and the warnings from the driver through speciﬁc actions. A particularly important advantage is the ability for trafﬁc signals to communicate the signal phase and timing of vehicle information to support the provision of advice and active safety warnings to drivers. Consequently, there are many literature on V2I.

Due to the limited capacity of road networks, the congestion of road traffic is one of the most serious problems in most major cities and results in a considerable number of problem [72]. This article proposes an approach where roadside facility (eg, controllers lights traffic at road intersections) provide information on the cycle of traffic lights at approaching vehicles by V2I (Infrastructure to Vehicle). Based on this information, the vehicles jointly determine their optimal speeds and other appropriate actions to cross the road junction with minimum delays, avoiding shut- down. The evaluation results show that this approach provides a significant gain in terms of average reduction in travel time.

One problem that is commonly found in transportation systems is the disruption 1.3. INTELLIGENT TRANSPORTATION SYSTEM 27 of emergency service vehicles such as ambulances and ﬁre engines, due to congestion [73]. This article has developed a simulation that provides route guidance and navigation for emergency vehicle using a cooperative communication based on V2I. The aim is to provide assistance for the emergency vehicle to effectively reach the destination by coordinating trafﬁc information. The results of the simulation show that the use of the cooperative V2I-based communication can help the emergency vehicle to reduce travel time and increase the average speed by avoiding the congested area.

Figure 1.10: Vehicle to Infrastructure

There is growing interest in energy transportation and environmental issues [74]. Next, the ability to reduce the environmental impact of vehicles is a great impor- tance for intelligent traffic management. The recent development in the vehicle to infrastructure (V2I) provides an effective means for the ongoing management of the driving. This study presents a critical part of working towards a dynamic fleet management system that takes advantage of information and communication of real-time traffic. Based on the optimal control theory, a methodological approach 28CHAPTER 1. INTRODUCTION OF TRAFFIC MODELING AND CONTROL METHODS is developed to control the environmental impacts of vehicle fleets. In particular, the trajectories of vehicles that minimize the local environmental objectives are achieved by applying a method of discrete dynamic programming. Numerical examples show that the method is effective in local applications of V2I-based traffic management and can be extended to more complex problems of optimal control in the dynamic management of the fleet.

This article describes the approach of an intelligent traffic management system based on V2I [75]. A control algorithm based on fuzzy-based control algorithm i s developed. It takes into account the comfortable distance and speed of each vehicle to avoid a collision and get a better flow of traffic. The proposed solution has been validated by a study based communication IEEE 802.11p. The whole system has shown good performance in tests in real world scenarios, firstly by computer simulation and secondly using real vehicles.

It is difficult to manage the flow of traffic in intersection, because the number of vehicles grows rapidly, [76]. This paper proposes an intelligent signaling system based on the client-server communication. First, moving vehicles send request messages to the station by using the intersection V2I. Then, the control center analyzes the request message based on the state of intersection. Finally, the center sends the decision to vehicles. As a result the average waiting time and the number of vehicles stopping at the intersection is greatly reduced.

From the literature above, we can see that the V2I is used widely in intelligent transport system. Therefore, the delay of trafﬁc, travel time, fuel consumption and pollution can be reduced.

1.3.3.2/C OMMUNICATION OF VEHICLETO VEHICLE

The communication of Vehicle to Vehicle is the wireless connection between the vehicles, from which they can exchange real-time information such as position and velocity [77–81]. The V2V is sponsored by the "United States Department of Transportation (DOT)" and the "National Highway Trafﬁc Safety Administration (NHTSA)." The V2V is also one of the most important part in the Intelligent Trans- portation System (ITS) because the use of ITS data communication from vehicle to vehicle can improve trafﬁc management. Consequently, the control center can improve safety on the road by sending a warning message to the connected ve- 1.4. CONCLUSION AND OBJECTIVES OF THE THESIS 29 hicle. Then the vehicle can take preventive measures to avoid the accident.

The paper proposes two algorithms to solve the stream allocation problem in the vehicle communications [82]. The ﬁrst is a centralized algorithm that allocates stream by keeping track of vehicles. The second is a mixed control algorithm that combines stream interference measurements based on vehicle with the centralized algorithm.

Many driver assistance systems offered by car manufacturers on the basis of data sent from sensors can automatically brake the car to avoid collisions [83]. The purpose of this article is to compare the capacity of the highway between the application of single sensors and integrated application of sensors. First, this paper presents the technology to avoid collisions. Next, the method of estimation of the road capacity is introduced. The results show that the two technologies can increase highway capacity. The increase in capacity is a function of the fraction of vehicles using the technology. If all vehicles only use sensors, the increase of the capacity of the road is about 43 %. So if all vehicles use sensors and communication vehicle to vehicle at the same time, the increase is about 273 %.

1.4/C ONCLUSIONANDOBJECTIVESOFTHETHESIS

In this chapter, we introduced the literature on conventional traffic control systems and intelligent transportation systems. In the conventional traffic control system, we present how to describe and model the transport. Then some well-know traffic control methods are presented. In the intelligent transport system, the exchange of information between intersections and vehicles are carried by wireless technologies. Therefore, there are two communication methods: V2I and V2V. Then we summarize the intelligent traffic control methods.

The objective of this thesis is to seek a cooperative control method for transportation. In the next chapter, we propose a microscopic dynamic model taking into account the dynamic movement of vehicles, where the movement of each vehicle is considered respectively. In the 3rd section, trafﬁc control methods will be presented with an exact method (Dynamic Programming) and heuristic method (Artiﬁcial Bee Colony). In the 4th chapter, many cases of simulation will be performed to present the performance of the proposed methods. Finally in the last chapter, we conclude our work.

DYNAMICMODELINGOFTRANSPORT NETWORKS

2.1/I NTRODUCTION

For each traffic control problem, there are two important parts: first one is to build a mathematical model; second one is to find an optimal algorithm to solve it. The first part is presented in this chapter. The other part will be presented in the next chapter. In the traditional mathematical model for the traffic control, it is assumed that all vehicles should arrive at intersection as soon as possible and stop before the intersection to wait for the right-of-way. The traffic flow is organized by the phase. The right-of-way is given to each phase on the basis of a sequence. Therefore, the parameter of traffic control system, such as combination of streams, the duration of each phase and the phase sequence, are optimized to reduce the length of waiting queue, the waiting time and the evacuation time, etc. The shortcomings of this model come from the fact that vehicles can not communicate with the control center in real-time. Therefore, firstly, control strategies should be based on historical data or sensors. When the real traffic environment changes suddenly, the efficiency drops sharply. On the other hand, the right-of-way shall be allocated to a group of streams, instead of being assigned to each vehicle independently.

With the improved V2I, these structures can be improved because the vehicles can exchange information with control center via the wireless communication.

Some trafﬁc control models try to modify the speed proﬁles of vehicles avoid the stop before the intersection. In other words, the vehicles can change their speed

31 32 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS profile based on the information sent by the traffic control center to increase the chance of encountering the green light. However the Fixed Time control is applied in the intersection. An example is shown in Fig. 2.1. The type of traffic

Speed

Dmax

Time red green

Figure 2.1: Modification of speed profile without adjusting the traffic control strategies control in the intersection is the fixed time control. The red velocity profile shows the movement of the vehicle without the connection with the control center. In general, the vehicle is traveling on the road before the intersection with the maximum speed. When it meets a red light, it stops before the intersection to wait for the green light. The green speed profile describes the movement of the vehicle with V2I. This vehicle can obtain the schedule of green time before reaching the intersection. Then it can adjust its speed profile to avoid unnecessary deceleration and pass the intersection with an initial velocity to reduce the crossing time at the intersection. The weakness of this model is that it does not optimize traffic control in cooperation. Therefore, some green resource time may be wasted, for example, sometimes, a little green time is given to the lane without vehicle.

Other trafﬁc control models optimize the passing sequence for each vehicle to pass the intersection with the assumption that all the vehicles should wait for the right-of-way before the intersection. In other words, the control center optimizes the passing sequence and distributes the right-of-way to each vehicle separately. However, the type of models do not modify the speed proﬁle of vehicle dynamically to minimize the evacuation time. For example, in the intersection shown in Fig. 2.2, there are three vehicles. This model assumes that all vehicles stop before the intersection as quickly as possible and wait for the right of way. There is not the phase, and each vehicle is considered independently. The security con- 2.1. INTRODUCTION 33 V3

Figure 2.2: Optimizing pass sequence without changing the vehicles’ speed profiles straint is that a vehicle can only start to cross the intersection when there is not the vehicle belonging to incompatible streams (referring to 2.2.2) in the intersection. For each vehicle, the passing time in the intersection is fixed, because each vehicle starts to pass through the intersection with zero speed. The pass sequence is optimized with the objective of the minimum evacuation time. The Figure 2.3 shows the optimal sequence with the passage time (2s) for each vehicle. The total evacuation time is 14s and the total waiting time is 1s. The weakness of this model is that it does not optimize the speed profile cooperatively before the intersection and assumes that all the vehicles must stop before the intersection. Consequently, all vehicles have a heavy acceleration near the intersection. The passing time is long, because all the vehicles begin to pass the intersection from speed zero.

In our work we combine the two models above. The control center optimizes the 34 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS

Table 2.1: Definition of notation in the second chapter Notation Definition l The index of the entrance lane, l ∈ [1, 8]. s This variable should be combined with other element to present a notation. For the variable s, it presents the sth segment of the lane in the communication area, s ∈ [1, 4]. Referring to the Fig. 2.6. Nl The total number of new vehicles on the first segment of the lane l. (j, l), (j, l, p) subscript. The jth vehicle on the lane l. This vehicle is in the pth position of the passing sequence. j ∈ [1, Nl], l ∈ [1, 8]. ETs The time for vehicle to enter the sth segment of lane, s ∈ [1, 4]. a, f superscript. The real value and the ideal value, respectively. These two superscripts should be combined with other variables. For example, the notation of ET3 means the entrance time for vehicle in the 3th segment of communication zone (intersection). And another notation of ET3 f means the ideal time of vehicle’s entering the intersection, which is also the minimal time of arriving at the intersection. lt, rt, gs subscript. It means the operation of the vehicle in the intersection: left turn, right turn and go straight, respectively. EVs The speed with which the vehicle enters into the sth segment of lane. TTs, TT The time when the vehicle spends in traveling the sth segment of lane or the entire lane. Therefore, there is the following equation: X4 TT = TT s. s=1 Ls The length of sth segment of lane. Vmax, Vmin The maximum and minimum allowed speed on the road except for the intersection. VImax The maximum allowed speed of the vehicle in the intersection. For reasons of security, the value of this variable cannot be greater than the Vmax (VImax ≤ Vmax), according to the operation in the intersection. Irow, Icolumn The row and the column of the network intersections. TD, FC The time delay and fuel consumption for one vehicle or a sequence of vehicles in the entire trip. HW The headway between two successive vehicles in the same lane. TS The time step in the simulation. Amax, Dmax The maximal acceleration and deceleration for each vehicle.

passing sequence on the basis of the period for the vehicle to arrive at the intersection, instead of a ﬁxed arrival time. Then, the vehicle adjusts the speed proﬁle 2.2. STRUCTURE OF THE STUDIED TRANSPORT NETWORK 35

Speed v1 v3 v2

Dmax Amax pt=2s time (s) 10 11 12 14

Figure 2.3: Results of the passing sequence to meet this sequence. Therefore, the road before the intersection is divided into two parts. In the ﬁrst part, the control center collects the vehicles’ information and optimizes the passing sequence. In the second part, the vehicles adjusts their speed proﬁles on the basis of the given sequence. A more detailed presentation will be provided in Section 2.4.

The rest of this chapter is organized as follows: the section 2.2 shows the structure of the intersections network; next section 2.3.1 gives the objective and constraints; the part 2.4 explains the mathematical model for trafﬁc control problem. The last section concludes this chapter. All notations used in this work are deﬁned in Tab. 2.3.

2.2/S TRUCTUREOFTHESTUDIEDTRANSPORTNET-

WORK

The Figure 2.4 shows a network including four intersections. It has two rows and two columns. In each row and column outside the network, it is assumed that there is a virtual intersection, which expresses the origin and destination of the vehicle. In other words, each vehicle enters the network from one of the virtual intersections and leaves for another. The identity of each intersection (IID) is given as a function of its position in the network. Accordingly, the routing of each vehicle (VI) can be expressed by a sequence of IID. Such as, VI = 10, 11, 12, 13 , it means, first of all, a vehicle enters the network from the first row of the left; then the vehicle passes through the two intersections of the first row; Finally, it leaves 36 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS the network in the first row to the right. 01 02

1110 12 13

20 21 22 23

31 32 Figure 2.4: Intersections network

For the reason of simplicity, it is assumed that all the intersections are identical, such as the size and the structure. With the V2I communication, each vehicle can communicate with the intersection and can be treated individually through the intersection. The communication area between an intersection and vehicles is marked by the red dotted line. Network intersections exchange vehicles in the boundary of the communication area.

2.2.1/G ENERATIONOFNEWVEHICLES

For each new vehicle on each entrance stream of the network, it contains some essential information. Its initial velocity is assumed to be equal to the maximum 2.2. STRUCTURE OF THE STUDIED TRANSPORT NETWORK 37 speed, and its destination is distributed equally to all other virtual intersections. The number of new vehicles produced in each interval is assumed to obey the Poisson Distribution, which accurately represents the actual trafﬁc system [84– 86]. The Figure. 2.5 shows an example of the distribution of vehicles. The blue dot indicates a vehicle in the time axis, and there are different numbers of vehicles in the same time interval (t1, t2, t3 ), which is considered as a random process. Then, the Poisson Distribution is generally chosen to present this process. The following formula shows the probability density function. v6 v5 v4 v3v2v1 t3 t1t2 time

Figure 2.5: Poisson Distribution

ϕxe−ϕ p(x) = (2.1) x! where p (x) denotes the probability when x new vehicles will be generated during the given time interval. The variable ϕ describes the average trafﬁc volume.

When a new vehicle is generated, it will enter the communication area, send the following information to the control center:

1. the identity of the vehicle;

2. the entrance time to the communications area.

3. the initial speed.

4. the destination of the vehicle.

5. the path and the approach in which the vehicle enters the communication.

6. the minimum entrance time at the intersection ET3 f .

2.2.2/C OMPATIBLE AND INCOMPATIBLE STREAMS

In order to explain the compatible and incompatible streams, The ﬁgure 2.6 presents one of the intersections. There are four entrances in the intersection. 38 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS lane 8 lane lane 7 lane

L4 L3 L2 L1 s=4 s=3 s=2 s=1 lane 6 lane 5 lane 1 lane 2 L1 L2 L3 L4 s=1 s=2 s=3 s=4 lane 3 lane 4 lane zone of communication Figure 2.6: Model of isolated intersection

Table 2.2: Incompatible streams ﬂow 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 2.3. OBJECTIVES OF CONTROL AND SAFETY CONSTRAINTS 39

Each entrance lane has two fixed functions in the intersection, like turn left or turn right and go straight. On each input stream, the queue of a specific traffic flow occurs. This means a portion of the input flow of vehicles. The route used by a flow of traffic to cross an intersection is called a path. A stream can apply more than one path in crossing the intersection (for example, streams 4 and 6 in Fig. 2.6.). When two paths do not crossover in the intersection, their stream are appointed as compatible because the vehicles from these stream can simultaneously go through the intersection. Otherwise, they are incompatible stream. The Figure 2.6 and Tab. 2.2 illustrate all pairs of incompatible stream, the crossing points on the path are marked with red circles, as the notation l l0 means that the streams l and l0 are incompatible.

2.3/O BJECTIVESOFCONTROLANDSAFETYCON-

STRAINTS

2.3.1/O BJECTIVESOFCONTROL

There are several criteria to measure the quality of the trafﬁc control system. Such as the time delay, the waiting time, the average waiting queue and the fuel consumption. In our work, time delay and fuel consumption are selected as criteria.

For each vehicle, its time delay TD( j,l) is defined as the time difference between actual travel time in the real traffic state and the ideal travel time in free state, as shown in the formula (2.2). Then, the optimal function is to find a passing sequence to minimize the time delay for all vehicles, as shown in the Eq. (2.3). If speed profile satisfying the minimal time delay is not unique, the one with the minimum fuel consumption is selected as the final solution.

a f TD( j,l) = TT( j,l) − TT( j,l) (2.2) X8 XNl min{ TD( j,l)} (2.3) l=1 j=1 40 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS

2.3.2/S AFETYCONSTRAINTS

In the traditional method, the security restrictions are guaranteed by applying the phases and sequences to avoid collision in the intersection. In other words, incompatible ﬂows are grouped into different phases, and the right-of-way is given to each phase based on a sequence. For example, the intersection shown in Fig.

