first optimal process . . .

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 belfortmontbeliard.

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.

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.

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.

PLAN OF THE THESIS

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.

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 AND CONTROL METHODS

1.1/ INTRODUCTION 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 alternately 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 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/ TRAFFIC CONTROL IN THE CONVENTIONAL SYS-TEMS 1.2.1/ TRANSPORT 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/ HEADWAY

This part introduces the headway (t Inter ). 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/ FLOW OF VEHICLES (Q)

This variable represents the distribution of vehicles in the range. Generally, we calculate the average flow Q m for the interval[t 1 , t 2 ]. On one hand, it can be measured as the number of vehicles passing the same point of observation X for the interval [t 1 , t 2 ], as shown by Eq. (1.1) and Fig. 1.2. Inter .

Q m (t 1 , t 2 , X) = N(t 1 , t 2 , X) t 2 -t 1 (1.1)
Q m = 1 t m inter (1.2) t m inter = t 2 -t 1 N(t 1 , t 2 , X) (1.3) 1.2.1.3/ DENSITY (D)
This variable refers to the spatial distribution of the vehicles. In general, the average density is calculated D m and there are two methods. The first method, there are vehicles that are in an area bounded by two points of observation (X 1 , X 2 ) at time t, as shown by Eq. 1.4 and Fig 1 .3.

D m (X 1 , X 2 , t) = N(X 1 , X 2 , t) X 2 -X 1 (1.4)
where the term N (X 1 , X 2 , t) is the number of vehicles that are in the section of the road between two points (X1, X2) at time t. In the second method, the density can be described by the average spacing of the vehicle s m .

Q m = 1 s m (1.5) s m = X 2 -X 1 N(X 1 , X 2 , t)
(1.6)

1.2.1.4/ SPEED OF VEHICLE

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 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 V m describes the average movement of the vehicle during the interval T . It is measured by the following formulation:

V m = T 0 v(t) dt T (1.

1.2.2/ TRAFFIC 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/ MACROSCOPIC 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. Consequently, 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:

ρ t (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:

ρ t + (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 a link macro -micro. The model is given by the following equations:

ρ t + (ρv) x = 0 (1.11) v t + vv x + ρV (ρ)v x = 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/ MICROSCOPIC 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

v n+2 v n+1 v n t n+2 inter t n+1
inter 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:

ẍn (t) = C ẋn (t) -ẋn-1 (t) x n (t) -x n-1 (t) (1.13)
the symbol x n (t) is the location of the n th vehicle and the symbol x n-1 (t) is the location of the (n -1) th vehicle (the previous car of the n th vehicle). This equation shows that the current acceleration of the n th vehicle ẍn (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) [START_REF] Kesting | Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity[END_REF]. 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 following equations:

vIDM (s, v, v) = a[1 -( v v 0 ) δ -( s * (v, v) s ) 2 ] (1.14) s * (v, v) = s 0 + vT + v v 2 √ ab (1.15)
where the term s * (v, v) 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:

vfree (v) = a[1 -( v v 0 ) δ ] (1.16)
where when the variable v approaches the variable v 0 the term vfree (v) approaches zero. It implies that the driver decreases gradually the acceleration as it approaches its desired speed v 0 .

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:

vbrake (s, v, v) = -a( s * s ) 2
(1.17)

s * (v, v) = s 0 + vT + v v 2 √ ab (1.18)
where the term vT dominates in normal driving. The vehicle attempts to maintain a special interval T in monitoring other vehicles. The term v 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/ CONVENTIONAL METHODS OF TRAFFIC CONTROL

In order to describe a traffic control system, there are a few key terms that should be presented first [START_REF] Koonce | Traffic signal timing manual[END_REF]:

• 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.

• 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 unexpected 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) [START_REF] Robertson | Transyt: a traffic network study tool[END_REF].

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 excessive 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 [START_REF] Vincent | Self-optimising traffic signal control using microprocessors. the trrl mova strategy for isolated intersections[END_REF].

1.2.4/ SOME EXISTING TRAFFIC CONTROL SYSTEMS

There are many well-known existing traffic control systems. The paper [START_REF] Robertson | Transyt: a traffic network study tool[END_REF] The paper [START_REF] Vincent | Self-optimising traffic signal control using microprocessors. the trrl mova strategy for isolated intersections[END_REF] 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 [START_REF] Sims | The sydney coordinated adaptive traffic (scat) system philosophy and benefits[END_REF] 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 offers 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 [START_REF] Hunt | The scoot on-line traffic signal optimisation technique[END_REF] proposed by PB.Hunt authors describes the Split Cycle Offset Optimization 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 evidence 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 [START_REF] Mauro | Utopia[END_REF] 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 [START_REF] Gartner | Opac: A demand-responsive strategy for traffic signal control[END_REF] 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/ INTELLIGENT TRANSPORTATION SYSTEM

The Intelligent Traffic System (ITS) is an application that integrates electronics, computer communication technologies and management strategies. Consequently, 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. 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 [START_REF] Gehrig | Dead reckoning and cartography using stereo vision for an autonomous car[END_REF].

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 [START_REF] Payre | Intention to use a fully automated car: Attitudes and a priori acceptability[END_REF][START_REF] Luettel | Autonomous ground vehicles-concepts and a path to the future[END_REF]. By optimizing auto-roads, the necessary number of vehicles can be reduced up to 15 % [START_REF] Payre | Intention to use a fully automated car: Attitudes and a priori acceptability[END_REF][START_REF] Luettel | Autonomous ground vehicles-concepts and a path to the future[END_REF][START_REF] Vine | Autonomous cars: The tension between occupant experience and intersection capacity[END_REF][START_REF] Jamson | Behavioural changes in drivers experiencing highly-automated vehicle control in varying traffic conditions[END_REF]. The Platoon driving would save up to 20-30 % of fuel consumption [START_REF] Weyer | Human-machine cooperation in smart cars. an empirical investigation of the loss-of-control thesis[END_REF]. These cars can also reduce accidents and deaths on the road which are the eighth highest cause of death worldwide in 2013 [START_REF] Toroyan | Global status report on road safety[END_REF], reduce stress [START_REF] Rudin-Brown | Behavioural adaptation to adaptive cruise control (acc): implications for preventive strategies[END_REF], decrease the need of parking space at a up to 25 % [START_REF] Musso | Sidt scientific seminar 2013 automated vehicles and the rethinking of mobility and cities[END_REF], reduce an average of 38 hours of travel time by person per year, and save the US economy 1.3 billion per year [START_REF] Shanker | Autonomous cars, self-driving the new auto industry paradigm[END_REF]. • 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 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/ 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 (1227.60 MHz). This higher rate gives higher precision distance measurement 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-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 [START_REF] Sang | Gnss navigation system accuracy requirement for vehicle driving automation[END_REF][START_REF] Lewandowski | Gps: primary tool for time transfer[END_REF][START_REF] Woo | Research into navigation algorithm for unmanned ground vehicle using real time kinemtatic (rtk)-gps[END_REF]. It is also very useful in intelligent transport systems [START_REF] Gehring | Practical results of a longitudinal control concept for truck platooning with vehicle to vehicle communication[END_REF][START_REF] Neuendorf | The vehicle platoon controller in the decentralised, autonomous intersection management of vehicles[END_REF][START_REF] Michaud | Coordinated maneuvering of automated vehicles in platoons[END_REF][START_REF] Hsu | Development of an automatic parking system for vehicle[END_REF][START_REF] Sunitha | Fuzzy based automatic multi-level vehicle parking using lab view[END_REF].

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/ WIRELESS 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. 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 [START_REF] Johansson | Short range radio based ad-hoc networking: performance and properties[END_REF][START_REF] Hapsari | Short range radio device evaluation[END_REF][START_REF] Teo | Low-power short-range radio cmos subharmonic rf front-end using cg-cs lna[END_REF][START_REF] Dettmer | Digital short-range radio[END_REF]. They are installed with a short-range radio transmitter that operates on a lower ISM band (such as 433 MHz). It can broadcast an identifier 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/ COMMUNICATION 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 [START_REF] Miller | Vehicle-to-vehicle-to-infrastructure (v2v2i) intelligent transportation system architecture[END_REF][START_REF] Liu | Network-coding-assisted data dissemination via cooperative vehicle-tovehicle/-infrastructure communications[END_REF][START_REF] Sukuvaara | Wireless traffic service platform for combined vehicle-to-vehicle and vehicle-to-infrastructure communications[END_REF][START_REF] Charalampopoulos | V2i applications in highways: How rsu dimensioning can improve service delivery[END_REF][START_REF] Biagi | Short paper: Dynamic network selection in v2i systems[END_REF][START_REF] Bouchemal | Modeling and performance evaluation of v2i communications[END_REF][START_REF] Bok | A multiple rsu scheduling for v2ibased data services[END_REF][START_REF] Kwon | Agent-based on-line traffic condition and information analysis system for wireless v2i communication[END_REF][START_REF] Liu | Cooperative multi-agent traffic signal control system using fast gradient-descent function approximation for v2i networks[END_REF][START_REF] Zeng | A novel location-based channel congestion control scheme in v2i networks[END_REF]. 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 [START_REF] Djahel | Toward v2i communication technology-based solution for reducing road traffic congestion in smart cities[END_REF]. 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 shutdown. 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 of emergency service vehicles such as ambulances and fire engines, due to congestion [START_REF] Afdhal | Enhanced route guidance and navigation for emergency vehicle using v2i-based cooperative communication[END_REF]. This article has developed a simulation that provides route guidance It is difficult to manage the flow of traffic in intersection, because the number of vehicles grows rapidly, [START_REF] Al-Mashhadani | Enhancing traffic flow using vehicle dashboard traffic lights with v2i networks[END_REF]. 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. The paper proposes two algorithms to solve the stream allocation problem in the vehicle communications [START_REF] Eskafi | Dynamic channel allocation for vehicle-to-vehicle communications in automated highway systems[END_REF]. 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 [START_REF] Tientrakool | Highway capacity benefits from using vehicle-to-vehicle communication and sensors for collision avoidance[END_REF].