2.6 can be divided into four phases, which can be expressed by P1, P2, P3 and P4:

P1 = (1, 5), P2 = (2, 6), P3 = (3, 7), P4 = (4, 8) (2.4)

Note that the combination of the ﬂow is not unique. The following shows another example:

P1 = (1, 2), P2 = (3, 4), P3 = (5, 6), P4 = (7, 8) (2.5)

Although there are several probabilities of phase, the one chosen is always based on the historical data and traffic demand. In other words, the phase can not be dynamically modified according to the real traffic environment. In addition, in order to share the resource of the intersection, the right-of-way is given to the different phase in the alternate way based on a sequence, such as P1 ⇒ P2 ⇒ P3 ⇒ P4. Generally, the sequence is also stable during a period of time.

This configuration of organizing the traffic flow can improve transportation. How- ever, it can not fully use every second of green time, because their time plan is based on the phase, which has the minimum limitation. Accordingly, it is possible that there is no vehicle waiting to pass through the intersection on the road with the green light, while some vehicles waiting before the red light on other roads, which leads to the loss of green time.

Therefore, in order to improve this defect, in our work, the right-of-way is sent to each vehicle respectively. That is to say, for each vehicle, the time ET3a, when it is allowed to pass the intersection, should be decided by considering the situation in all the streams. One of the constraints of security in our work is that one vehicle can not start to pass the intersection until that all the previous vehicles in the given passing sequence from the incompatible streams have completely passed the intersection, as shown in Formula (2.6). This is the ﬁrst constraint, because the vehicles from them can not pass the intersection simultaneously. This rule 2.3. OBJECTIVES OF CONTROL AND SAFETY CONSTRAINTS 41 can exploit the intersections resources more effectively and dynamically than the phase setting. For example, for the reason of readability, there are only three f f f vehicles on the road, supposing ET3(1,1) = 10, ET3(1,2) = 11, ET3(1,6) = 12 and TT3 = 2. The incompatible relation among these streams is shown in the Tab. 2.2 a and the Fig.2.6. According to the proposed method, we can get ET3(1,1,1) = 10, a a ET3(1,2,2) = 11, ET3(1,6,3) = 12 and the total travel delay is 0s. However, for the best a a a results of the phase setting, we can get ET3(1,1,1) = 10, ET3(1,2,2) = 11, ET3(1,6,3) = 13 and the total travel delay is 1s.

a a a 0 0 ET3( j,l,p) ≥ ET3( j0,l0,p0) + TT3( j0,l0,p0) (l l &&p > p ) (2.6) a a 0 0 0 ET3( j,l) − ET3( j0,l0) ≥ HW (l = l, j , j &&p > p ) (2.7)

The second constraint comes from the same lane, which is named as the Head- way. This variable means the minimal safety interval between two adjacent vehicles from the same lane, as Fig. 2.7 and formula. 2.7 show.

Distance j j' v l v l L1+L2

HW Time

Figure 2.7: Headway

The last part of constraints means the inﬂuence of lane change. The reason of lane change is the followings. Each lane has its ﬁxed operation in the intersection, such as turn left, turn right and go straight. Then, if the original lane of the 42 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS vehicle do not correspond to its operation in the intersection, it has to change the lane before entering the intersection. If two vehicles from the same approach in different lanes have to change the lane, they can not do it at the same time, and the minimal time headway has to be imposed to avoid the collision, as shown in Fig. 2.8, because their trajectories overlap. L1 L2 a new vehicle (j‘ ,1,p') ET3 (j,2,p)

new vehicle (j,2,p) a ET3 (j',1,p') a a ET3 (j',1,p')>ET3 (j,2,p)+HW (p'>p)

Figure 2.8: Lane change

2.4/M ATHEMATICAL MODEL

In order to get the optimal function in the Formula (2.3-??), For each vehicle, its trajectory is divided into four segments in the communication zone, which is pre- scribed by dashed square in Fig. 2.6. In each segment, the vehicle has different performance, such as manipulation or communication process with the control center. This is explained by the example of the straight trajectory at the stream 2 in Fig. 2.6, as follows.

The ﬁrst segment L1. Each vehicle enters this segment with the maximal road speed Vmax. Once it enters this segment, it communicates with the control center of the intersection. This center receives the information from the vehicle and marks it as new vehicle. The manipulation in this segment for the vehicle is to keep the Vmax till arriving at the second segment and to wait for receiving its allowed passing time from the control center. 2.4. MATHEMATICAL MODEL 43

The second segment L2. Once a new vehicle arrives at this segments from any input streams, a new optimal process (NOP) is activated. A NOP means that the control center makes an optimization of the passing sequence in the intersection for all the new vehicles in the first segment, in other words, the new vehicles in the first segment is the scope in each optimization, instead of that in the whole communication zone before the intersection (L1 and L2), like paper [87]. This framework can produce the following benefits.

1. the calculation time is reduced by taking a smaller number of vehicle in each optimization;

2. the traffic efficiency in the intersection can be improved. Because after receiving its passing sequence, each new vehicle is marked as old and adjust it speed profile in the second segment based on the given information.

The third segment. In this segment, each vehicle accelerates to or keeps the maximal road speed to minimize the passing time.

The fourth segment. The vehicle’s operation in this segment is similar to the third segment.

In general, in order to get the minimal time delays, the communication protocol between control center and vehicles is two-way: the former optimizes each passing sequence based on the running information of each new vehicle, then the vehicle adjusts its speed proﬁle to meet the given passing sequence. Fig. 2.9 illustrates this process.

For operation of vehicle on each segment, it is summarized as follows: first of all, in L1, the vehicle should always keep the maximal speed to wait for the right-of- way from the intersection; then, in L2, the vehicle should modify its speed based on the given sequence to optimized the fuel consumption; at last, in L3 and L4, the vehicle should accelerate to or keep the VImax/Vmax to reduce the travel time. Therefore, only the speed profile in the second segment L2 can be optimized to reduce the fuel consumption, because the control strategies of vehicles in L1, L3, and L4 are fixed (accelerate to or keep VImax/Vmax). Fig. 2.10 illustrates the above processes.

As the section 2.3.2 shows, Each vehicle is processed separately. Then the solution is to ﬁnd a sequence of passing the intersection for all the vehicles to be optimized. This sequence includes not only the order of passing the intersection, 44 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS

Vehicle Control center information from vehicles Optimize Optimize the speed the passing profile sequence passing sequence

Figure 2.9: Structure of communication but also precise time of starting to pass the intersection for all the vehicles. In other words, this sequence is formed by the ET3a.

As Formula (2.6) shows, in order to calculate this constraint, the TT3a should be get accurately. Considering the movement of the vehicle, the element of TT3a means the time spent by the vehicle in passing the intersection. Then, for each vehicle with the ﬁxed parameter (acceleration, maximal speed, etc.), this element depends mainly on the time of entering the intersection EV3 and the distance for passing the intersection2.4.1.2. However the EV3 depends on the ET3.

2.4.1/M OVEMENTOFTHEVEHICLE

2.4.1.1/R ELATIONSHIP BETWEEN MAXIMUM SPEED AND ARRIVAL TIME AT THE INTERSECTION

In order to calculate the EV3 based on the ET3, the zone of ET3 is divided into four segments, according to the threshold limit value (TLV) of EV3 (T LV =

{Vmax, Vmin, 0}), since in different part, the method of calculating EV3 is different. The T LV corresponds to key points of ET3 (KP = {KP1, KP2, KP3}). Here, it is assumed that the L2 should be long enough for the vehicle to decelerate to the Vmin from Vmax and accelerate to the Vmax (Vmax ≥ VImax) from Vmin. This rule is for the reason of readability, because the method of calculating speed proﬁle is 2.4. MATHEMATICAL MODEL 45

V(m/s) Vmax VImax Dr Ar Vr

Vmin T(s) ET1 ET2 ET3 ET4

L1 L2 L3 L4

ET1 EV1 ET3 EV3 leave time

Figure 2.10: Process of traversing a communication zone

similar when the L2 isn’t long enough.

2 2 2 2 L2 ≥(Vmin − Vmax)/(2Dmax) + (Vmax − Vmin)/(2Amax) (2.8)

Next, the ways of calculating KP = {KP1, KP2, KP3} are presented.

KP1—TLV (Vmax). The KP1 expresses the maximal time when the vehicle can arrive at the intersection with VImax. In other words, it is impossible for the vehicle to arrive at the intersection with VImax after time KP1. The vehicle control strategies for getting KP1 are as follows: ﬁrst, the vehicle decelerates to Vmin with Dmax. Second, it keeps in Vmin. Finally, it accelerates to VImax with Amax in time KP1.

KP2—TLV (Vmin). The KP2 means the maximal time of arriving at intersection with Vmin for a vehicle. That is to say, it is impossible for the vehicle to arrive at the intersection with Vmin after KP2. The vehicle control strategies for achieving KP2 are: ﬁrst of all, the vehicle decelerates to Vmin with Dmax, then it keeps this speed till arriving at the intersection.

KP3—TLV (0). KP3 presents the time, after which the vehicle must stop before 46 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS the intersection. The vehicle control strategies of obtaining KP3 are: ﬁrst of all, the vehicle decelerates to Vmin with Dmax, then it keeps Vmin, ﬁnally, it decelerates to stop before the intersection with Dmax.

After the three key points above have been calculated, the maximal EV3 in each segment can be calculated based on ET3. This proﬁle is shown in Fig. 2.11 and summarized in Tab. 2.3. V (m/s) Vmax EV3max

Vmin T (s) ET1 ET2 ET3f KP1 KP2 KP3 Figure 2.11: Proﬁle of relationship between the ET3 and the maximal EV3

KP1 = ET2 + (Vmin − Vmax)/Dmax + (VImax − Vmin)/Amax+ 2 2 2 2 (L2 − (Vmin − Vmax)/(2Dmax) − (VImax − Vmin)/(2Amax))/Vmin (2.9) 2 2 KP2 = ET2 + (Vmin − Vmax)/Dmax + (L2 − (Vmin − Vmax)/(2Dmax))/Vmin (2.10) 2 KP3 = ET2 − Vmax/Dmax + (L2 + Vmax/(2Dmax))/Vmin (2.11) p EV3 = Vmin + Amax((Vmax − Vmin)2/Dmax + 2(L2 − VminTT2)) (2.12) p EV3 = Vmin − (Vmax − Vmin)2 + 2Dmax(L2 − VminTT2)) (2.13)

2.4.1.2/R ELATIONSHIPBETWEENMINIMALPASSINGTIMEANDINITIALSPEED OFENTERINGTHEINTERSECTION

There are two factors affecting the minimal TT3. One is the length of passing the intersection L3i (i = r, s, l), which depends on the operation of vehicle, i.e., 2.4. MATHEMATICAL MODEL 47

Table 2.3: relationship between the ET3 and the maximal EV3a Interval of ET3a Range of the maximal EV3a Formulation of EV3a [ET3 f , KP1] VImax VImax (KP1, KP2] [Vmin, VImax) Eq. (2.12) (KP2, KP3) (0, Vmin] Eq. (2.13) (KP3, ∞) 0 0

going straight, turning right or left. The vehicle passes the intersection in different length, as shown in Fig.2.12. And the way of calculating this length is expressed by formulas (2.14-2.16). These methods are similar in the others streams.

3 4L3 4 3 L3 L3l

1 L3 L3s 4 1 2 L3 L3r

1 4 L3

Figure 2.12: Different lengths in passing the intersection 48 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS

L3r = πL3/8 (2.14)

L3s = L3 (2.15)

L3l = 3πL3/8 (2.16)

Another factor is EV3. First of all, the length MD should be calculated. MD means the minimal distance needed by the vehicle to accelerate from EV3 to VImax with

Amax. If the L3i is longer than MD, the vehicle accelerates to VImax and keeps it to ﬁnish the remainder L3i. Otherwise, it keeps acceleration in L3i.

MD = (VImax2 − EV32)/(2Amax) (2.17)   − (VImax EV3)/Amax+  TT3 = (L3 − (VImax2 − EV32)/(2Amax))/VImax if L3 > MD (2.18)  i i  p  2 (−EV3 + EV3 + 2AmaxL3i)/Amax if L3i ≤ MD   VImax if L3i > MD EV4 =  (2.19)  EV3 + TT3 ∗ Amax if L3i ≤ MD

2 2 TT4 = (Vmax − VImax)/Amax + (L4i − (Vmax − VImax )/(2Amax))/Vmax (2.20)

2.4.2/F UELCONSUMPTIONMODEL

In a method of optimizing the fuel consumption, it is essential to include a model of fuel consumption [88]. There is a large number of fuel consumption patterns, such as the VT comprehensive power-based oil model (VT-CPFM) [89], the virginia tech microscopic model ( VT-Micro) [90] and the vehicle line drive model [91]. In our work, the VT-Micro model is chosen, because it allows to calculate the fuel consumption by the instantaneous velocity and acceleration, instead of the average value. The VT-Micro model is expressed in the formula (2.21).

 P3 P3 (L ×vx×ay)  e x=0 y=0 (x,y) : a ≥ 0 MOE v, a  (2.21) ( ) =  P3 P3 (M ×vx×ay)  e x=0 y=0 (x,y) : a < 0

The term MOE(v, a) is the instantaneous fuel consumption in the speed v and the acceleration a. The terms Lx,y and Mx,y are regression coefﬁcients of VT-Micro. 2.4. MATHEMATICAL MODEL 49

Table 2.4: Coefﬁcients for the model VT-Micro Coefﬁcients v0 v1 v2 v3 positive (a) a0 -7.73452 2.799E-2 -2.228E-4 1.09E-06 a1 0.22946 6.8E-3 -4.402E-05 4.80E-08 a2 -5.61E-3 -7.7221E-4 7.90E-07 3.27E-08 a3 9.77E-05 8.38E-6 8.17E-07 -7.79E-09 negative (a) a0 -7.73452 2.804E-2 -2.1988E-4 1.08E-06 a1 -1.799E-2 7.72E-3 -5.219E-5 2.47E-07 a2 -4.27E-3 8.3744E-4 -7.44E-06 4.87E-08 a3 1.8829E-4 -3.387E-5 2.77E-07 3.79E-10

Here we will give an example of the VT-Micro model. According to the equation. (2.21), it requires the following variables to calculate the fuel consumption of vehicles:

• the instantaneous speed. This means that the VT-Micro model does not concern the average speed of vehicle to calculate the fuel consumption. And VT-Micro model can capture the characteristic of the speed in every second.

• the instantaneous acceleration. This variable involves the VT-Micro model considers the inﬂuence of the acceleration in the fuel consumption.

• the coefﬁcients for positive and negative acceleration, as shown in Table 2.4 [92].

We assume that the vehicle begins with the acceleration 5 (km/h/s) from zero speed, then Tab. 2.5 gives the results of the fuel consumption of the vehicle in every second. From 2.5, we can see that the fuel consumption increases with speed at a constant acceleration.

The VT-Micro is a discrete model for calculating the fuel consumption. Therefore, the continuous speed proﬁle must be discretized. In our works, each part of the time period tp is divided into dpe units based on the time step tstep. For example, the function of the fuel consumption for a vehicle in the segment s2 is given as follows. In other segments, this function is similar. 50 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS

Table 2.5: Simulation results for the VT-Micro Model Time (s) speed (km/h) acceleration(km/h/s) fuel consumption (ml) 1 5 5 1.50 2 10 5 1.82 3 15 5 2.19 4 20 5 2.58 5 25 5 3.01 6 30 5 3.48 7 35 5 3.98 8 40 5 4.50 9 45 5 5.04 10 50 5 5.60

X3 XNp FUEL = MOE(v(p,h), ap) ∗ t(p,h) (2.22) p=1 h=1

v(p,h) = v(p,h−1) + ap ∗ t(p,h) (2.23)

t(p,h) = min (tstep, tp − tstep ∗ (h − 1)) (2.24)

Np = dtp/tstepe (2.25)

where v(1,0) = v(2,0) = Vr, v(3,0) = VImax. There is always more than one speed proﬁle satisfying in (ET3 EV3). In other words, there is at least one line that can connect the point (ET2, EV3) to another point (ET3, EV3 ) under the safety constraints, because the point ( ET3, EV3) is chosen in the reasonable area, as shown in Fig. 2.11 and Tab. 2.3. Then we analyze the total possibility of speed proﬁles in different reasonable area.

• ET3 = ET3 f . In this case, there is only one possibility. The vehicle complete the entire trip with the maximal speed.

• ET3 f < ET3 < KP1. In this case, there is not a single speed proﬁles satisfying the given constraints, as different proﬁle can be achieved by choosing the variables Vr, Dr, Ar, as shown in the Fig. 2.13. To reduce the zone of Ar, this case is divided into two sub-cases depending on whether the Vr exceeds Vimax or not, as shown in equation (2.26). If the value of ET3 is

greater than the sum of ET2 and Tvi, the value of Vr must exceed Vimax, because of the constraint of distance. Then Ar should be deceleration in- 2.4. MATHEMATICAL MODEL 51

Speed Vmax

VImax

Dr Ar Vr

Time ET1 ET2 ET3 ET4 Leave

Figure 2.13: Optimized speed proﬁle

stead of acceleration. Otherwise, the value Vr may be smaller than Vimax and Ar should be accelerating rather than decelerating.

• KP1 ≤ ET3. There is only one possibility to reach the intersection with the given speed EV3 in the time ET3 .

2 2 Tvi = (Vmax − VImax)/Dmax + (L2 − (Vmax − VImax )/(2 ∗ Dmax))/(VImax) (2.26)

When there is more than one speed profile satisfying the constraints, the one on the minimum fuel consumption is selected as the final speed profile to save energy. In this article, it is found by an exhaustive search. For the reason of clarity, we make the speed profile with the following features, as shown in Fig. 2.13:

• the speed proﬁle consists of no more than three parts.

• The acceleration in the second part is always zero.

Therefore, the speed proﬁle in the second segment can be described by three variables: 52 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS

Algorithm 1: Search algorithm for the optimal fuel consumption Data: ET2, EV2, ET3, EV3; Result: Dr, Vr, Ar; f 1 if ET3 == ET3 ||ET3 ≥ KP1 then 2 There is only one appropriate speed proﬁle; 3 else 4 Calculate Tvi; 5 if ET3 < Tvi then 6 for Dr : Dmax → 0; Ar : Dmax → 0 do 7 if Dr and Ar meet the constraints of distance L2 and time TT2 then 8 Calculate fuel consumption and save the best;

9 else 10 for Dr : Dmax → 0; Ar : 0 → Amax do 11 if Dr and Ar meet the constraints of distance L2 and time TT2 then 12 Calculate fuel consumption and save the best ;

13 The best solution is saved and the process ends;

• ﬁrst part of speed proﬁle: deceleration with Dr.

• second part of speed proﬁle: constant speed with Vr.

• third part of speed proﬁle: acceleration with Ar.

The process is given in the algorithm (1) in detail.

2.4.3/C HOICEOFROUTEFOREACHVEHICLEINTHEINTERSEC- TIONNETWORK

The subsection shows the method of choosing the route for each vehicle in the network. In other words, the vehicle must choose some intersections to arrive at its destination. As shown in 2.4, for the reason of simplicity, there are only two intersections in each row and column in the network, respectively. In fact, the method introduced can be applied to a larger network.

In this network, there is a small control server in each intersection and a big control center to coordinate the small servers. The small servers gather the information from the approaching vehicles and calculate the trafﬁc volume in the current intersection. Then the control center receives this information and resent 2.4. MATHEMATICAL MODEL 53

traffic volume of server 1 server 3 ...... traffic volume of others servers server 2 traffic volume of server 1 ...... traffic volume of others servers

control center server 1 Gather information from the traffic volume of vehicles and calculate server 1 the traffic volume in intersection Select the next intersection traffic volume of and optimize the passing others servers sequence for vehicles

Figure 2.14: Structure for the exchange of information between the network and intersections it to each small server in each simulation step. In other words, the trafﬁc volume in each intersection should be updated in each simulation step. As a result, each small server can get the real-time trafﬁc volume of the other intersections. At last, each small server choose the next intersection for its vehicles based on this information and the destination of its vehicles. The Fig. 2.14 shows the above process.

Only the next intersection for the vehicle is optimized in each step, instead of a list of intersection to finish the whole trip. Because the number of vehicle in each intersection changes rapidly. For example, at first, some intersections are vacant. Then many vehicles prefer to finish their trip by passing these intersection, which may lead to traffic congestions. Therefore, in each step of choice of itinerary, the 54 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS next intersection for each vehicle is done by the following principles steps:

• the number of possible directions to the destination is calculated. The possible direction means that the vehicle always try to ﬁnd the intersection with the minimal distance of trip. If this number is unique, the vehicle takes this way. Otherwise, the next step is done to ﬁnd the best intersection.

• The intersection less congestion in the direction of vehicle is chosen. The congestion of intersection is evaluated by the total number of vehicles waiting to pass the intersection. If the itinerary with the same distance is not only one possibility, the vehicle chooses the one less congestion in order to reduce the time delay in the intersection.

As a result, the vehicle can adjust its itinerary dynamically in each intersection based on the dynamic trafﬁc condition to decrease the travel time without aug- menting the travel distance. For example, we take the vehicles which enter the intersection from the east approach to explain the above method.

In the above algorithm (2), the lines 1-8 mean the case that there is only one itinerary with the minimal travel distance and the vehicles have to choose this itinerary. The lines 9-20 present the method of choosing the next intersection with the smaller trafﬁc volume, when there are more than one itinerary having the minimal travel distance.

In order to make the algorithm to be better understood, we give some examples. The Tab. 2.7 shows the number of vehicles in each intersection and the results are presented in the Tab. 2.6. We explain the 1-6 vehicles based on the rule of minimum travel distance and the vehicles 7-8 under the rule of lower trafﬁc volume. In the vehicle 1, there is only one route VI = 23, 22, 12, 13, therefore, that vehicle must turn right at the intersection 22. The reason is similar to the 2-6 vehicles. There are two routes for the vehicle 7 to arrive at its destination: VI1 = 23, 22, 21, 11, 10 and VI2 = 23 22 12, 11 10. Because the travel volume in the intersection 12 is lower than that in the intersection 21, the vehicle 7 select the intersection 12 as its next intersection. For the vehicle 8, it is the same reason. 2.4. MATHEMATICAL MODEL 55

Algorithm 2: Algorithm for choosing the route for each vehicles entering the intersections from the east sou des Data: IID(x,y), IID(x,y); Result: Msou; des sou des sou 1 if (IIDx ≥ IIDx − 1)&&(IIDy > IIDy ) then 2 Turn left; des sou des sou 3 else if (IIDx ≥ IIDx − 1)&&(IIDy < IIDy ) then 4 Turn right; sou des 5 else if (IIDy = IIDy )|| sou des sou des 6 (IIDy = 1)&&(IIDy = 0)&&(IIDx > IIDx + 1)|| sou des sou des 7 (IIDy = Irow)&&(IIDy = Irow + 1)&&(IIDx > IIDx + 1) then 8 Turn right; 9 else sou des 10 if (IIDy > IIDy ) then sou sou 11 if (TV(x−1,y−1) > TV(x−1,y)) then 12 Go straight; 13 else 14 Turn right ; 15 else sou des 16 if (IIDy < IIDy ) then sou sou 17 if (TV(x−1,y+1) > TV(x−1,y)) then 18 Go straight; 19 else 20 Turn left ;

21 Simulation completed;

Table 2.6: Example to choose the route Input Output Vehicles IIDsou IIDcur IIDdes Operation IIDnex 1 23 22 13 Turn right 12 2 23 22 02 Turn right 12 3 22 21 31 Turn left 31 4 13 12 23 Turn left 23 5 12 11 10 Go straight 10 6 23 22 31 Go straight 21 7 23 22 10 Turn right 12 8 13 12 20 Go straight 11

Table 2.7: Volume of trafﬁc in the intersections Intersection 11 12 21 22 Travel volume 20 15 25 22 56 CHAPTER 2. DYNAMIC MODELING OF TRANSPORT NETWORKS

2.5/C ONCLUSION

This section has focused on how to build the mathematical model for traffic control problem. This model considers the communication between vehicles and the control center. This is a two-way communication. The control center optimizes the flow sequence based on the information transmitted by the vehicles, and each vehicle changes its speed profile according to the given sequence. In other words, when the control center optimizes the passing sequence, it is based on the arrival time interval at the intersection for vehicles. To calculate this range, the vehicle behavior is presented. Then for the different arrival times, the maximum arrival speed is affected due to the minimum speed limit in the road. The maximal arrival speed and the operation in the intersection decide the passing time, therefore, the problem of optimization is transformed into a sequence problem. 3

PROPOSEDCONTROLAPPROACHES

3.1/I NTRODUCTION

In order to solve the optimization problem of finding the best sequence with the minimization time delay, there are mainly two types of methods: exact and heuristics methods. The exact methods can always find the global optimal solutions for the given problems in theory, such as, the Dynamic Programming (DP) [93–96], the Branch and Bound (BB) [97–102] and the Linear Programming (LP) [103–105], etc. In general, the best solution can be always found by the exact methods. However, for some difficult problem, this kind of method takes a long time to get the best solution. And the heuristic methods are used to find the approximate solutions within a reasonable calculation time, such as the Artificial Bee Colony (ABC) [106–109], the Genetic Algorithm (GA) [110–112] and the Ant Colony Optimization (ACO) [113–115], etc. Therefore, in our works, we propose the above two kinds of methods to get the optimal sequences based on the traffic volume and size of network of intersection.

3.1.1/S OME LITERATURE RELATED TO THE EXACT METHODS

The Dynamic Programming is a type of the exact method [116]. It solves a difﬁcult problem by breaking it down into a series of simple sub-problems. Each sub- problem can be solved easier than the original problem. Finally, the initial problem is solved by using the values previously calculated from the simpler sub-problems. Therefore, there are three properties for the DP:

• Sub-overlapping problems. This means that the initial problem can be de-

57 58 CHAPTER 3. PROPOSED CONTROL APPROACHES

composed into a small space of sub-problems, instead of generating new sub-problems boundlessly during the recursive process. That is to say, the space of sub-problems should be ﬁxed and does not augment in the process of iteration.

• Sub-optimal structure. This property means that the solution to the optimal complex origin problem can be obtained by combining the optimal solution of its sub-problems.

• Based on the structure of the memory. This property means that each sub- problem is calculated only one time during the whole procedure. Then the best solution for each sub-problem is under-stored. The next time when the same sub-problem occurs in the calculation of other sub-problems, we can use the previously calculated and stored solution, instead of recalculating it. Accordingly, the computation time can be saved by sacriﬁcing a part of the storage space.

Then we will present the four general steps to solve an optimal problem by the DP, as the followings:

• Describe the mathematical formula for the optimal solution based on the given problem. We need to deﬁne a table of variables on which depends the original problem.

• Give the recursive formula for the optimal solution. In other words, we must know the relationship between all sub-problems and calculate each sub- problem. This step shows that the initial problem can be decomposed into a series of simple and relevant sub-problem.

• Calculate the value for each sub-problem. In this thesis, the ﬁtness value is the total time delay for a passing sequence of vehicles, as shown in the equation. (2.3).

• Build an optimal solution. For this step, there are some additional information necessary to add to each sub-problem in the step 2. In general, each sub-problem is assigned to a number based on the value of its parameters, in order to simplify the construction of the optimal solution. 3.1. INTRODUCTION 59

Therefore, the DP is adapted to ﬁnd the best passing sequence with the minimization time delay for vehicles to go through the intersection. Each sequence can be decomposed into many sub-problems (sub-sequences), at last the global optimal sequence can be built from all the sub-problems. Moreover, there are many related works in the literature that attempt to solve the trafﬁc control problems by DP [87, 117–122].

The document proposed by the author B.Yin [117, 123, 124] optimize the traffic lights at intersections by a forward search of Programming Dynamic with a decision tree. This algorithm considers both the fixed phase sequence and the variable phase control sequence in the traffic signals. The simulation results are compared with the Fixed Time control (FT) and the Adaptive Control (AC) in the time period to show its high efficiency and good quality.

The document proposed by the author Abbas-Turki [87] introduces a method of controlling trafﬁc lights in a simple and isolated intersection by the Dynamic Pro- gramming. Each vehicle is considered individually. The vehicle can exchange information with the intersection by the connection of V2I. Accordingly, the right- of-way can be distributed to each vehicle independently and the different types of vehicles, such as the police car and emergency vehicles, can be distinguished easily for the priority control. Simulation results show that the proposed method can reduce tremendously the evacuation time.

The document proposed by the author HH.Tsin [118] shows a road trafﬁc control in the network of intersections. Each intersection is controlled by the local controller with the Fuzzy Logic and the cooperation between the intersection is controlled by the Dynamic Programming. For example, the optimization of the green time in each phase of the cycle. The aim of this work is to achieve a cooperation control between the junctions, with the reduction in time delays. Simulation results show that the time delays can be reduced considerably, and the proposed method meets the need of real-time control.

The work proposed by the author KK.Raj [119] introduces the Eco-speed control optimized by the Dynamic Programming in several stages at the signalized intersections. The aim is to adjust the speed profile of the vehicle based on information received from the traffic control center for the optimization of the fuel consumption. Simulations based on agents show that the proposed method saves 19 % of fuel consumption and saves 32 % time of traffic near intersections. 60 CHAPTER 3. PROPOSED CONTROL APPROACHES

The document proposed by the author S.Yu [120] presents the routing problem of vehicles under the overall origin-destination pairs by the Dynamic Programming based on the value of Q (quality). The key process is to continuously optimize the route for the vehicles according to the travel time in each road section, which is updated in real time based on the trafﬁc volume. The results demonstrate that the proposed algorithm is better than the conventional method of the shortest path.

The document proposed by the author D.Teodorovic´ [125] introduces an intelligent system to control an isolated intersection. This system makes revisions of green time by combining the Neural Networks and the Dynamic Programming. The simulation results show that the proposed method can get the near optimal solution.

3.1.2/S OME LITERATURE RELATED TO THE HEURISTIC METHOD

As presented in the paper [126], with the exact methods, sometimes it is difficult for researchers to always find the global optimal solution in the complex traffic control problem, which contains the green time, phasing combination and sequence, the cycle and so on. Therefore, the heuristic methods are widely used to find a close optimal solution with the reasonable time of calculation.

The Evolutionary Algorithm (EA) is an kind of heuristic method, which is led by biological evolution, such as, production, crossover, mutation and so on. Each individual represents a candidate solution for the optimal problem. The quality of the individual is determined by the value function. There are a lot of EAs that have been applied in the optimization of trafﬁc control, such as the Genetic Algorithm (GA) [111], the Artiﬁcial Bee Colony (ABC) [106], the Ant Colony Optimization (ACO) [113], and the Particle Swarm Optimization (PSO) [127], etc.

In the literature, the Genetic Algorithm is widely applied in the control of trafﬁc lights in recent years [128–131]. In the document [128], a trafﬁc control based on GA is presented, which can get a near-optimal synchronization plan by optimizing parameters simultaneously, such as the phase sequence, green time, etc. The simulation results show that the proposed method is very effective.

The document [130] presents that the GA can be used to improve performance at the network traffic by optimizing the timing of traffic lights. The document [132] shows that the proposed method can improve the performance in the traffic net- 3.1. INTRODUCTION 61 work.

In the document [132], the authors propose an adaptive algorithm in real time to optimize the traffic signal by the genetic algorithms. This control system com- prises three major components: a model of traffic, a management system and an optimal control module with the Genetic Algorithm. All of these components work in cooperation to improve the efficiency of circulation. The simulation results prove the effectiveness of the proposed model and method.

The ACO algorithm is another evolutionary method used widely in transport. In the document [133], an optimal problem-saturated trafﬁc network is solved by the ACO. Simulation results show that the ACO is more effective than GA in the more saturated trafﬁc conditions. The authors also point out that parallel computing can be achieved in the ACO, due to its particular structure, to reduce the computing time.

The Particle Swarm Optimization (PSO) proposed by Kennedy and Eberhart [127] is a scalable method that is not widely applied in the optimal traffic control problem. However, it is possible that this method can be used in controlling the difficult traffic problem [134]. In the document proposed by Wei et al [135], the authors improve the results of the controller based on fuzzy logic in applying the PSO in the setting of its parameters. In papers [136], the optimal cycle plans are found by the PSO algorithm in microscopic traffic simulation software.

In this chapter, in order to optimize the passing sequence for the vehicles in the intersection, the DP is chosen as an example of the exact method, because the DP can avoid the recalculation of the same sub-problems comparing with other exact methods. A sequence can be easily decomposed into many sub-sequence by reducing the number of vehicle in the sequence. And the global optimal sequence can be built from the optimal sub-problems. For the example of the heuristic method, the ABC is chosen. Because, a sequence can be treated as a source, and the bees can ﬁnd the best source rapidly by exchanging the information.