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/ CONCLUSION AND OBJECTIVES OF THE THESIS

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 3 rd section, traffic control methods will be presented with an exact method (Dynamic Programming) and heuristic method (Artificial Bee Colony). In the 4 th 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. 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 The index of the entrance lane, l ∈ [1,[START_REF] Vincent | Self-optimising traffic signal control using microprocessors. the trrl mova strategy for isolated intersections[END_REF]. s This variable should be combined with other element to present a notation. For the variable s, it presents the s th segment of the lane in the communication area, s ∈ [1,4]. Referring to the Fig.

N l

The total number of new vehicles on the first segment of the lane l. (j, l), (j, l, p) subscript. The j th vehicle on the lane l. This vehicle is in the p th position of the passing sequence.

j ∈ [1, N l ], l ∈ [1, 8]. ET s
The time for vehicle to enter the s th 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 ET 3 means the entrance time for vehicle in the 3 th segment of communication zone (intersection).

And another notation of ET 3 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 s th segment of lane.

T T s, T T

The time when the vehicle spends in traveling the s th segment of lane or the entire lane. Therefore, there is the following equation:

T T = 4 s=1
T T s.

Ls

The length of s th segment of lane. V max , V min

The maximum and minimum allowed speed on the road except for the intersection.

V I max

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

I row , I column

The row and the column of the network intersections.

T D, 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.

T S

The time step in the simulation.

A max , D max

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

2.2.1/ GENERATION OF NEW VEHICLES

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 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 [START_REF] May | Traffic flow fundamentals[END_REF][START_REF] Fv | Road research technical paper[END_REF][START_REF] Mannering | Principles of highway engineering and traffic analysis[END_REF]. The Figure.

p(x) = ϕ x e -ϕ x! (2.1)
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 ET 3 f .

2.2.2/ COMPATIBLE 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.

2.3/ OBJECTIVES OF CONTROL AND SAFETY CON-STRAINTS

2.3.1/ OBJECTIVES OF CONTROL

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 T D ( 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.

T D ( j,l) = T T a ( j,l) -T T f ( j,l) (2.2) min{ 8 l=1 N l j=1 T D ( j,l) } (2.3)

2.3.2/ SAFETY CONSTRAINTS

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 P 1 , P 2 , P 3 and P 4 :

P 1 = (1, 5), P 2 = (2, 6), P 3 = (3, 7), P 4 = (4, 8) (2.4)
Note that the combination of the flow is not unique. The following shows another example:

P 1 = (1, 2), P 2 = (3, 4), P 3 = (5, 6), P 4 = (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

P 1 ⇒ P 2 ⇒ P 3 ⇒ P 4 .
Generally, the sequence is also stable during a period of time.

This configuration of organizing the traffic flow can improve transportation. However, 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 ET 3 a , 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 can exploit the intersections resources more effectively and dynamically than the phase setting. For example, for the reason of readability, there are only three vehicles on the road, supposing

ET 3 f (1,1) = 10, ET 3 f (1,2) = 11, ET 3 f (1,6) =
ET 3 a ( j,l,p) ≥ ET 3 a ( j ,l ,p ) + T T 3 a ( j ,l ,p ) (l l &&p > p ) (2.6) ET 3 a ( j,l) -ET 3 a ( j ,l ) ≥ HW (l = l, j j &&p > p ) (2.7)
The second constraint comes from the same lane, which is named as the Headway. This variable means the minimal safety interval between two adjacent vehicles from the same lane, as Fig. 2.7 and formula. 2.7 show. new vehicle (j,2,p)

new vehicle (j' ,1,p') ET3 a (j,2,p) ET3 a (j',1,p') >ET3 a (j,2,p) +HW (p'>p) L1 L2
ET3 a (j',1,p') 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 [START_REF] Wu | Discrete intersection signal control[END_REF]. 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-ofway 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 V I max /V max 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 V I max /V max ). 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,

Vehicle

L 2 ≥(V 2 min -V 2 max )/(2D max ) + (V 2 max -V 2 min )/(2A max ) (2.8)
Next, the ways of calculating KP = {KP1, KP2, KP3} are presented. After the three key points above have been calculated, the maximal EV3 in each segment can be calculated based on ET 3. This profile is shown in Fig. 2.11 and summarized in Tab. 2.3.

KP1-TLV (Vmax

ET1 T (s) V min V max V (m/s) ET2 ET3 f KP1 KP2 KP3 EV3 max
KP1 = ET 2 + (V min -V max )/D max + (V I max -V min )/A max + (L2 -(V 2 min -V 2 max )/(2D max ) -(V I 2 max -V 2 min )/(2A max ))/V min (2.9) KP2 = ET 2 + (V min -V max )/D max + (L2 -(V 2 min -V 2 max )/(2D max ))/V min (2.10) KP3 = ET 2 -V max /D max + (L2 + V 2 max /(2D max ))/V min (2.11) EV3 = Vmin + Amax((Vmax -Vmin) 2 /Dmax + 2(L2 -VminT T 2)) (2.12) EV3 = Vmin -(Vmax -Vmin) 2 + 2Dmax(L2 -VminT T 2)) (2.13)

2.4.1.2/ RELATIONSHIP BETWEEN MINIMAL PASSING TIME AND INITIAL SPEED OF ENTERING THE INTERSECTION

There are two factors affecting the minimal T T 3. One is the length of passing the intersection L3 i (i = r, s, l), which depends on the operation of vehicle, i.e.,