First of all, we present the process of applying the DP in controlling the trafﬁc. Then the limit of the exact method is shown. Finally, the ABC method is applied to ﬁnd a near optimal solution with a more reasonable calculation time. 62 CHAPTER 3. PROPOSED CONTROL APPROACHES

3.2/E XACTMETHOD —DYNAMIC PROGRAMMING (DP)

This section presents the Dynamic Programming in the application algorithm to solve the studied problem. Based on V2I technologies, each vehicle can be processed independently. Then there is no fixed phase in the traffic control strategy. The vehicles are grouped dynamically based security constraints. The vehicles from the incompatible streams can not pass the intersection at the same time, as presented in section 2.3.2. The right-of-way is sent to each vehicle separately and each vehicle is allowed to go through the intersection as if it has the right-of-way. The order of the distribution of the right-of-way can make up a sequence. And the objective of proposed method is to find a optimal sequence with the minimization of time delay.

3.2.1/R ECURSIONFORMULAOF DP

The formulation TD(n1, ..., nl, ..., nL, ..., n8, L) shows the total delay for a passing sequence, where on the lane l, the number of vehicles included in the sequence is nl (nl ∈ [0, Nl]) and the last vehicle comes from the lane L. According to the ideas of DP, the sequence can be broken down into a series of sub-problems. In this trafﬁc control problem, the sub-sequences is get by deducting the last vehicles in the sequence. Then the total number of vehicles on each lane included in the sub-problems can be achieved. However, there are 8 possibilities for the lane on which the last vehicle allowed to pass through the intersection locates in the sub-problems. Therefore, each problem can be divided into into 8 sub-problems:

(n1, ..., nl, ..., nL − 1, ..., n8, 1), ..., (n1, ..., nl, ..., nL − 1, ..., n8, 8). Next the method of calculating the time delay for each problem based on its sub-problem is presented. The total time delay of the current passing sequence is the sum of the time delay between the last car and its corresponding previous sub-problem. Therefore, we can get the recursion formula for DP in the Eq. (3.1). In each recursion, only one vehicle is processed. The recursion does not stop until the initialization conditions that there is only one vehicle on the road (referring to 3.2.3).

0 0 0 0 0 TD(n1, ..., nl, ..., nL, ..., n8, L) = min {TD(n1, ..., nl , ..., nL0 , ..., n8, L ) + TD(nL,L)} (3.1) L0∈{1,8} 3.2. EXACT METHOD — DYNAMIC PROGRAMMING (DP) 63

0 0 where nl = nl for l , L, otherwise nL = nL − 1 for l = L, l ∈ [1, 8]. Because only the last vehicle located on the lane L is reduced to get the sub-sequences. If the Eq. (3.1) is extended, the results are presented in the equation. (3.2).

TD(n1, ..., nl, ..., nL, ..., n8, L) = min{TD(n1, ..., nl, ..., nL − 1, ..., n8, 1) + TD(nL,L);

TD(n1, ..., nl, ..., nL − 1, ..., n8, 2) + TD(nL,L);

TD(n1, ..., nl, ..., nL − 1, ..., n8, 3) + TD(nL,L);

TD(n1, ..., nl, ..., nL − 1, ..., n8, 4) + TD(nL,L);

TD(n1, ..., nl, ..., nL − 1, ..., n8, 5) + TD(nL,L);

TD(n1, ..., nl, ..., nL − 1, ..., n8, 6) + TD(nL,L);

TD(n1, ..., nl, ..., nL − 1, ..., n8, 7) + TD(nL,L);

TD(n1, ..., nl, ..., nL − 1, ..., n8, 8) + TD(nL,L); } (3.2)

The figure 3.1 illustrates the formula (3.1-3.2). For example, each lane has the following number of vehicles: 1, 2, 2, 1, 1, 2, 1, 3, respectively. There are 64 points of departure and one of them is TD(1, 0, 0, 0, 0, 0, 0, 0, 1), which means that there is only one vehicle on the road. The final point is TD(1, 2, 2, 1, 1, 2, 1, 3, ?), which shows that all vehicles are included in the passing sequence. However, we do not know which lane the last vehicle locates. Then the final point has 8 probabilities. For one of these probabilities, one problem TD(0, 2, 2, 1, 1, 2, 1, 3, 8) means that the last vehicle comes from the lane 1 and the element TD(1,1) presents the time delay for the last vehicle. The total time delay for each sub-problem is the sum of time delay between its previous sub-problem and the last vehicle. Finally, the algorithm chooses the solution with minimal time delay as the final passing sequence.

3.2.2/H ISTORICAL INFLUENCE OF EACH PROCESS OF OPTIMIZA- TIONBASEDON DP

The new vehicles enter the communication area one after another for a long time. In each optimization of passing sequence, only the vehicles located in the zone of communication can be optimized, because the intersection can get the information from the vehicle hors the zone of communication. Then, the new vehicles must be divided into different groups according to their entrance time. Each group of new vehicles corresponds to an optimal process of DP and should be optimized 64 CHAPTER 3. PROPOSED CONTROL APPROACHES

Initialisation Middle End TD(0,2,2,1,1,2,1,3,1)+TD TD(1,0,0,0,0,0,0,0,1) (1,1) TD(1,2,2,1,1,2,1,3,1) min

TD(0,2,2,1,1,2,1,3,8)+TD(1,1) TD(1,2,2,1,1,2,1,3,?) TD(1,0,0,0,0,0,0,0,8) min

TD(1,2,2,1,1,2,1,2,1)+TD(3,8) TD(0,0,0,0,0,0,0,1,8) min TD(1,2,2,1,1,2,1,3,8)

TD(1,2,2,1,1,2,1,2,8)+TD(3,8)

Figure 3.1: Example of recursion formula at the same time to get the right-of-way. After the optimal sequence is achieved for each group in the intersection, the new vehicles will receive their right-of-ways by the connection of V2I and are marked as old vehicles. If a new vehicle enters the communication area before that all the old vehicles pass the intersection, these old vehicles keep their right-of-ways, instead of recalculating the passing sequence, to avoid the sudden change of speed. Then, a new process of optimization will be executed for new vehicles. However, some old vehicles (have get the right-of-way) may be still in the zone of communication. And the inﬂuence imposed by these old vehicles should be considered. Otherwise, the potential collision can occur.

According to the security requirements in the Eq. (2.6-2.7), the following information must be recorded for each optimal process in each lane:

• The entrance time ET3 and the passing time TT3 for the last vehicle allowed to pass the intersection in the previous optimal process. Accordingly, all new vehicles must pass the intersection under this inﬂuence. This element is applied to avoid the potential collision in the intersection between the vehicles from the incompatible streams.

• The entrance time ET3 when the last vehicle, which comes from the different stream in the same approach, enters the intersection. This element avoids the potential collision caused by lane change model, as shown in Fig. 2.8.

For example, the Table. 3.1 shows the running data of the last vehicle on each 3.2. EXACT METHOD — DYNAMIC PROGRAMMING (DP) 65 lane in the previous optimal process. For simplicity, there is only one new vehicle. We assume that the new vehicle comes from the lane 1. It does not change the lane before entering the intersection. Its minimal arrival time in the intersection ET3 f is 18s. Then its allowed entrance time to pass the intersection ET3a should be 26s instead of 18s. Because the last vehicle that comes from the same lane 1 enters the intersection in the time 20s. Then the time ET3a for the new vehicle should not be smaller than the time 21s. In addition, the new vehicle should not be allowed to enter the intersection until that all the vehicles from the incompatible lanes in the previous process have crossed the intersection completely. The latest vehicle comes from the lane 8, and the new vehicle should not allowed to start to pass the intersection until the time 26s. Finally, the time of allowing to entering the intersection for the new vehicle ET3a should be 26s.

Table 3.1: Example of the historical data for the previous optimal process Lane 1 2 3 4 5 6 7 8 ET3 20 18 22 23 17 21 19 25 TT3 1 1 1 1 1 1 1 1 ET3lc 20 16 18 14 17 9 15 21

3.2.3/I NITIALIZATION OF DP

The initialization of the DP is only one vehicle on the road. In other words, the recursion stops when there is only one vehicle in the sub-problem, as shown in the Eq. (3.3). The part that sum of nl equals to 1 means that there are only one vehicle on all the lane. And nL presents the total number of vehicle on the lane L. Among all the initial sub-problems, some are not practical according to the iterative Eq. (3.1). For example, it is assumed that the first vehicle locates in the lane 1. Then there are 8 corresponding initial subproblems. Among these sub- problems, only the sub-problem TD(1, 0, 0, 0, 0, 0, 0, 0, 1) is reasonable, because it means there is a vehicle located in the way 1 and the last vehicle comes from the path 1. This is consistent with reality. The other 7 sub-problems are unreasonable, such as the sub-problem TD(1, 0, 0, 0, 0, 0, 0, 0, 2), which presents the last vehicle comes from the lane 2. However, the total number of vehicles in this lane is zero. In other words, there is no vehicle on the lane 2.Therefore, this initial sub-problem is false and should be abandoned. The time delay for the impossible sub-problem is defined as infinite (∞) to prevent the optimal global solution from choosing it. 66 CHAPTER 3. PROPOSED CONTROL APPROACHES

For reasonable initial sub-problem, its time delay should be calculated under the inﬂuence of the previous optimal process, as indicated in section 3.2.2. In general, There are 64 initial sub-problems and the number of reasonable sub-problems are only 8.

  X8  TD : n = 1 and n = 1  (nL,L) l L  l=1 TD(n1, ..., nl, ..., nL, ..., n8, L) = (3.3)  X8  ∞ : n = 1 and n = 0  l L l=1

Then the total time delay for each initial sub-problem should be calculated. How- ever, some of these sub-problems are not practical according to the iterative Eq. (3.1). For example, it is assumed that the first vehicle locates in the lane 1. Then there are 8 corresponding initial subproblems. Among these sub-problems, only the sub-problem TD(1, 0, 0, 0, 0, 0, 0, 0, 1) is reasonable, because it means there is a vehicle located in the way 1 and the last vehicle comes from the path 1. This is consistent with reality. The other 7 sub-problems are unreasonable, such as the sub-problem TD(1, 0, 0, 0, 0, 0, 0, 0, 2), which presents the last vehicle comes from the lane 2. However, the total number of vehicles in this lane is zero. In other words, there is no vehicle on the lane 2. It is contradictory to the reality. There- fore, these unreasonable initial sub-problems should be abandoned by putting an infinite time delay (∞). For reasonable initial sub-problem, its time delay should be calculated under the influence of the previous optimal process, as indicated in section 3.2.2. In general, There are 64 initial sub-problems and the number of reasonable sub-problems are only 8.

3.2.4/I NDEXOFSUB-PROBLEMS

This section presents the method of numbering all the sub-problems to make the way of ﬁnding the best solution easier. The total number of sub-problems is presented in Eq. (3.4). The formula of Nl +1 means that there is Nl +1 possibilities for the lane l, where the part of Nl expresses the total number of new vehicles on the lane l, and the additional one indicates the possibility without the vehicle on this lane. 3.2. EXACT METHOD — DYNAMIC PROGRAMMING (DP) 67

Table 3.2: Weight for each item in TD(n1, ..., nl, ..., nL, ..., n8, L) element n1 n2 n3 n4 Y8 Y8 Y8 Y8 weight (wl) 8 (Nl + 1). 8 (Nl + 1). 8 (Nl + 1). 8 (Nl + 1). l=2 l=3 l=4 l=5

element n5 n6 n7 n8 L Y8 Y8 Y8 weight (wl) 8 (Nl + 1). 8 (Nl + 1). 8 (Nl + 1). 8 1 l=6 l=7 l=8

In order to index each sub-problem, a weight wl is given to each lane l according to the total number of vehicles on each lane. In other words, a coefﬁcient is distributed to each element TD(n1, ..., nl, ..., nL, ..., n8, L) based on the total number of new vehicles on each lane Nl, as shown in the Tab. 3.2. Finally, the code of each subproblem (CS ) is the sum of each item multiplied by the corresponding coefﬁcient, as the Eq. (3.5) shows.

Y8 8 (Nl + 1); l ∈ [1, 8] (3.4) l=1 X8 CS = (nl ∗ wl) + (L ∗ 1); (3.5) l=1

For example, if the total number of new vehicles on each lane is as the following: 2, 3, 5, 4, 2, 3, 5, 2, there are 57, 600 (= 8 ∗ 3 ∗ 4 ∗ 6 ∗ 5 ∗ 3 ∗ 4 ∗ 6 ∗ 3) opportunities in total. The coefﬁcient of each lane is indicated in the Tab. (3.3).

Table 3.3: Example of the weight element n1 n2 n3 n4 weight (wl) 207360 51840(=6*8640) 8640(=5*1728) 1728(=3*567)

element n5 n6 n7 n8 L weight (wl) 576(=4*144) 144(=6*24) 24(=8*3) 8 1 68 CHAPTER 3. PROPOSED CONTROL APPROACHES

3.2.5/O PTIMIZATION PROCESS FOR THE PASSING SEQUENCE AC- CORDINGTOTHE DP

Algorithm 3: Algorithm of the whole simulation process

1 The initialization of the simulation system;

2 while the simulation does not stop do

3 Count the output vehicles from each intersection;

4 for from 1 to the total number of output vehicles do

5 if the vehicle leaves the network then

6 Save the simulation results of the output vehicle and remove it from the network;

7 else

8 Send the output vehicle to other intersections as new vehicle;

9 Generate new vehicles for each intersection;

10 Count the total number of vehicles waiting to pass each intersection;

11 Send this number to the network from each intersection;

12 Download this number in each intersection;

13 if a new vehicle comes into the second section in each intersection then

14 Optimize the itinerary for each new vehicle in each intersection, as indicated in the section 2.4.3;

15 Execute an optimal process based on DP (refering to Algorithm. 4) or ABC (refering to Algorithm. 5) to achieve a passing sequence;

16 Each new vehicle plans its speed proﬁle according to the pass sequence with the target of minimal fuel consumption, as described in section 2.4.2;

17 Mark all new vehicles as older vehicles;

18 Advance a simulation step ;

This section describes the algorithm proposed in detail by the pseudo code. First, the process simulation system is presented in the algorithm (3). This algorithm connects all the above section as a simulation system to solve the problem of trafﬁc control. Then the application of the DP algorithm to ﬁnd the optimal path sequence is shown. The search algorithm of the passing sequence by the ABC method is presented in the next section.

On the line 1, the basic parameters of the simulation system should be given, such 3.2. EXACT METHOD — DYNAMIC PROGRAMMING (DP) 69 as the size of the intersection, running time, the traffic volume and so on. In the lines 2-18, it is the body of the main loop for the simulation system. This system does not stop until the given execution time or some human interventions. During each simulation step, some vehicles may leave from an intersection and enter other intersections. Therefore, we must count the output vehicles, as shown in the line 3. In the lines 4-8, if the output vehicles arrive at their destination and leave from the network, we will record their simulation results and delete them from the network. Otherwise, they will enter another intersection as the new vehicles to reach their destination. In each input lane, the new vehicles are expected to be generated based on the Poisson Distribution, as indicated in section 2.2.1. In the lines 10-12, each intersection counts the total number of vehicles waiting to pass the intersection and shares this information with other intersections via the control center. This variable presents whether the intersection is congested. In the lines 13-17, a optimal process is activated when there is a new vehicle coming in the second segment L2 in the intersection, because only vehicles in the first segment are optimized simultaneously. Then, in the line 14, every new vehicle should choose its next intersection based on its destination and traffic conditions of other intersections, as indicated in the section 2.4.3. Then, in the line 15, an optimal process that is based DP or ABC is performed to find an optimal passing sequence to reduce the time delay. After each vehicle plans its profile of velocity in the second segment based on the passing sequence with the minimal fuel consumption. Finally, all new vehicles should be marked as older vehicles because they have got their right-of-way in the intersection. In line 18, the system goes forward by one step and the simulation time adds a time step.

The algorithm (4) has the optimal process of DP applied in each intersection to ﬁnd a passing sequence. In the line 1, the total number of new vehicles is counted to index each sub-problem. The higher this number is, the higher the sum of number of sub-problems will be. The initialization of the DP is accomplished in the line 2. We number each original sub-problem and calculate its time delay under the historical inﬂuence from the previous optimal process of DP. In the lines 3-9, the DP recursion is executed. Each sub-problem can be accessed by the loop in lines 3-4. In the line 5, the index of the current sub-problem is numbered based on the number of vehicles in each lane and the number of lane located by the last vehicle.