MD = (V Imax 2 -EV3 2 )/(2Amax) (2.17) T T 3 =                    (V Imax -EV3)/Amax+ (L3 i -(V Imax 2 -EV3 2 )/(2Amax))/V Imax if L3 i > MD (-EV3 + EV3 2 + 2AmaxL3 i )/Amax if L3 i ≤ MD (2.18) EV4 =            V Imax if L3 i > MD EV3 + T T 3 * Amax if L3 i ≤ MD (2.19)
T T 4 = (Vmax -V Imax)/Amax + (L4 i -(Vmax 2 -V Imax 2 )/(2Amax))/Vmax (2.20)

2.4.2/ FUEL CONSUMPTION MODEL

In a method of optimizing the fuel consumption, it is essential to include a model of fuel consumption [START_REF] Rakha | Eco-driving at signalized intersections using v2i communication[END_REF]. There is a large number of fuel consumption patterns, such as the VT comprehensive power-based oil model (VT-CPFM) [START_REF] Rakha | Simple comprehensive fuel consumption and co2 emissions model based on instantaneous vehicle power[END_REF], the virginia tech microscopic model ( VT-Micro) [START_REF] Ahn | Estimating vehicle fuel consumption and emissions based on instantaneous speed and acceleration levels[END_REF] and the vehicle line drive model [START_REF] Barth | Modal emissions modeling: A physical approach[END_REF].

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).

MOE(v, a) =        e 3 x=0
3 y=0 (L (x,y) ×v x ×a y ) : a ≥ 0 e • 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 [START_REF] Alsabaan | Applying vehicular networks for reduced vehicle fuel consumption and co2 emissions[END_REF].

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 p units based on the time step t step . 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.

v (p,h) = v (p,h-1) + a p * t (p,h) (2.23)
t (p,h) = min (t step , tp -t step * (h -1)) (2.24)
N p = tp/t step (2.25) where

v (1,0) = v (2,0) = Vr, v (3,0) = V Imax.
There is always more than one speed profile satisfying in (ET 3 EV3). In other words, there is at least one line that can connect the point (ET 2, EV3) to another point (ET 3, EV3 ) under the safety constraints, because the point ( ET 3, 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.

• ET 3 = ET 3 f . In this case, there is only one possibility. The vehicle complete the entire trip with the maximal speed.

• ET 3 f < ET 3 < KP1. In this case, there is not a single speed profiles satis- • KP1 ≤ ET3. There is only one possibility to reach the intersection with the given speed EV3 in the time ET 3 .

T vi = (Vmax -V Imax)/Dmax + (L2 -(Vmax 2 -V Imax 2 )/(2 * Dmax))/(V Imax) (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: 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/ CHOICE OF ROUTE FOR EACH VEHICLE IN THE INTERSEC-TION NETWORK

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 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 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 augmenting 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 V I = 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:

V I 1 = 23,

2.5/ CONCLUSION

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.

PROPOSED CONTROL APPROACHES

3.1/ INTRODUCTION

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) [START_REF] Bertsekas | Dynamic programming and optimal control[END_REF][START_REF] Caramanis | Dynamic programming and optimal control[END_REF][START_REF] Borrelli | Dynamic programming for constrained optimal control of discrete-time linear hybrid systems[END_REF][START_REF] Stefanoiu | Optimization in engineering sciences: Metaheuristic, stochastic methods and decision support[END_REF], the Branch and Bound (BB) [START_REF] Lawler | Branch-and-bound methods: A survey[END_REF][START_REF] Narendra | A branch and bound algorithm for feature subset selection[END_REF][START_REF] Mitten | Branch-and-bound methods: General formulation and properties[END_REF][START_REF] Yan | A branch and bound algorithm for new traffic signal control system of an isolated intersection[END_REF][START_REF] Yan | A scheduling model and complexity proof for autonomous vehicle sequencing problem at isolated intersections[END_REF][START_REF] Yan | Control of traffic lights in intersection: A new branch and bound approach[END_REF] and the Linear Programming (LP) [START_REF] Dantzig | Linear programming and extensions[END_REF][START_REF] Gass | Linear programming[END_REF][START_REF] Bertsimas | Introduction to linear optimization[END_REF], 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) [START_REF] Karaboga | A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm[END_REF][START_REF]On the performance of artificial bee colony (abc) algorithm[END_REF][START_REF] Karaboga | A novel clustering approach: Artificial bee colony (abc) algorithm[END_REF][START_REF] Borne | Optimization in engineering sciences. exact methods[END_REF], the Genetic Algorithm (GA) [START_REF] Goldberg | Genetic algorithms and machine learning[END_REF][START_REF] Davis | Handbook of genetic algorithms[END_REF][START_REF] Fonseca | Genetic algorithms for multiobjective optimization: Formulationdiscussion and generalization[END_REF] and the Ant Colony Optimization (ACO) [START_REF] Dorigo | Ant colony optimization[END_REF][START_REF] Dorigo | Ant colony optimization and swarm intelligence[END_REF][START_REF] Dorigo | Ant colony optimization theory: A survey[END_REF], 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/ SOME LITERATURE RELATED TO THE EXACT METHODS

The Dynamic Programming is a type of the exact method [START_REF] Cormen | Introduction to algorithms[END_REF]. It solves a difficult problem by breaking it down into a series of simple sub-problems. Each subproblem 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 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 subproblem 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 subproblem. 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. 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 [START_REF] Wu | Discrete intersection signal control[END_REF][START_REF] Yin | Forward search algorithm based on dynamic programming for real-time adaptive traffic signal control[END_REF][START_REF] Heung | Coordinated road-junction traffic control by dynamic programming[END_REF][START_REF] Kamalanathsharma | Multi-stage dynamic programming algorithm for eco-speed control at traffic signalized intersections[END_REF][START_REF] Yu | A q valuebased dynamic programming algorithm with boltzmann distribution for optimizing the global traffic routing strategy[END_REF][START_REF] Mcdonough | Stochastic dynamic programming control policies for fuel efficient in-traffic driving[END_REF][START_REF] Yu | A global routing strategy in dynamic traffic environments with a combination of q value-based dynamic programming and boltzmann distribution[END_REF].

The document proposed by the author B.Yin [START_REF] Yin | Forward search algorithm based on dynamic programming for real-time adaptive traffic signal control[END_REF][START_REF] Yin | Comparing dynamic programming based algorithms in traffic signal control system[END_REF][START_REF]Traffic network micro-simulation model and control algorithm based on approximate dynamic programming[END_REF] The document proposed by the author HH.Tsin [START_REF] Heung | Coordinated road-junction traffic control by dynamic programming[END_REF] 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 [START_REF] Kamalanathsharma | Multi-stage dynamic programming algorithm for eco-speed control at traffic signalized intersections[END_REF] 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.

The document proposed by the author S.Yu [START_REF] Yu | A q valuebased dynamic programming algorithm with boltzmann distribution for optimizing the global traffic routing strategy[END_REF] 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.Teodorović [START_REF] Teodorović | Dynamic programming neural network real-time traffic adaptive signal control algorithm[END_REF] 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/ SOME LITERATURE RELATED TO THE HEURISTIC METHOD

As presented in the paper [START_REF] Zhang | Traffic signal timing and optimization[END_REF], 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) [START_REF] Davis | Handbook of genetic algorithms[END_REF], the Artificial Bee Colony (ABC) [START_REF] Karaboga | A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm[END_REF], the Ant Colony Optimization (ACO) [START_REF] Dorigo | Ant colony optimization[END_REF], and the Particle Swarm Optimization (PSO) [START_REF] Poli | Particle swarm optimization[END_REF], etc.

In the literature, the Genetic Algorithm is widely applied in the control of traffic lights in recent years [START_REF] Park | Traffic signal optimization program for oversaturated conditions: genetic algorithm approach[END_REF][START_REF] Park | Enhanced genetic algorithm for signal-timing optimization of oversaturated intersections[END_REF][START_REF] Ceylan | Traffic signal timing optimisation based on genetic algorithm approach, including drivers routing[END_REF][START_REF] Kesur | Advances in genetic algorithm optimization of traffic signals[END_REF]. In the document [START_REF] Park | Traffic signal optimization program for oversaturated conditions: genetic algorithm approach[END_REF], 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 [START_REF] Ceylan | Traffic signal timing optimisation based on genetic algorithm approach, including drivers routing[END_REF] presents that the GA can be used to improve performance at the network traffic by optimizing the timing of traffic lights. The document [START_REF] Lee | Real-time optimization for adaptive traffic signal control using genetic algorithms[END_REF] shows that the proposed method can improve the performance in the traffic net-work.

In the document [START_REF] Lee | Real-time optimization for adaptive traffic signal control using genetic algorithms[END_REF], the authors propose an adaptive algorithm in real time to optimize the traffic signal by the genetic algorithms. This control system comprises 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 [START_REF] Rakha | Integration framework for modeling ecorouting strategies: Logic and preliminary results[END_REF], 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 [START_REF] Poli | Particle swarm optimization[END_REF] 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 [START_REF] Teodorović | Swarm intelligence systems for transportation engineering: Principles and applications[END_REF]. In the document proposed by Wei et al [START_REF] Wei | Intersection signal control approach based on pso and simulation[END_REF], the authors improve the results of the controller based on fuzzy logic in applying the PSO in the setting of its parameters. In papers [START_REF] García-Nieto | Swarm intelligence for traffic light scheduling: Application to real urban areas[END_REF], 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.