The 8 previous sub-problems to the current sub-problem is obtained by deleting 70 CHAPTER 3. PROPOSED CONTROL APPROACHES

Algorithm 4: Optimal process based on the algorithm of DP 1 Count the total number of new vehicles in the ﬁrst segment from each input lane Nl; 2 Calculate and index each initial sub-problems; 3 for n1, ..., n8 from 0 to N1, ..., N8 respectively do 4 for L from 1 to 8 do 5 Number current sub-problem; 6 Find his eight previous sub-problems; a 7 Calculate the ET3 for the last vehicle according to previous 8 sub-problems, respectively; 8 Calculate the time delay of the last vehicle and the current sub-problem on the basis of previous sub-problems, respectively; 9 Compare the total time delay based on the various previous sub-problems and record one with the minimal time delay for the current sub-problem;

10 Comparing the time delay in the 8 final sub-problems to find the best solution; 11 Save the historical influence of the current optimal process;

the last vehicle in the line 6. For example, in the Fig. 3.1, we assume that the current sub-problem is TD(1, 2, 2, 1, 1, 2, 1, 3, 1). Then the last vehicle locates in lane 1. Then a vehicle is removed from the lane 1 to get its 8 previous sub- problems: TD(0, 2, 2, 1, 1, 2, 1, 3, 1) , ..., TD(0, 2, 2, 1, 1, 2, 1, 3, 8). In the line 7, the time allowed to enter the intersection for the last vehicle in the current sub-problem should be calculated. For the same example, in the line 7, we should get the a ET3 for Vehicle (nL, L) under the various previous sub-problems. In the line 8, as shown in Chapter 2, the maximal EV3a is calculated based on the ET3a, referring to the Fig. 2.11. Then the TT3a can be calculated also, as shown in the Eq. (2.18). Finally, the time delay for the last vehicle and the current subproblem can be calculated on the basis of various previous sub-problems. In the line 9, we can get the different total time delay for the current sub-problem, then the minimal one is selected as the final solution. In the line 10, the 8 final sub-problems are compared according to their time delay to get the best solution. In the line 11, the historical influence should be updated based on the current best solution.

3.3/L IMITATIONS OF DP

Although the DP can always get the best solution in theory for a problem with optimal substructure, it is sometimes difficult for the computer to get the optimum 3.3. LIMITATIONS OF DP 71 solution in real time because of the huge solution space. In the DP, the computa- tional complexity increases exponentially with the augmentation of the size of the problem. For the proposed traffic control, when the traffic volume increases, the total number of vehicles treated in each optimal process increases accordingly. Therefore, the sum of the sub-problems increases rapidly. Next we give an example. It is assumed that the number of new vehicles Nl is the same in each input lane in an optimal process. The total number of sub-problem is 8 ∗ Nl based on the Eq. (3.5). Next the Nl is increased gradually to see the change in the sum of sub-problems.

Table 3.4: Sum of the sub-problems according to the variables Nl Nl 1 2 3 4 5 6 Sub-problems 2048 52488 524288 3125000 13436928 46118408

7 x 10 5

4.5

3.5

2.5

1.5 Total number of sub − problems 1

0.5

0 1 2 3 4 5 6 Number of new vehicles in each lane

Figure 3.2: Relation between the total number of the sub-problem and the total new vehicles in each lane

The results are shown in Tab. 3.4 and Fig. 3.2. From the results above, we can see that the solution space increases rapidly when the variable Nl increases. Therefore, this phenomenon leads us to ﬁnd a heuristic method to obtain a near 72 CHAPTER 3. PROPOSED CONTROL APPROACHES best solution in a reasonable calculation time. In the following section, we will present the method of Artiﬁcial Bee Colony (ABC) to achieve the above goal.

3.4/A PPROXIMATE METHOD —ARTIFICIAL BEE COLONY (ABC)

The artiﬁcial bee colony is proposed by the author D.Karaboga in 2005 [137], to solve the complex optimization problem by imitating the intelligent behavior of the swarm of bees to ﬁnd the food source.

In the behavior of the swarm of bees, the following variables are the most basic elements:

• Food sources: it means the ﬂowers to bees. The value of a food source depends on many factors. Such as its distance from the nest and its rich- ness. All the bees prefer the best food sources to gather food with less cost. However, some food sources may be rich, but a bit far away from the nest. Other sources are near the nest but with a low concentration of energy. Therefore, for the sake of simplicity, the overall proﬁtability of a food source is represented by a single quantity by combining all the related factors.

• Employed bees: They exploit a particular food source ﬁrstly. Then they re- turn to the hive with detailed information about that particular source, such as distance, direction, the ability of source, and so on. Then this information is shared with other bees by dancing. The size of employed bees is represented by the variable EBS .

• Onlooker bees: They estimate the value of food source by watching the dance of employed bees. The better value of the food source have the higher possibility to be chosen by the onlooker bees. The size of onlooker bees is represented by the variable OBS .

• Scout bee, it is transformed from a employed bee to ﬁnd a new food source randomly when this employed bee’s food source is abandoned.

Therefore, in the model of the ABC algorithm, there are three groups of bees in the bee colony: employed bees, onlooker bees and scout bee. A half of the colony 3.4. APPROXIMATE METHOD — ARTIFICIAL BEE COLONY (ABC) 73

consists employed bees and another half includes onlooker bees. For each food source, there is only one employed bee. In other words, the number of employed bees equals that of food sources around the hive. The employed bee whose food source is exhausted by the bees becomes a scout bee. The main steps of ABC are given in the algorithm(5).

Algorithm 5: Process of applying the ABC algorithm to find a passing sequence 1 The employed bees are sent to find the initial food sources; 2 while The demand is not reached do 3 The employed bees are sent to find the new food sources based on the current one and the value of these foods are calculated ; 4 The probability value for each source is calculated, based on which onlooker bees choose the food source; 5 If a source is abandoned by bees, the exploitation must be stopped for this source; 6 a scout bee is sent to randomly find a new food source ; 7 The current best food source is stored ;

8 End;

A food source is a solution to the problem to be optimized. The value of a food source corresponds to the quality of the solution. Onlooker bees choose food sources from the employed bees by using a selection process based on probability. As the value of a food source increases, the value of the probability that the food source is chosen by onlooker bees also increases. This character shows the basic properties of the positive and negative feedback in the self-organizing system. Each colony has a scout bee who is the explorer for the colony. There is no foraging advice for the explorer. Then it is possible for it to ﬁnd any type of food source. This phenomenon shows the change of basic property in the self-organizing system. Occasionally, scout bee may accidentally discovers a rich food source, which is entirely unknown. In the ABC algorithm, one of the employed bees is selected and ranked as scout bee. The selection is controlled by a control parameter called the "limit". If a solution representing a food source is not improved by a predetermined number of tests, this food source is abandoned and the employed bee is converted into an explorer. The total number of attempts to release a food source is equal to the value of "limit", which is an important parameter in the control of ABC. Therefore, in the ABC algorithm, employed bees and onlooker bees perform the operational process in the search space, and scout bee controls the exploration process. 74 CHAPTER 3. PROPOSED CONTROL APPROACHES

The section is organized as follows: ﬁrstly the encoding method of the food source is introduced. Secondly, the exchange operator for the operating process is presented. Thirdly, the selection of the roulette wheel is represented. Finally, we give all the ABC process in the application to ﬁnd a passing sequence.

3.4.1/C ODEOFSOLUTION

This section presents two methods of coding the food source. Then these method are compared to find the best. A code provides an optimal solution to the problem. For the first method, due to that the objective is to find an optimal passing sequence for each vehicle, we can express the solution by encoding each identity th of the vehicle V( j,l) (the j vehicle on the lane l), as indicated in the Eq. (3.6). The total number of code (TPP) are presented in the Eq. (3.7), which includes the feasible and infeasible solutions. Those feasible solutions are the codes respecting the rule that the overtaking is prohibited. And vice versa.

S v = {V( j,l),...}, l ∈ [1, 8]; j ∈ [0, Nl]. (3.6) X8 TPP = ( Nl)! (3.7) l=1

For the second method, the characteristic that overtaking is prohibited is taken into account. In other words, the vehicles that enter the communication area from the same approach pass the intersection based on the following rule: First in and ﬁrst out. Therefore, the sequence can be encoded on the basis of the input lane from which the vehicle enters the intersection in place of the identity of each vehicle, as indicated in the Eq. (3.8). The formula (3.9)) introduces the TPP for the second method.

S l = {li, ...}, li ∈ [1, 8]. (3.8) X8 ( Nl)! TPP l=1 (3.9) = `8 ( l=1 Nl) 3.4. APPROXIMATE METHOD — ARTIFICIAL BEE COLONY (ABC) 75

Table 3.5: Example of coding the solution second method Number ﬁrst method feasible code veh 1 veh 2 veh 3 1 V(1, 1)V(2, 1)V(1, 3) Yes 113 1 2 3 2 V(1, 1)V(1, 3)V(2, 1) Yes 131 1 3 2 3 V(1, 3)V(1, 1)V(2, 1) Yes 311 2 3 1 4 V(2, 1)V(1, 1)V(1, 3) Not 5 V(1, 2)V(1, 3)V(1, 1) Not 6 V(1, 3)V(2, 1)V(1, 1) Not

The TPP in the second method is much lower than that in the ﬁrst method by only considering the feasible solutions. Consequently, infeasible solutions can be avoided in the operations of ABC, such as initialization and evolution.

For example, to illustrate and compare the two methods above, we assume that there are only three vehicles in the intersection, and all possible sequences are shown in Tab. 3.5. Both vehicles veh1 and veh2 enter the communication area and pass the intersection from the same lane 1. The veh1 is in front of the veh2. The veh3 comes from the lane 3. For the ﬁrst method, the TTP is equal to 6, according to the Eq. (3.7). For the second method, the TPP is 3 based on the Eq. (3.9). Therefore, the method 2 is better than the method 1.

3.4.2/O PERATOR OF EVOLUTION

1 In order to evolve the food source, a Swap operation Sequence (SS = SO( j,h) + 2 n SO( j,h)... + SO( j,h)) is applied in each food source to generate the new one [101]. A sequence is composed by a series of the Swap Operators (SO( j,h)). The operation for each operator includes two steps. Firstly, two numbers of the position ( j, h) are randomly generated in the passing sequence (food source). Then, the elements in these positions switch their places to generate a new food source as shown in the Eq. (3.10). The new food source will be still valid based on the second method for encoding a solution. Next, an example is shown in Fig. 3.3 to explain the process of the Swap Operator.

so S new = S l + SO( j,h) (3.10)

For the number of operator in the Swap operation Sequence is greater than one, 76 CHAPTER 3. PROPOSED CONTROL APPROACHES 2 1 3 3 1 2 4 3 1 2 4

SO(3,7) 2 1 4 3 1 2 3 3 1 2 4

Figure 3.3: Example of SO operation the new ﬁnal passing sequence (food source) is obtained by exchanging succes- sively with each operator SO in Swap operation Sequence SS , as shown in Fig. (3.4) and Eq. (3.11).

ss 1 2 n S new = S l + SS = (((S l + SO( j,h)) + SO( j,h)) + ...SO( j,h)) (3.11)

1 2 SS=(SO (4,9), SO (2,7)) 2 1 3 3 1 2 4 3 1 2 4 1 SO (4,9) 2 1 3 1 1 2 4 3 3 2 4 2 SO (2,7) 2 4 3 1 1 2 1 3 3 2 4

Figure 3.4: Example of SS operation 3.4. APPROXIMATE METHOD — ARTIFICIAL BEE COLONY (ABC) 77

3.4.3/S ELECTIONBASEDONTHEROULETTEWHEEL

The goal of the selection process is to select randomly the individuals from the current generation to evolve the next generation. The principle is that the strongest individuals have a greater chance of survival than the lower one. It refers to the fact that the best individuals will tend to have a better chance of survival and will go ahead further. According to the total time delay in each solution (passing sequence), the Fitness Value FV is calculated in the Eq. (3.12). Be- cause the goal is to get the minimal time delay which may be equal to zero. Then, the variable FV should be the inverse of the sum between the time delay and the number 1. Then, the possibility for each FV is calculated in Eq. (3.13). The notation of P(i) presents the possibility that the ith bee is chosen. The variable Q(i) is the cumulative possibility for the ith food source.

FV(i) = 1/(1 + TD(i)) (3.12) FV(i) P(i) = (3.13) XEBS FV(i) i=1 Xi Q(i) = FV( j) (3.14) j=1

Therefore, the selector wheel is performed in the following order:

• Generate a random value RV in the range [0,1];

• If the RV is less than Q(1), the ﬁrst food source is selected;

• If the RV is less than Q(i) and is greater than Q(i − 1), the ith food source is selected;

An example is given in Tab. 3.6. If a random value is generated as 0.5, the third food source is chosen. If there is another random value 0.7, the onlooker bee chooses the third food source. 78 CHAPTER 3. PROPOSED CONTROL APPROACHES

Table 3.6: Example of the roulette wheel selection Food source TD FV P(i) Q(i) 1 12 0.08 19.65% 19.65% 2 15 0.06 15.97% 35.62% 3 8 0.11 28.39% 64.01% 4 19 0.05 12.77% 76.78% 5 10 0.09 23.22% 100%

Algorithm 6: Process of ABC

1 Initialization: (EBS ), (OBS ), limit, cycle, maxcycle, etc; 2 Generate a random passing sequence for the employed bees; 3 for cycle from 0 to maxcycle do 4 The evolution of employed bees; 5 The operation of onlooker bees; 6 The operation of scout bee;

7 The simulation is complete;

3.4.4/P ROCESS OF APPLYING ABC TO OPTIMIZE THE PASSING SEQUENCE

The algorithm (6) shows the process of applying the ABC to optimize the passing sequence. In the line 2, a initial food source (passing sequence) is randomly generated for each employed bee before the iteration. In the lines 3-6, they present

the loop body. This cycle is controlled by the maximum number of loop maxcycle. The simulation does not stop until the cycle time reaches the setting value. In the line 4, each employed bee develops a new source with a random exchange sequence, referring to Eq. (3.10), according to its current food source. Then, the value (time delay) is calculated for the new source. If the new source is worse than the old, the new source is abandoned and the value of trail adds one, which means the total unimproved cycle for the source. Otherwise, the employed bee replaces the old food source with the new one and the trail is sent to be zero. In the line 5, each onlooker bee chooses a food source by the roulette wheel. The higher the fitness value is, the greater the possibility for the food to be selected will be. Then the chosen food source must be evolved by the onlooker bee to find a new one. If the new source is better than the current one, the new one replaces the current one. Otherwise, the old one is kept and the variable trail adds one to express its total cycles without improvement. The scout bee is sent to find a new source when the trail from a food source is greater than the setting value. The 3.5. CONCLUSION 79 value of trail is chosen based on the experiment.

3.5/C ONCLUSION

In this chapter, the proposed traffic control method is introduced in both the exact method and the heuristic method. For the exact method, we use the DP to optimize the passing sequence. In this passing sequence, all the compatible streams are grouped dynamically based on the different arrival conditions of the vehicles. The DP decomposes the problem by removing the last vehicle in each sequence to get the sub-problems. Then all possible solution are included in the optimal process of DP. Therefore, in our work, the optimal passing sequence with the minimization of time delay can always be found by applying the DP. However, when the traffic volume and the size of intersection increase, the calculation time and the solution space may be very huge by applying the DP . Therefore, the heuristics method (ABC) is used to find a better solution to get an approximate solution with a smaller calculation time. The ABC imitates the behavior of bees chasing the food source. These bees can quickly find the best food source.

SIMULATION AND RESULTS

4.1/I NTRODUCTION

In this chapter, a series of simulations are performed. The simulation results are analyzed and compared with other works to show the performance of the proposed cooperative traffic model in the chapter 2 and the control methods in the chapter 3. The general measures of performance are the time delay, the fuel consumption and the calculation time under the different traffic volumes and the sizes of network. Firstly, the proposed method is applied in an isolated intersection. Then it will be used in a network of intersections to show its performance in a more complex traffic situation.

4.2/S IMULATION CASE IN AN ISOLATED INTERSECTION

In this paragraph, the simulation is executed in an isolated intersection in the different trafﬁc volumes. First of all, the ﬁrst optimal procedure of DP is presented to show its operation process detailedly. Then, results of simulation in the proposed method are compared with that under the Fixed Time Control (FT). Finally, the comparisons of the simulation results between the DP and the ABC are given.

81 82 CHAPTER 4. SIMULATION AND RESULTS

4.2.1/E XAMPLE OF APPLYING THE DYNAMIC PROGRAMMINGIN OPTIMIZING THE PASSING SEQUENCE IN DETAIL

In this section, an example of applying the DP to optimize the passing sequence is detailed. The simulation results are compared to the FT control in different traffic volumes. The simulation system is coded in C ++ 11 and runs on a desktop computer with eight processors of 3.4 GHz. All the new vehicles are generated based on the Bernoulli Distribution. If there are two possible exit paths in the same input lane, such as the input lane 2, the new vehicles are equally distributed to the exit paths. Some parameters are presented in Tab 4.1. For the FT, all input streams are divided into four phases as shown in Fig. 4.1. The green time in each phase is 20s. For example, Fig. 4.2 shows the schedule in the first 100s. In this section, there are two main parts. In the first part, simulation information in the first optimal process is presented:

• All simulation data in the ﬁrst process of DP is presented.