3.2/ EXACT METHOD -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/ RECURSION FORMULA OF DP

The formulation T D(n 1 , ..., n l , ..., n L , ..., n 8 , L) shows the total delay for a passing sequence, where on the lane l, the number of vehicles included in the sequence is n l (n l ∈ [0, N l ]) 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:

(n 1 , ..., n l , ..., n L -1, ..., n 8 , 1), ..., (n 1 , ..., n l , ..., n L -1, ..., n 8 , 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). 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 T D(1, 0, 0, 0, 0, 0, 0, 0, 1), which means that there is only one vehicle on the road. The final point is T D(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 T D(0, 2, 2, 1, 1, 2, 1, 3, 8) means that the last vehicle comes from the lane 1 and the element T D (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/ HISTORICAL INFLUENCE OF EACH PROCESS OF OPTIMIZA-TION BASED ON 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 TD(0,2,2,1,1,2,1,3,1)+TD (1,1) TD(1,2,2,1,1,2,1,3,1)

TD(1,2,2,1,1,2,1,3,8) min TD(0,2,2,1,1,2,1,3,8)+TD (1,1)
TD(1,2,2,1,1,2,1,2,1)+TD (3,[START_REF] Vincent | Self-optimising traffic signal control using microprocessors. the trrl mova strategy for isolated intersections[END_REF] TD(1,2,2,1,1,2,1,2,8)+TD (3,[START_REF] Vincent | Self-optimising traffic signal control using microprocessors. the trrl mova strategy for isolated intersections[END_REF] TD(1,2,2,1,1,2,1,3,?) min min TD(1,0,0,0,0,0,0,0,1)

TD(1,0,0,0,0,0,0,0,8) TD(0,0,0,0,0,0,0,1,8) 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:

Initialisation Middle End

• The entrance time ET 3 and the passing time T T 3 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 ET 3 when the last vehicle, which comes from the different stream in the same approach, enters the intersection. This element avoids

3.2.3/ INITIALIZATION 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 n l equals to 1 means that there are only one vehicle on all the lane. And n L 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 subproblems, only the sub-problem T D(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 T D(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.

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.

T D(n 1 , ..., n l , ..., n L , ..., n 8 , L) =                    T D (n L ,L) : 8 l=1 n l = 1 and n L = 1 ∞ : 8 l=1 n l = 1 and n L = 0 (3.3)
Then the total time delay for each initial sub-problem should be calculated. However, 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 T D(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 T D(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. Therefore, 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/ INDEX OF SUB-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 N l + 1 means that there is N l + 1 possibilities for the lane l, where the part of N l expresses the total number of new vehicles on the lane l, and the additional one indicates the possibility without the vehicle on this lane. 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 (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/ LIMITATIONS 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 solution in real time because of the huge solution space. In the DP, the computational 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 N l is the same in each input lane in an optimal process. The total number of sub-problem is 8 * N l based on the Eq. (3.5). Next the N l is increased gradually to see the change in the sum of sub-problems. Therefore, this phenomenon leads us to find a heuristic method to obtain a near 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/ APPROXIMATE METHOD -ARTIFICIAL BEE COLONY (ABC)

The artificial bee colony is proposed by the author D.Karaboga in 2005 [START_REF] Karaboga | On the performance of artificial bee colony (abc) algorithm[END_REF], 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 richness. 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 return 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 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 [START_REF] Kesting | Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity[END_REF].

Algorithm 5: Process of applying the ABC algorithm to find a passing sequence

The employed bees are sent to find the initial food sources; while The demand is not reached do

The employed bees are sent to find the new food sources based on the current one and the value of these foods are calculated ;

The probability value for each source is calculated, based on which onlooker bees choose the food source;

If a source is abandoned by bees, the exploitation must be stopped for this source;

a scout bee is sent to randomly find a new food source ;

The current best food source is stored ;

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.

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/ CODE OF SOLUTION

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 of the vehicle V ( j,l) (the j th vehicle on the lane l), as indicated in the Eq. (3.6). The total number of code (T PP) 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, N l ]. (3.6)
T PP = ( 8 l=1 N l )! (3.7)
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 = {l i , ...}, l i ∈ [1, 8]. (3.8)
T PP = ( 8 l=1 N l )! ( 8 l=1 N l ) (3.9)
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 T PP 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/ OPERATOR OF EVOLUTION

In order to evolve the food source, a Swap operation Sequence (S S = S O 1 ( j,h) + S O 2 ( j,h) ... + S O n ( j,h) ) is applied in each food source to generate the new one [START_REF] Yan | A scheduling model and complexity proof for autonomous vehicle sequencing problem at isolated intersections[END_REF]. A sequence is composed by a series of the Swap Operators (S O ( 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.

S so new = S l + S O ( j,h) (3.10)
For the number of operator in the Swap operation Sequence is greater than one, S ss new = S l + S S = ((( 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). Because 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 i th bee is chosen. The variable Q(i) is the cumulative possibility for the i th food source.

S l + S O 1 ( j,h) ) + S O 2 ( j,h) ) + ...S O n ( j,h) ) (3.11)
FV(i) = 1/(1 + T D(i)) (3.12)
P(i) = FV(i) EBS i=1 FV(i) (3.13)
Q(i) = i j=1 FV( j) (3.14)
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 i th 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. The evolution of employed bees;

The operation of onlooker bees;

The operation of scout bee;

The simulation is complete;

3.4.4/ PROCESS OF APPLYING ABC TO OPTIMIZE THE PASSING

SEQUENCE

The algorithm [START_REF] Koonce | Traffic signal timing manual[END_REF] 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 max cycle .

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 value of trail is chosen based on the experiment.

3.5/ CONCLUSION

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/ INTRODUCTION

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/ SIMULATION 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. • 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. significantly lower than that in the FT, which explain that the DP is better than FT in reducing the time delay T D. 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 T D. 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. The total number of vehicles on each lane is shown on the column l and j in the 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. T(0,0,1,2,0,1,1,2,4)

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

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

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

T(0,0,1,0,0,1,0,1,3) 78 88 T(0,0,0,0,0,1,0,0,6) T(0,0,0,0,0,1,0,1,8) 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 parameters:

tm3 1 1 = 0, tm3 2 1 = 1, tm3 6 1 = 2, tp3 1 1 = T P3 2 1 = T P3 6 1 = 2.
Under the proposed method, we can obtain the following optimal results in the DP control: ta3 1 1 = 0, ta3 2 1 = 1, ta3 6 1 = 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: tac 1 1 = 0, tac 2 1 = 1, tac 6 1 = 3, which means that the total delay is 1s . On the other hand, it is assumed that the lanes 2 and 6 belong to the same phase, which leads to the following results: tac 1 1 = 4, tac 2 1 = 1, tac 6 1 = 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. 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 T T 3. 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 pass the intersection, as proved by the variable T T 3. Therefore, the DP control is more effective than FT control.

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 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.

4.3.1/ COMPARISON WITH SOME WORKS

In the first part, we will compare the simulation results of our proposed method based on the DP with the work [START_REF] Wu | Discrete intersection signal control[END_REF] in a network of intersection. Firstly, we will given to show the differences between these two methods. Finally, the simulation results are compared and analyzed between the above two methods. In the work [START_REF] Wu | Discrete intersection signal control[END_REF], 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 [START_REF] Wu | Discrete intersection signal control[END_REF] 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 is better than that in the work [START_REF] Wu | Discrete intersection signal control[END_REF], which refers to the following reasons:

• The variable ET 3 stop in the Tab. 4.6 means that the waiting time before the intersection in the work [START_REF] Wu | Discrete intersection signal control[END_REF] 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 variables ET 3 stop and ET 3 f . The variable ET 3 f 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 ET 3 stop . 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 ET 3 a . All vehicles can start to pass the intersection earlier than that in the work [START_REF] Wu | Discrete intersection signal control[END_REF], 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 [START_REF] Wu | Discrete intersection signal control[END_REF] 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 ET 3 a is much lower than that in the work [START_REF] Wu | Discrete intersection signal control[END_REF], 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 [START_REF] Wu | Discrete intersection signal control[END_REF]. 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 [START_REF] Wu | Discrete intersection signal control[END_REF].

• 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 [START_REF] Wu | Discrete intersection signal control[END_REF].

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 [START_REF] Wu | Discrete intersection signal control[END_REF],

all vehicles have a huge fluctuation of speed near the intersection. But in 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 [START_REF] Wu | Discrete intersection signal control[END_REF], 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 realtime. 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 [START_REF] Katsaros | Performance study of a green light optimized speed advisory (glosa) application using an integrated cooperative its simulation platform[END_REF] and the proposed method. Firstly, the method in the work [START_REF] Katsaros | Performance study of a green light optimized speed advisory (glosa) application using an integrated cooperative its simulation platform[END_REF] 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. In the work [START_REF] Katsaros | Performance study of a green light optimized speed advisory (glosa) application using an integrated cooperative its simulation platform[END_REF], 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 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 [START_REF] Katsaros | Performance study of a green light optimized speed advisory (glosa) application using an integrated cooperative its simulation platform[END_REF] 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. 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 vehicles can enter the intersection with the limited speed V I max . 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 ET 3, rather than finding a possible speed, as in the GLOSA. This is a key point in reducing the passing time T T 3, because every vehicle can pass the intersection faster with a high entrance speed, as shown in the Fig. 4.14. The average value T T 3 is almost the same in the proposed method, because of the fact that each vehicle can keep the V I max in passing the intersection. And the average value T T 3 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. 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. 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. 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 twoways 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. 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). 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

4.4/ CONCLUSION

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 [START_REF] Wu | Discrete intersection signal control[END_REF] and article [START_REF] Katsaros | Performance study of a green light optimized speed advisory (glosa) application using an integrated cooperative its simulation platform[END_REF]. 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. 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 [START_REF] Wu | Discrete intersection signal control[END_REF] to reduce the time delay, the waiting time, and so on. For the waiting time, all the vehicle can pass the intersection without stop before the intersection in the proposed method. However, in the work [START_REF] Wu | Discrete intersection signal control[END_REF], 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 [START_REF] Wu | Discrete intersection signal control[END_REF] 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 [START_REF] Wu | Discrete intersection signal control[END_REF]. Another simulation case in the network is compared with the work [START_REF] Katsaros | Performance study of a green light optimized speed advisory (glosa) application using an integrated cooperative its simulation platform[END_REF]. For the stop time, the proposed method help all the vehicles to avoid the stop before the intersection by dynamically distributer the right-ofway 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.

FUTURE RESEARCH

Some special types of vehicles can be considered in the proposed method. And the algorithm of optimizing the fuel consumption will be improved by applying a heuristic algorithm to reduce the calculation time.