• The example of coding the sub-problem is introduced.

• The speed proﬁles of the ﬁrst two vehicles are presented to visually prove the differences between FT and DP.

• The reasons why the DP is better than FT are concluded.

In the second part, the total simulation results are compared between the DP and the FT under different trafﬁc volumes. The total simulation time is 1 hour.

Table 4.1: Parameters of simulation in an isolated intersection Parameters Vmax Vmin Amax Dmax TV Value 60 (km/h) 10 (km/h) 4 (km/h/s) -4 (km/h/s) 500 (veh/h/l)

Parameters L12 L23 L33 HW TS Value 100 (m) 250 (m) 20 (m) 1 (s) 0.1 (s)

4.2.1.1/S IMULATION RESULTS IN THE FIRST OPTIMAL PROCESS OF DP

All simulation results in the ﬁrst optimal process of DP are presented in Tab. 4.2. The proposed control method is better than the FT in the criteria of time delay TD and fuel consumption FC for each vehicle, which is explained by simulation 4.2. SIMULATION CASE IN AN ISOLATED INTERSECTION 83

Phase 1 Phase 2 Phase 3 Phase 4

5 6 3 8 4 1 2 7 Figure 4.1: Phase configuration in FT control results. The ET3 (entrance time in the intersection) and TT3 (travel time in the intersection) are the main factors influencing the TD. These two factors in DP are significantly lower than that in the FT, which explain that the DP is better than FT in reducing the time delay TD. For fuel consumption, the proposed method can save more energy than the FT by the following reasons:

• the travel time of vehicles in the FT is longer than that in the DP, which is proven by the TD. As a result, it expresses that the vehicle is moving at a lower average speed or even stops before the intersection in the FT control. However vehicle consumes the fuel when it stops.

• The EV3 (entrance speed in the intersection) under the proposed method is higher than that in the FT, which means that the vehicle can avoid the unnecessary decelerations before the intersection.

Table 4.2: Simulation results of all vehicles in the ﬁrst optimal process S eq ET3a TT3a EV3a TDa FC l j ET1 ET3 f DP FT DP FT DP FT DP FT DP FT DP FT 1 1 10 10 8 29 29.2 80 1.41 6.5 60 0 0.2 58.5 58.2 109.5 3 1 3 3 4 25 25.47 40 1.41 6.5 60 0 0.47 22.5 58.9 93.7 1 5 5 2 23 23.47 60 0.47 3.76 60 0 0.47 44.5 57.6 102.1 4 2 7 8 4 25 25.41 61 1.2 6 60 0 0.41 43.5 58.4 102.7 1 8 9 4 25 26.89 80 1.41 6.5 60 0 1.89 62.5 63.4 111.2 5 2 9 11 8 29 29 81 1.41 6.5 60 0 0 59.5 57.8 109.9 6 1 1 1 2 23 23 23 0.47 0.47 60 60 0 0 56.5 56.5 1 6 2 3 24 24 40 1.41 6.5 60 0 0 23.5 57.8 94.2 7 2 11 4 8 29 30.61 41 1.41 6.51 60 0 1.61 19.5 62.5 92.4 1 2 6 4 25 25 60 0.47 3.76 60 0 0 42.5 56.5 101.2 8 2 4 7 7 28 28 61 1.2 6 60 0 0 40.5 57.5 90.2

4.2.1.2/M ETHOD OF CODING THE SOLUTION IN THE FIRST OPTIMAL PROCESS

The total number of vehicles on each lane is shown on the column l and j in the Tab. 4.2. According to the Eq. (3.4), the total number of sub-problems is equal to the following value 2∗1∗2∗3∗3∗2∗3∗3∗8 = 5184. The weight for each element in the 84 CHAPTER 4. SIMULATION AND RESULTS

Traffic light Green Red Green Red Green Red Green Red Time (s) 0 20 40 60 80 100

Figure 4.2: Schedule in FT control passing sequence is indicated in the Tab. 4.3. As a result, we can label each sub- problem according to the total number of vehicles included in the sequence on each lane and the number of lane on which the last vehicle locates in the current sub-problem. After all the sub-problems are calculated, as shown in Fig. 4.3, the total time delays in the 8 final sub-problems are compared to find the best solution. Here, their places are the following numbers: 5177, ..., 5184, respectively. Then the minimal time delay is achieved in the place 5183. Therefore, the final solution is T(1, 0, 1, 2, 2, 1, 2, 2, 7), which means that the last vehicle in the optimal passage sequence is derived from the lane 7. Then the optimal path for the best solution can be found on the basis of the corresponding place of the previous sub-problem.

4.2.1.3/S OMEVEHICLES’ SPEED PROFILES IN THE FIRST OPTIMAL PROCESS OF DP

The speed profile for the first vehicle on the lane 1 is shown in Fig. 4.4. Under the FT, although the vehicle can reach the intersection quickly, it must stop and wait before the intersection because the traffic light is red on its lane. However, in the DP control, the vehicle can pass the intersection sooner and faster. Be- 4.2. SIMULATION CASE IN AN ISOLATED INTERSECTION 85

Table 4.3: Coefﬁcient in the place of coding each lane Lane 1 2 3 4 5 6 7 8 lf Coefﬁcient 2592 2592 1296 432 144 72 24 8 1

TT=6.07 TT= TT=9.93 TT=11.67 TT=6.07 TT=13.61 TT=5.05 TT=7.07

5177 5178 5179 5180 5181 5182 5183 5184

T(1,0,1,2,2,1,2,2,7)

1392 1847 2421 5153

T(0,0,1,0,0,1,0,2,8) T(0,0,1,1,0,1,1,2,7) T(0,0,1,2,1,1,1,2,5) T(1,0,1,2,2,1,1,2,1)

1379 1820 2276 2565

T(0,0,1,0,0,1,0,1,3) T(0,0,1,1,0,1,0,2,4) T(0,0,1,2,0,1,1,2,4) T(0,0,1,2,2,1,1,2,5)

88 78

T(0,0,0,0,0,1,0,1,8) T(0,0,0,0,0,1,0,0,6)

Figure 4.3: Example of achieving the optimal solution

60 FT DP

30 Vitesse (km/h)

0 0 20 40 60 80 100 120 Temps (s)

Figure 4.4: Speed proﬁle of 1th vehicle in the lane 1 cause the right-of-way is assigned to each lane dynamically instead of a ﬁxed phase. The vehicle only needs to adjust its speed slightly in order to pass the intersection quickly. Therefore, it is clear that the DP control can avoid unnecessary 86 CHAPTER 4. SIMULATION AND RESULTS deceleration.

FT 50 DP

30 Vitesse (km/h)

0 0 10 20 30 40 50 60 Temps (s)

Figure 4.5: Speed proﬁle of 1th vehicle in the lane 3

4.2.1.4/R ESULTS ANALYSIS

From the above simulation results, it is evident that the DP has a better performance in the criteria of the average time delay and the fuel consumption comparing with the FT, for the following reasons:

• There is no fixed phase configuration in the DP control. The combination of compatible streams is dynamic based on vehicles’ arrival at each optimal process. Then, the intersection resource can be shared more efficiently than that in the phase control. Such as, there are only three vehicles which are located on the lanes 1, 2 and 6, respectively. Assuming the following 1 2 6 1 2 6 parameters: tm31 = 0, tm31 = 1, tm31 = 2, tp31 = TP31 = TP31 = 2. Under the proposed method, we can obtain the following optimal results in the DP 1 2 6 control: ta31 = 0, ta31 = 1, ta31 = 2. Therefore, the total delay is zero in the DP control. In contrast, if the FT is applied, the total delay is greater than that in the DP. Here we assume that two different combinations of phase to show the total time delay. Firstly, on one hand it is assumed that lanes 1 and 2 are in the same phase. Then, the following results can be obtained: 1 2 6 tac1 = 0, tac1 = 1, tac1 = 3, which means that the total delay is 1s . On 4.2. SIMULATION CASE IN AN ISOLATED INTERSECTION 87

the other hand, it is assumed that the lanes 2 and 6 belong to the same 1 2 6 phase, which leads to the following results: tac1 = 4, tac1 = 1, tac1 = 2. As a result, the total delay is equal to 4 s in this setting of phase. Therefore, the DP control is better than the FT with the ﬁxed phase conﬁguration, by combining dynamically vehicles.

• The period of green time is not ﬁxed in the DP control and there is not the setting of phase. The right-of-way is given to each vehicle precisely on the basis of its entrance time in the communication area. In other words, the vehicle can only pass the intersection in its green time. However, in the FT, each phase has the maximal and minimal limits of period. When the number of arrival vehicles is less than predicted one, some green time will be wasted. Therefore, the DP control method can exploit more effectively the resource of intersection by avoiding the situation that the lane with the green time has no vehicle waiting to pass the intersection.

• All vehicles can start to cross the intersection with the maximal possible speed in the DP control method. Because according to given passing sequence, the DP control always tries to ﬁnd the maximal entrance speed to reduce the passing time in the intersection. Therefore, the intersection resource can be released more quickly and can be used by other vehicles as soon as possible. However, in the FT, all vehicles try to arrive at the intersection as soon as possible and wait for the green time before the intersection. Then most vehicles should start to pass the intersection from the speed zero. Therefore, the number of vehicles that can pass the intersection in a period of green time is small. Therefore, the DP control is better than the FT by releasing the intersection resources more quickly.

4.2.1.5/S IMULATION PERFORMANCE UNDER THE DIFFERENT TRAFFIC VOL- UMES

The simulation system has different performances under the different trafﬁc volumes. The main criteria are shown in Tab. 4.4, such as the time delay, fuel consumption, the calculation time and so on. The comparison of the average time delay between the DP and the FT is depicted in Fig. 4.6 under the different trafﬁc volumes. The average time delay in the DP control method increases slowly when 88 CHAPTER 4. SIMULATION AND RESULTS

40 FC 35 33.97 DP

30 27.58

15 Time delay (s)

0.11 0.73 0 100 500 Traffic volume (veh/h/l)

Figure 4.6: Comparison of average time delay under the different trafﬁc volumes

100 94.9 90.3 FC 90 DP

60 57.7 59.4

Fuel consumption (ml) 30

0 100 500 Traffic volume (veh/h/l)

Figure 4.7: Comparison of fuel consumption under the different traffic volumes the traffic volume augments, which means that there is no traffic congestion in the intersection and all vehicles can arrive at their destinations quickly. However, the average delay in the FT control is much higher than that in the DP control under the different traffic volumes, which can be explained by the average value of EV3 and TT3. The average value of EV3 in the FT control is extremely lower than that in the DP control. Then the vehicles in the FT control must spend more time to 4.2. SIMULATION CASE IN AN ISOLATED INTERSECTION 89 pass the intersection, as proved by the variable TT3. Therefore, the DP control is more effective than FT control.

Table 4.4: Performance under different trafﬁc volumes TV (veh/h/l) 100 500 DP 0.042 0.2531 Time delay (s) FT 27.58 33.97 DP 57.7 59.4 Fuel consumption (ml) FC 90.3 94.9 DP 60 60 Average EV3 (km/h) FC 14.8 8.8 DP 1.12 1.12 Average TT3 (s) FC 4.46 4.88 DP 1.1 117.8 Calculation time for optimizing time delay (ms) FC 10-4 10-4 DP 6 19 Calculation time for optimizing fuel consumption (ms) FC 2 2

4.2.2/C OMPARISON BETWEEN ABC AND DP IN AN ISOLATED IN- TERSECTION

In this section, a case of simulation cases are executed to compare the performance in controlling traffic between the ABC and the DP. In the ABC control, the number of food sources should dynamically depend on the total number of vehicles to reduce the calculation time. Otherwise, it is assumed that the number of food source is set to be a fixed value. On the one hand, if the food number is big, it works well in a high traffic volume. However, it takes more time and wastes some calculation time in the small traffic volume because the total number of vehicle needed to be optimized in each optimal process is small. Then we can only apply a small size of the food source to get the optimal solution. On the other hand, if food number is sent to be small, it works well in the small traffic volume. But it is worse in the high traffic volume. Sometimes we can not even find the most optimal solution because of the small number of food sources. Therefore, the dynamic number of food sources is a better method. The total number of food sources is equal to twice the sum of new vehicles in the first segment to be optimized for each optimal period. The number of employed bees is a half of the food sources. The others are the onlooker bees. The variable limit equals to 3. The 90 CHAPTER 4. SIMULATION AND RESULTS maximal cycle of iterations is three times of the total number of new vehicles. The other parameters are displayed in the Tab. 4.1.

120 117.8 ABC DP 100

64.9 60

Calculation time (ms) 40

24.2 20 20 14.7 8.2 9.3 5.3 2.3 1.1 0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.8: Comparison of calculation time between ABC and DP under different trafﬁc volumes

350

ABC 300 DP 295.3

253.1 250 243.4 215.8 200 165.9 150.3 150 Time delay (ms) 101.5 100 94.5

50 44.4 42.2

0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.9: Comparison of time delay between ABC and DP under different trafﬁc volumes

The comparisons between the DP and ABC are shown based on the following criteria: the average calculation time and the average time delay. Firstly, the 4.2. SIMULATION CASE IN AN ISOLATED INTERSECTION 91 results of the average calculation time for these two methods are presented in Fig. 4.8. In a traffic volume of 100 (veh/h/l), the calculation time in ABC exceeds slightly than that in DP, which means that the DP can achieve results faster than the ABC in the low traffic volume. However, when the traffic volume increases, the calculation time augments exponentially in the DP, which can be observed in Fig. 4.8. And the calculation time in the ABC develops slowly with the augmentation of the traffic volume. In the traffic volume of 500 (veh/h/l), the ABC can even save 83 % of the calculation time in comparison with DP. In other words, the ABC can get the near best results almost five times faster than the DP in a traffic volume of 500 (veh/h/l).

The comparison of the time delay between the ABC and DP is shown in the Fig. 4.9. The time delay in the ABC is a litter higher than that in the DP, because the ABC method can only achieve a near optimal solution and the DP can always get the optimal solution in theory. However, the rate of deviation in the time delay is small between these two methods. The smallest gap was 5.2 % in a traffic volume 100 (veh/h/l), because there are not many vehicles in each optimal process and it is easier for the ABC to find the optimal passing sequence. The largest difference is 16.67 % in the traffic volume of 500 (veh/h/l) because the number of vehicles increase in each optimal process. Then the total number of the possible passing sequences increases and it is more difficult for ABC to find the optimal solution. Therefore, although the gap increases with the augmentation of traffic volume, ABC may obtain a near optimal solution, with a much lower calculation time in comparison with the DP.

The Fig. 4.10 presents the comparison of fuel consumption between the ABC and the DP in an isolated intersection under the traffic volumes from 100 (veh/h/l) to 500 (veh/h/l). In the start point of traffic volume 100 (veh/h/l), the method of ABC can get the smaller deviation of fuel consumption with the DP (3.5%). The bigger difference of fuel consumption locates in the higher traffic volume 500 (veh/h/l) in the comparison (12.1 %). The fuel consumption in both control methods increases slightly with the augmentation of traffic volumes. Because the total time delay is reduced by optimizing the passing sequence for all the vehicles to pass the intersection and all of them try to find the best speed profile with the minimal fuel consumption in the second segment. Therefore, both methods can achieve a good performance in the fuel consumption. The difference between the ABC and DP in the fuel consumption is small in different traffic volumes. 92 CHAPTER 4. SIMULATION AND RESULTS

80 ABC 70 DP 66.6 63.3 64.2 61.9 59.7 59.4 60 57.7 58 58.6 59

30 Fuel consumption (ml)

0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.10: Comparison of fuel consumption between ABC and DP under the different trafﬁc volumes

4.3/S IMULATIONCASEINANETWORKOFINTERSEC-

TIONS

In this section, the proposed methods are applied in a network of intersections, as shown in Fig. 2.4. The simulation results are compared with the works [87] [138] to evaluate the performance of proposed algorithms. The initial speed for each vehicle to enter the communication area is the maximum speed. The other parameters are presented in Tab. 4.5. The units of each type of variable are: time (s), speed (m/s), acceleration (m/s2), trafﬁc volume ( veh/h/l), and length (m). The simulation results are compared with other works under different trafﬁc volumes by the following criteria: the waiting time before the intersection, the passing time in the intersection, the time delay, the entrance speed to the intersection, fuel consumption, the calculation time for the optimization of time delays and fuel consumption.

4.3.1/C OMPARISONWITHSOMEWORKS

In the ﬁrst part, we will compare the simulation results of our proposed method based on the DP with the work [87] in a network of intersection. Firstly, we will 4.3. SIMULATION CASE IN A NETWORK OF INTERSECTIONS 93

Table 4.5: Simulation parameters in a network of intersections lt rt gs Vmax Vmin VImax VImax VImax TV 14 4 0.8Vmax 0.6Vmax Vmax 500

L1 L2 L3 L4 THW tstep 100 200 10 300 1 0.1

Icow Icolumn Amax Dmax 2 2 2 -2 introduce brieﬂy the trafﬁc control method in the work [87]. Next, an example is given to show the differences between these two methods. Finally, the simulation results are compared and analyzed between the above two methods.

work 87 DP

10 Vitesse (m/s)

0 0 10 20 30 40 50 60 Temps (s)

Figure 4.11: Comparison of speed proﬁles for the second vehicle

In the work [87], the proposed method has the following process: firstly, all vehicles are trying to reach and stop at the intersection as quickly as possible to wait for the right-of-way; secondly, the vehicles’ arrival times are sent to the control center by V2I connection; Thirdly, the control center optimizes the passing sequence for all new vehicles; Finally, each vehicle passes through the intersection based on the given passing sequence from the speed zero. To illustrate the method in the work [87] and to show differences between the two methods, an example is given. For simplicity, assuming that there are only five vehicles on the road in an isolated intersection, as shown in Fig. 2.6, and their basic input data and the simulation results are given in the Tab. 4.6. Another case of simulation is 94 CHAPTER 4. SIMULATION AND RESULTS executed in the intersection network, as shown in Fig. 2.4 under a traffic volume of 50 (veh/h/l). The simulation results are presented in the Tab. 4.7. The speed profiles of the 2nd veh and the 3rd veh are shown in Fig. 4.11.

Table 4.6: Comparison of simulation results between the work [87] and the proposed DP method Vehicle veh 1 veh 2 veh 3 veh 4 veh 5 Input lane 2 6 4 4 8 Destination East West North North South ET 1 0 3 2 4 7 ET3stop Work [87] 24.9 27.9 26.9 28.9 31.9 ET3 f DP 21.4 24.4 23.4 25.4 28.4 Work [87] 3.2 3.2 3.2 3.2 3.2 TT3 DP 0.7 0.7 0.7 0.7 0.7 Work [87] 1 2 3 4 5 Sequence DP 1 3 2 4 5 Work [87] 24.9 27.9 31.1 32.1 31.9 ET3a DP 21.4 24.4 23.4 25.4 28.4 Work [87] 0 0 0 0 0 EV3 DP 14 14 14 14 14 Work [87] 50.8 50.8 55 54 50.8 TT DP 43.6 43.6 43.6 43.6 43.6 Work [87] 7.2 7.2 11.4 10.4 7.2 TD DP 0 0 0 0 0

According to the above simulation examples, the method proposed in this paper is better than that in the work [87], which refers to the following reasons:

• The variable ET3stop in the Tab. 4.6 means that the waiting time before the intersection in the work [87] because all vehicles must stop before the intersection and wait for the right-of-way to pass the intersection. This operation wastes a lot of time for vehicles, as shown by the difference between the f f variables ET3stop and ET3 . The variable ET3 means the minimal arrival time at the intersection with the maximal speed for the vehicles.

• The proposed method considers and applies the dynamic movement of the vehicle before the intersection, because in each optimal process, the passing sequence is optimized based on the reasonable period of arrival time for

each vehicle instead of a ﬁxed value ET3stop. Accordingly, it is not obligatory for vehicles to stop before the intersection. Then they can pass the intersection as soon as possible, as shown by the variable ET3a. All vehicles can 4.3. SIMULATION CASE IN A NETWORK OF INTERSECTIONS 95

Table 4.7: Simulation results in the intersection network Criteria TD Fuel EV3 TT3 stop time calculation time work [87] 12.5 0.142 0 2.88 11.1 0.016 DP 0.31 0.094 11.51 0.75 0 0.00017

start to pass the intersection earlier than that in the work [87], which means that it takes less time for the vehicles to wait for the right-of-way.

• In the proposed method, all vehicles can begin to pass the intersection with a high speed instead of the speed zero. Because in the work [87] all vehicles start to enter the intersection with the speed zero, as indicated in Tab. 4.6- 4.7 by the variable EV3, but in the proposed method, the control center always tries to ﬁnd the maximal possible input speed at the intersection for the vehicles according to their entrance time.

• In the proposed method, the passing passage ET3a is much lower than that in the work [87], because the vehicles can start to pass the intersection with a higher speed EV3. Then they can spend less time in crossing the intersection. For example, in the Tab. 4.6, the passing times for all vehicles are only 0.75 s which is four times lower than that in the work [87]. Accordingly, it allows the intersection to evacuate the vehicle more quickly. As a result, the intersection may be used by other vehicles earlier. In the simulation case in a network, the proposed method saves 74 % of the passing time in the intersection for vehicles, as indicated in the Tab. 4.7.

• According to simulation results of the waiting time before the intersection, the proposed method can help all the vehicles to pass the intersection without stopping and saves 100 % comparing with the work [87].

• Therefore, the proposed method can make all vehicles arrive at their destination with a very low time delay. In the current trafﬁc volume, the proposed method can save 97.5 % of the time delay comparing with the work [87]. These simulation results mean that the vehicles can run with a high speed near the maximal limit speed during the whole trip.

• The proposed method can reduce the fuel consumption by avoiding unnecessary acceleration and deceleration near the intersection. In the work [87], all vehicles have a huge ﬂuctuation of speed near the intersection. But in 96 CHAPTER 4. SIMULATION AND RESULTS

the proposed method, the vehicles can pass the intersection with a small adjustment of speed to enter the intersection.

• The proposed method can reduce the complexity of optimization by applying a smaller optimal zone without reducing control performance. In the work [87], the optimal range in each optimization is the entire communication area. As a result, when the dimension of intersection and the traffic volume is high, the optimal space is too huge to find the solution in real- time. Therefore, in this comparison, the traffic volume is only 50 veh/h/l in an intersection network. This performance is presented by the calculation time for the optimization of time delay.

In the second part, we show the comparison of the simulation results between the work [138] and the proposed method. Firstly, the method in the work [138] is brieﬂy presented. Then, the simulation results are compared under the trafﬁc volumes ranging from 100 (veh/h/l) to 500 (veh/h/l) in the network of intersections shown in the Fig. 2.4. The criteria to be compared are the time delay, fuel consumption, average waiting time, etc.

Speed

Vmax

Time

Trouge Tvert

Figure 4.12: Illustration of speed proﬁle of the work [138]

In the work [138], the authors present the method "Green Light Optimized Speed Advisory (GLOSA)", where vehicles can communicate with the control center by the V2I connection. The control center applies the fixed time control (FC). The 4.3. SIMULATION CASE IN A NETWORK OF INTERSECTIONS 97 vehicles can receive the schedule of traffic lights from the control center by V2I before reaching the intersection. Based on this information, the vehicles adjust their speed profile to avoid the red light in the intersection to reduce the time delay and fuel consumption. But the method in the work [138] only optimizes the speed profile without changing the control method in cooperation. The figure 4.12 shows the above process.

The "blue" speed proﬁle shows the movement of the vehicle without the assistance of GLOSA. Then the car just tries to arrive at the intersection as fast as possible and waits for the green time. The "black" speed proﬁle shows the movement of the vehicle assisted by GLOSA. The vehicle decelerates before the intersection to avoid the stop.

120 109.69 GLOSA 100 DP

60 58.05 Time delay (s) 40

23.46 20.73 21.2 20

0 0 0 0 0 0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.13: Comparison of average stop time before the intersection

As shown in Fig. 4.13, The average waiting time in the proposed method is always equal to zero under the different traffic volumes, which is much lower than that in the GLOSA. This means that all vehicles can avoid stopping before passing the intersection in the proposed method. Because the proposed method dynamically groups the compatible streams based on the incoming vehicles, and distributes the right-of-way specifically for each vehicle, instead of fixing the phases, green time, and phase sequence. Therefore, the proposed method is more effective than GLOSA to make the vehicles to avoid the stop before the intersection.

As seen in the Fig. 4.14, the average value EV3 in the proposed method is 98 CHAPTER 4. SIMULATION AND RESULTS

15 GLOSA DP 11.51 11.51 11.51 11.51 11.5

10 Speed (m/s) 5

2.99 2.69 2.28 1.96 1.59

0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.14: Comparison of average entrance speed in the intersection

3 GLOSA DP 2.54 2.46 2.5 2.39 2.27 2.31

1.5 TT3 (s)

1 0.75 0.75 0.75 0.75 0.75

0.5

0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.15: Comparison of average travel time in the intersection almost the same and very high under the various traffic volumes because all vehicles can enter the intersection with the limited speed VImax. As a result, the entrance speed EV3 in the proposed method is higher than that in the GLOSA, because the proposed method always tries to find the maximum possible speed for each vehicle based on the allowed time to enter the intersection ET3, rather than finding a possible speed, as in the GLOSA. This is a key point in reducing the 4.3. SIMULATION CASE IN A NETWORK OF INTERSECTIONS 99 passing time TT3, because every vehicle can pass the intersection faster with a high entrance speed, as shown in the Fig. 4.14. The average value TT3 is almost the same in the proposed method, because of the fact that each vehicle can keep the VImax in passing the intersection. And the average value TT3 is smaller in the proposed method than that in the GLOSA, due to the higher value of EV3 in the proposed method. Therefore, the intersection can be shared more efficiently by the traffic flows in the proposed method.

The calculation time of the simulation consists of two parts. The first part is the calculation time for the optimization of time delays. It is very low and gradually increases when the traffic volumes augment, as shown in the Fig. 4.16. This means that, in the optimization of time delay, the proposed model meets the real- time demand, and can reduce the complexity of optimization without reducing the control performance by a more cooperative control. The second part is the calculation time for the optimization of the fuel consumption, as shown in Fig. 4.17. It takes some time in the proposed method to get the optimal driving operation in the second segment, because the proposed method performs an exhaustive search to find the optimal solution with minimal fuel consumption, which can be improved by applying heuristics method, such as genetic algorithms, to achieve an approximate solution with a lower calculation time.

180 176 GLOSA 160 DP

140

120

100

81 80

Calculation time (ms) 60

40 40

20 13 0.0001 2.5 0.0001 0.0001 0.0001 0.0001 0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.16: Comparison of calculation time for the optimization of time delays

The ﬁgure 4.18 shows the comparison of average time delays between the 100 CHAPTER 4. SIMULATION AND RESULTS

700 649 GLOSA 600 DP

500

400 382 357 363 369

300 Calculation time (ms) 200

100

0 0 0 0 0 0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.17: Comparison of calculation time for the optimization of fuel consumption

GLOSA and the proposed method. Specifically, the time delay is defined as the time difference between actual travel time and ideal travel time in free flow for each vehicle, as expressed in the formula (2.2). The average time delay in the proposed method is smaller than 1 (s) under the different traffic volumes, which proves that most vehicles can travel in the free state. With the augmentation of the traffic volumes, the time delays in the proposed method increase more slowly than that in the GLOSA, because the vehicles can enter the intersection with a higher speed and spend less passing time in the proposed method, as shown in Fig. 4.14-4.15. The proposed method can save at least 98.9 % of the time delays in the traffic volume 100 (veh/h/l) and at most 99.4 % in the traffic volume 500(veh/h/l), comparing with that in the GLOSA.

The proposed method can also perform better in optimizing the fuel consumption, with the comparison of the GLOSA, which depends on the following reasons: 1) the vehicles have a smaller waiting time, as the Fig. 4.13 shows. Consequently, they can avoid the model of "stop-and-go" which wastes a lot of fuel. 2) all the vehicles look for the speed profile with the minimal fuel consumption in the second segment, instead of just finding a reasonable solution. With the augmentation of the traffic volume, the proposed method can save the fuel consumption from 28.78 % to 49.28 % with the comparison of the GLOSA. 4.3. SIMULATION CASE IN A NETWORK OF INTERSECTIONS 101

140 130.93 GLOSA 120 DP

100

80 78.46

60 Time delay (s) 43.1 39.98 40 38.97

0.43 0.58 0.64 0.71 0.8 0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.18: Comparison of Average time delay

In brief, with the augmentation of the trafﬁc volumes, the proposed method can still perform well. Therefore, the proposed model is better than the GLOSA model in the key criteria, which depends on the following reasons:

• the intersection and vehicles are operated in collaboration. This is a two- ways cooperation, instead of single adjustment that the vehicles change their speed proﬁles according to the Fixed Time Control strategy.

• The control center always tries to ﬁnd the maximal speed for all the vehicles to enter the intersection to reduce passing time in the intersection.

4.3.2/C OMPARISON BETWEEN ABC AND DP INANETWORKOF INTERSECTIONS

The sub-section presents a comparison of time delay, calculation time for the optimization of time delay and the fuel consumption between the ABC and DP in a network of intersections.

The figure 4.20 presents the comparison of time delay between the ABC and the DP in a network of intersections. In the start point of traffic volume 100 (veh/h/l), smaller difference occurs (11.63%), which is higher than that in an isolated intersection. The bigger deviation locates in the higher traffic volume 500 (veh/h/l). 102 CHAPTER 4. SIMULATION AND RESULTS

0.25

GLOSA DP 0.209 0.2

0.17

0.15 0.1397 0.141 0.144

0.1 0.095 0.095 0.095 0.096 0.096 Fuel consumption (ml/m)

0.05

0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.19: Comparison of average fuel consumption

1000 990 ABC DP 900 870 800 800 760 710 700 660 640 600 580

500 480 430 400 Time delay (ms)

300

200

100

0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.20: Comparison of time delay in a network of intersections

With the augmentation of trafﬁc volume, the time delay increases in both control methods.

The calculation time under the control method of the DP is compared with that under the ABC in the Fig. 4.21. In the smaller traffic volume (100 veh/h/l), the ABC demands the calculation time that is slightly greater than that in the DP, because of the fixed process and the maximal number of cycles. In the higher traffic 4.3. SIMULATION CASE IN A NETWORK OF INTERSECTIONS 103

180 176

ABC 160 DP

140

120

100

81 80

Calculation time (ms) 60

40 40 23 20 16.1 13 11 6.2 2.6 2.5 0 100 200 300 400 500 Traffic volume (veh/h/l)

Figure 4.21: Comparison of calculation time in a network of intersections volume (100 veh/h/l), the ABC method can nearly save 7 times of calculation time comparing with the DP. In general, for the ABC, the economic rate of calculation time increases with the augmentation of trafﬁc volume in the comparison of DP.

0.14 ABC DP 0.12 0.108 0.11 0.105 0.102 0.099 0.1 0.095 0.095 0.095 0.096 0.096

0.08

0.06 Fuel consumption (ml/m) 0.04

0.02

0 100 200 300 400 500 Traffic volume

Figure 4.22: Comparison of fuel consumption in a network of intersections

The comparison of fuel consumption between the ABC and DP is shown in the Fig. 4.22. The ABC can achieve the best results in the lower traffic volume (100 veh/h/l) comparing with the DP (5.26%). The bigger deviation between the two 104 CHAPTER 4. SIMULATION AND RESULTS methods occurs in the higher traffic volume (100 veh/h/l). With the increase of traffic volume, the difference of fuel consumption between the ABC and the DP increases slightly.

4.4/C ONCLUSION

In this chapter, a series of simulation cases are executed in an isolated intersection and in a network of intersections to present the performance of the proposed method. The simulation results are compared with the FC, the work [87] and article [138]. Firstly, the proposed method is applied in an isolated intersection. The simulation results show that the proposed method has a better performance than FC in the following criteria: time delay, fuel consumption, waiting time. Secondly, the proposed method is applied to control a network of intersections with 2 × 2. The simulation results present that the proposed method can achieve a lower value of the time delay and fuel consumption comparing with the works [87] [138] by considering dynamically movement of vehicle based on the passing sequence. GENERAL CONCLUSION

In this work, we have proposed a dynamic cooperative trafﬁc control algorithm in an isolated intersection and a network of intersections without trafﬁc lights for the reduction of time delay and fuel consumption based on the V2I connection.

The main idea of the proposed algorithm is to combine the movement of vehicle with the traffic control. In other words, our solution is to find an optimal speed profile for each vehicle to connect its origin and destination according to the optimal objectives. In fact, for each vehicle, its objective is to arrive at its destination from the origin as fast as possible with the minimal fuel consumption under the related safe constraints. Then we treat the movement in the intersection as a special part of the speed profile, due to the fact that the intersection is one of the main places where the disturbance happens frequently, and this is a conflicting place shared by the vehicles from different incompatible streams. In other words, from the view of speed profile, the intersection is one of the most complicated places.

First of all, we explain the structure of optimal objectives before developing the traffic model and control methods. In our works, the objective of minimizing the time delay has the priority over that of fuel consumption, which is suitable for the case of finishing the entire trip with the minimal fuel consumption without sacrificing the travel time. That is to say, the objectives are divided into two levels. The time delay has a higher level than the fuel consumption. Therefore during the process of modeling and controlling the traffic, first of all, only the time delay is considered. Then if the speed profile satisfying the minimal time delay is not unique, the one with the lowest fuel consumption is found and taken as the final optimal solution.

According to the above structure of the optimal objectives, ﬁrst of all, we only consider the time delay in modeling and controlling of trafﬁc. Therefore, in order to get the minimal time delay, the vehicle should move as fast as possible. The ideal situation for the vehicle is to march always with the maximal allowed speed during the overall trip, and the time delay equals to zero. However, vehicles can not run always in the maximal speed because of the existence of intersections.

105 106 General Conclusion

Each vehicle negotiates with each other to get the time space to pass the intersection without the trafﬁc light. A time space means a period of time when the vehicle can use the resource of intersection. A time space includes two elements: the start point of time space and the length of time space. The former means the time when the vehicle is allowed to enter the intersection. The latter represents the period which the vehicle spends to pass the intersection. In fact, according to the objective of minimal time delay, the latter depends on the former absolutely under the given trafﬁc framework, such as the maximal acceleration of vehicle and allowed speed on the road. Because the latter depends on the following two elements: the maximal speed of entering the intersection and the driving strategy in the intersection. The higher this entrance speed is, the less time is needed by the vehicle to accelerate to the maximal speed in the intersection. In order to minimize the running time in the intersection, the optimal strategy for the vehicle is to accelerate to the maximal speed or keep in the maximal speed. Further- more the maximal speed of entering the intersection depends on the start point of time space (refers to 2.4.1.1) because of the constraint of minimal allowed speed. Therefore, the minimal time delay for each vehicle depends on its start point of time space in the intersection. And the optimal problem can be transformed into the optimization of passing sequence in entering the intersection for all the vehicles.

In order to find the optimal sequence, both the exact algorithm and the heuristic algorithm are applied in our works. For the former, we choose the Dy- namic Programming (DP) because the optimization of passing sequence satis- fies the optimal structure and iteration by deleting the last vehicle in the each sub-sequence. In other words, the final optimal sequence problem is divided into the sub-problems (passing sequences) by cutting the last vehicle. Then the time delay of each sub-problem equals to the sum of the time delay of its previous sub-problem and that of the last vehicles. The DP can always find the optimal solution (sequence). However the space of sub-problems and the calculation time increase hugely and rapidly with the augment of total number of vehicles. There- fore, the latter is applied to find a near optimal solution with a more reasonable calculation time. We choose the Artificial Bee Colony (ABC) as the heuristic algorithm in finding the optimal passing sequence. A passing sequence can be treated as a source of food for the bees. There are three types of bees: employed bees, onlooker bees, scout bee. The employed bee finds a random source of 107 food. The onlooker bee chooses one of foods based on the dance of employed bees according to the value of the food. The scout bee finds a random food during the iteration.

After getting the time space, each vehicle has to plan its speed profile to meet this request. Then first of all, the division of communication zone is explained. The whole zone is divided into four parts. The first and second parts locate before the intersection. The third part is the intersection. The fourth is the zone after the intersection. In the first part, all the vehicles keep the maximal speed. Only the vehicles locating in this part belong to the optimal range, for the sake of minimizing the total number of vehicles in each optimization. The second part is used to adjust the vehicles’ speed based on the given time space to pass the intersection with the objective of minimal fuel consumption, because of the fact that only in this part, the total number of speed profile satisfying the given time space maybe greater than one. In the third part, the vehicle should accelerate or keep the maximal speed to minimize the passing time. It is the same reason for the fourth part.

The simulations are executed in an isolated intersection and a network of intersections respectively under different traffic volumes. Firstly, the simulation is executed in an isolated intersection and the results are compared with the Fixed Time Control (FT), which shows that the proposed DP algorithm can achieve a better performance comparing with the FT in the criteria, such as the time delay, fuel consumption, waiting time. However, when the traffic volume and the size of intersection increase, the calculation time to get the passing sequence by the DP with the minimization of time delay augment rapidly. Because the DP is an exact method, and all the possible sub-problem are calculated to get the global optimal solution. Then the heuristic method (ABC) is applied and the simulation results are compared with the exact method (DP). The proposed ABC algorithm can save 83% of calculation time with a deviation of 16.67% in the traffic volume 500 (veh/l/h) in the comparison with the proposed DP algorithm. Which means that the ABC method can find a solution close to the global one with the small calculation time.

Secondly, the simulation is executed in a network of intersections under the traffic volumes from 100 (veh/l/h) to 500 (veh/l/h). The simulation results are compared with the works [87] [138]. The proposed method is better than the work in [87] to reduce the time delay, the waiting time, and so on. For the waiting time, all 108 General Conclusion the vehicle can pass the intersection without stop before the intersection in the proposed method. However, in the work [87], all the vehicles have to stop before the intersection to wait for right-of-way. As a result, all the vehicles have some huge deceleration and acceleration near the intersection. Moreover, the vehicles in the proposed method can pass the intersection with a higher speed than that in the work [87] to reduce the travel time in the intersection. As a result, the proposed method can save 94.5% of the time delay and 33.8% of the fuel consumption comparing with the work [87]. Another simulation case in the network is compared with the work [138]. For the stop time, the proposed method help all the vehicles to avoid the stop before the intersection by dynamically distributer the right-of- way to each vehicle, in the comparison with the GLOSA. The proposed method can also make the vehicle to enter the intersection earlier and faster than the GLOSA, by applying a cooperative traffic model. Therefore, the proposed method DP can save at least 98.9 % of the time delays in the traffic volume 100 (veh/h/l) and at most 99.4% in the traffic volume 500 (veh/h/l), in the comparison with the GLOSA. For the fuel consumption, the proposed method DP can save maximally 49.28% comparing with the GLOSA. The last simulation case is done between the exact method DP and the heuristic method ABC. The method ABC can get a solution with 19.19% de difference comparing with the results achieved by the DP in the traffic volume 500 (veh/h/l). The difference of fuel consumption in this traffic volume is about 12.73% between these two methods. However, the ABC can save about 7 times of the calculation time in the comparison with the DP in the traffic volume 500 (veh/h/l). Therefore, the ABC can get a near optimal solution by consuming less calculation time.

In conclusion, we proposed a cooperative trafﬁc model to reduce the time delay and fuel consumption for the vehicles based on the communication of V2I. The simulation results are compared with other works and show the good performance of the proposed model and methods.

FUTURERESEARCH

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1.1 Headway ...... 7

1.2 Flow of vehicles ...... 7

1.3 Density ...... 8

1.4 Fundamental diagram of trafﬁc ...... 9

1.5 Car following ...... 11

1.6 Intelligent Trafﬁc System ...... 19

1.7 Autonomous Vehicles ...... 20

1.8 Global Positioning System (GPS) ...... 21

1.9 Wireless communication ...... 24

1.10 Vehicle to Infrastructure ...... 27

2.1 Modification of speed profile without adjusting the traffic control strategies ...... 32

2.2 Optimizing pass sequence without changing the vehicles’ speed proﬁles ...... 33

2.3 Results of the passing sequence ...... 35

2.4 Intersections network ...... 36

2.5 Poisson Distribution ...... 37

2.6 Model of isolated intersection ...... 38

2.7 Headway ...... 41

2.8 Lane change ...... 42

2.9 Structure of communication ...... 44

2.10 Process of traversing a communication zone ...... 45

2.11 Proﬁle of relationship between the ET3 and the maximal EV3 ... 46

123 124 LIST OF FIGURES

2.12 Different lengths in passing the intersection ...... 47

2.13 Optimized speed proﬁle ...... 51

2.14 Structure for the exchange of information between the network and intersections ...... 53

3.1 Example of recursion formula ...... 64

3.2 Relation between the total number of the sub-problem and the total new vehicles in each lane ...... 71

3.3 Example of SO operation ...... 76

3.4 Example of SS operation ...... 76

4.1 Phase conﬁguration in FT control ...... 83

4.2 Schedule in FT control ...... 84

4.3 Example of achieving the optimal solution ...... 85

4.4 Speed proﬁle of 1th vehicle in the lane 1 ...... 85

4.5 Speed proﬁle of 1th vehicle in the lane 3 ...... 86

4.6 Comparison of average time delay under the different trafﬁc volumes 88

4.7 Comparison of fuel consumption under the different trafﬁc volumes 88

4.8 Comparison of calculation time between ABC and DP under different trafﬁc volumes ...... 90

4.9 Comparison of time delay between ABC and DP under different trafﬁc volumes ...... 90

4.10 Comparison of fuel consumption between ABC and DP under the different trafﬁc volumes ...... 92

4.11 Comparison of speed proﬁles for the second vehicle ...... 93

4.12 Illustration of speed proﬁle of the work [138] ...... 96

4.13 Comparison of average stop time before the intersection ...... 97

4.14 Comparison of average entrance speed in the intersection . . . . . 98

4.15 Comparison of average travel time in the intersection ...... 98

4.16 Comparison of calculation time for the optimization of time delays . 99 LIST OF FIGURES 125

4.17 Comparison of calculation time for the optimization of fuel consumption ...... 100

4.18 Comparison of Average time delay ...... 101

4.19 Comparison of average fuel consumption ...... 102

4.20 Comparison of time delay in a network of intersections ...... 102

4.21 Comparison of calculation time in a network of intersections . . . . 103

4.22 Comparison of fuel consumption in a network of intersections . . . 103

LISTOF TABLES

2.1 Deﬁnition of notation in the second chapter ...... 34

2.2 Incompatible streams ...... 38

2.3 relationship between the ET3 and the maximal EV3a ...... 47

2.4 Coefﬁcients for the model VT-Micro ...... 49

2.5 Simulation results for the VT-Micro Model ...... 50

2.6 Example to choose the route ...... 55

2.7 Volume of trafﬁc in the intersections ...... 55

3.1 Example of the historical data for the previous optimal process . . 65

3.2 Weight for each item in TD(n1, ..., nl, ..., nL, ..., n8, L) ...... 67 3.3 Example of the weight ...... 67

3.4 Sum of the sub-problems according to the variables Nl ...... 71 3.5 Example of coding the solution ...... 75

3.6 Example of the roulette wheel selection ...... 78

4.1 Parameters of simulation in an isolated intersection ...... 82

4.2 Simulation results of all vehicles in the ﬁrst optimal process . . . . 83

4.3 Coefﬁcient in the place of coding each lane ...... 85

4.4 Performance under different trafﬁc volumes ...... 89

4.5 Simulation parameters in a network of intersections ...... 93

4.6 Comparison of simulation results between the work [87] and the proposed DP method ...... 94

4.7 Simulation results in the intersection network ...... 95

127

LISTOF DEFINITIONS

l: The index of the entrance lane, l ∈ [1, 8]. s: This variable should be combined with other element to present a notation. For the variable s, it presents the sth segment of the lane in the communication area, s ∈ [1, 4]. Referring to the Fig. 2.6.

Nl: The total number of new vehicles on the ﬁrst segment of the lane l. (j, l), (j, l, p): subscript. The jth vehicle on the lane l. This vehicle is in the pth 1 position of the passing sequence. j ∈ [1, Nl ], l ∈ [1, 8]. ETs: The time for vehicle to enter the sth segment of lane, s ∈ [1, 4]. a, f: superscript. The real value and the ideal value, respectively. These two superscripts should be combined with other variables. For example, the notation of ET3 means the entrance time for vehicle in the 3th segment of communication zone (intersection). And another notation of ET3 f means the ideal time of vehicle’s entering the intersection, which is also the minimal time of arriving at the intersection. lt, rt, gs: subscript. It means the operation of the vehicle in the intersection: left turn, right turn and go straight, respectively. EVs: The speed with which the vehicle enters into the sth segment of lane. TTs, TT: The time when the vehicle spends in traveling the sth segment of lane X4 or the entire lane. Therefore, there is the following equation: TT = TT s. s=1 Ls: The length of sth segment of lane.

Vmax, Vmin: The maximum and minimum allowed speed on the road except for the intersection.

VImax: The maximum allowed speed of the vehicle in the intersection. For reasons of security, the value of this variable cannot be greater than the Vmax (VImax ≤ Vmax), according to the operation in the intersection.

Irow, Icolumn: The row and the column of the network intersections. TD, FC: The time delay and fuel consumption for one vehicle or a sequence of

129 130 LIST OF DEFINITIONS vehicles in the entire trip. HW: The headway between two successive vehicles in the same lane. TS : The time step in the simulation.

Amax, Dmax: The maximal acceleration and deceleration for each vehicle.

(n1, ..., nl, ..., nL, ..., n8, L): A passing sequence. The number of vehicles included in the sequence is nl (nl ∈ [0, Nl]) on the lane l. The last vehicle comes from the lane L (L ∈ [1, 8]).

CS : The code (label) of each sub-problem. wl: The weight for each lane in the calculation of code of the sub-problem.

S v: The sequence based on each vehicle’s identity.

S l: The sequence based on each vehicle’s input lane in the intersection. TPP: The total number of passing sequence. Document generated with LATEX and: the LATEX style for PhD Thesis created by S. Galland — http://www.multiagent.fr/ThesisStyle the tex-upmethodology package suite — http://www.arakhne.org/tex-upmethodology/ Abstract:

The traffic congestion is one of the most serious problems limiting the improvement of standing of life. The intersection is a place where the jams occur the most frequently. Therefore, it is more effective and economical to relieve the problem of the heavy time delay by ameliorating the traffic control strategies, instead of extending the infrastructures. The proposed method is a cooperative modeling to solve a problem of reducing traffic delays and decreasing fuel consumption simultaneously in a network of intersections without traffic lights, where the cooperation is executed based on the connection of Vehicle- to-Infrastructure (V2I). This resolution of the problem contains two main steps. The first step concerns the itinerary of which intersections are chosen by vehicles to arrive at their destination from their starting point. The second step is related to the following proposed cooperative procedures to allow vehicles to pass through each intersection rapidly and economically: on one hand, according to the real- time information sent by vehicles via V2I in the edge of the communication zone, each intersection applies Dynamic Programming (DP) or Artificial Bee Colony (ABC) to cooperatively optimize the sequence with minimal time delay so that the vehicles may pass the intersection under the relevant safety constraints; on the other hand, after receiving this sequence, each vehicle finds the optimal speed profiles with the minimal fuel consumption by an exhaustive search. A series of simulation are executed under different traffic volume to present the performance of proposed method. The results are compared with other control methods and research papers to prove the our new traffic control strategy.

Keywords: Intelligent Trafﬁc Systems, Communication Vehicle-to-Infrastructure, Network of Intersections, Dynamic Programming,

Artiﬁcial Bee Colony

Résumé :

La congestion du trafic dans nos villes est un problème qui entrave la qualité de vie. L’intersection est un endroit où les congestions se produisent le plus fréquemment. Par conséquent, au lieu d’étendre les infrastructures, il serait plus intéressant économiquement de s’ocupper de la résolution du problème des retards en développant les stratégies de contrôle de la circulation. Les travaux de cette thèse concerne l’étude des intersections dites « intelligentes » dépourvues de feux de signalisation, et où la coopération est réalisée à partir de la communication véhicule-infrastructure (V2I). L’objectif étant de proposer une modélisation coopérative de ces intersections visant à réduire à la fois les temps de retards et la comsommation de carburant. La méthode de résolution du problème comporte deux volets principaux. Le premier volet concerne l’itinéraire devant être choisi par les véhicules pour arriver à leur destination à partir d’un point de départ. Le deuxième volet étant les procédures coopératives proposées afin de permettre aux véhicules de passer rapidement et économiquement à travers chaque intersection. D’une part, selon les informations envoyées en temps réel par les véhicules via la communication V2I à l’intérieur d’une zone de communication, chaque intersection exécute un algorithme soit de « Programmation Dynamique » soit de « Colonie d’Abeilles Artificielles » suivant la taille du trafic et ceci afin de donner aux véhicules l’ordre de passage minimisant le temps de retard dans les intersections. D’autre part, et après avoir reçu l’ordre de passage, chaque véhicule doit calculer son profil optimal de vitesse lui assurant une consommation minimale de carburant. Une série de simulation a ainsi été exécutée sous différents volumes de trafic afin de montrer la robustesse et la performance des méthodes proposées. Les résultats ont aussi été comparés avec d’autres méthodes de contrôle de la littérature et leur efficacité a ainsi été validée.

Mots-clés : Systèmes de Traﬁc Intelligents, Communication Véhicule-Infrastructure, Réseau d’Intersections, Programmation Dy-

namique, Colonie d’Abeilles Artiﬁcielles