ACKNOWLEDGEMENTI

  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.

v 1 CONTENTS 2 Dynamic modeling of transport networks 31 2. 1

 12311 Introduction of traffic modeling and control methods 1.1 Introduction of traffic . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Traffic control in the conventional systems . . . . . . . . . . . . . . 1.2.1 Transport parameter . . . . . . . . . . . . . . . . . . . . . . 1.2.1.1 Headway . . . . . . . . . . . . . . . . . . . . . . . 1.2.1.2 Flow of vehicles (Q) . . . . . . . . . . . . . . . . . 1.2.1.3 Density (D) . . . . . . . . . . . . . . . . . . . . . . 1.2.1.4 Speed of vehicle . . . . . . . . . . . . . . . . . . . 1.2.1.5 Fundamental diagram of traffic . . . . . . . . . . . 1.2.2 Traffic Models . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2.1 Macroscopic traffic model . . . . . . . . . . . . . . 1.2.2.2 Microscopic traffic model . . . . . . . . . . . . . . 1.2.3 Conventional methods of traffic control . . . . . . . . . . . . 1.2.4 Some existing traffic control systems . . . . . . . . . . . . . 1.3 Intelligent Transportation System . . . . . . . . . . . . . . . . . . . 1.3.1 Autonomous vehicle . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Global Positioning System (GPS) . . . . . . . . . . . . . . . 1.3.3 Wireless communication . . . . . . . . . . . . . . . . . . . . 1.3.3.1 Communication of vehicle-to-infrastructure . . . . 1.3.3.2 Communication of Vehicle to Vehicle . . . . . . . . 1.4 Conclusion and objectives of the thesis . . . . . . . . . . . . . . . ix x Introduction . . . .

Figure 1 . 1 :Figure 1 . 2 :

 1112 Figure 1.1: Headway

  Figure 1.3: Density

7 ) 1 . 2 Figure 1 . 4 :

 71214 Figure 1.4: Fundamental diagram of traffic

Figure 1 . 5 : 1 .

 151 Figure 1.5: Car following

  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 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.

Figure 1 . 6 :

 16 Figure 1.6: Intelligent Traffic System

Figure 1 . 7 :

 17 Figure 1.7: Autonomous Vehicles

Figure 1 . 8 :

 18 Figure 1.8: Global Positioning System (GPS)

Figure 1 . 9 :

 19 Figure 1.9: Wireless communication

  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 :

 110 Figure 1.10: Vehicle to Infrastructure

1. 3 . 3 . 2 /

 332 COMMUNICATION OF VEHICLE TO 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 Transportation 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 hicle. Then the vehicle can take preventive measures to avoid the accident.

2 DYNAMICFigure 2 . 1 :Figure 2 . 2 :

 22122 Figure 2.1: Modification of speed profile without adjusting the traffic control strategies

Figure 2 . 3 :Figure 2 . 4 :

 2324 Figure 2.3: Results of the passing sequence

  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.

Figure 2 .

 2 Figure 2.5: Poisson Distribution

Figure 2 . 6 :

 26 Figure 2.6: Model of isolated intersection

  12 and T T 3 = 2. The incompatible relation among these streams is shown in the Tab. 2.2 and the Fig.2.6. According to the proposed method, we can get ET 3 a (1,1,1) = 10, ET 3 a (1,2,2) = 11, ET 3 a (1,6,3) = 12 and the total travel delay is 0s. However, for the best results of the phase setting, we can get ET 3 a (1,1,1) = 10, ET 3 a (1,2,2) = 11, ET 3 a (1,6,3) = 13 and the total travel delay is 1s.

Figure 2 . 7 :

 27 Figure 2.7: Headway

Figure 2 . 8 :

 28 Figure 2.8: Lane change

Figure 2 . 9 :

 29 Figure 2.9: Structure of communication

Figure 2 . 10 :

 210 Figure 2.10: Process of traversing a communication zone

  ). The KP1 expresses the maximal time when the vehicle can arrive at the intersection with V Imax. In other words, it is impossible for the vehicle to arrive at the intersection with V Imax 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 V Imax with Amax in time KP1.KP2-TLV (Vmin). The KP2 means the maximal time of arriving at intersectionwith 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 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.

Figure 2 . 11 :

 211 Figure 2.11: Profile of relationship between the ET 3 and the maximal EV3

3 x=0 3 y=0

 33 (M (x,y) ×v x ×a y ) : a < 0(2.21)The term MOE(v, a) is the instantaneous fuel consumption in the speed v and the acceleration a. The terms L x,y and M x,y are regression coefficients of VT-Micro.

Figure 2 . 13 :

 213 Figure 2.13: Optimized speed profile

Algorithm 1 :

 1 Search algorithm for the optimal fuel consumption Data: ET 2, EV2, ET 3, EV3; Result: Dr, Vr, Ar; if ET 3 == ET 3 f ||ET 3 ≥ KP1 then There is only one appropriate speed profile; else Calculate T vi ; if ET 3 < T vi then for Dr : Dmax → 0; Ar : Dmax → 0 do if Dr and Ar meet the constraints of distance L2 and time T T 2 then Calculate fuel consumption and save the best; else for Dr : Dmax → 0; Ar : 0 → Amax do if Dr and Ar meet the constraints of distance L2 and time T T 2 then Calculate fuel consumption and save the best ;

Figure 2 . 14 :

 214 Figure 2.14: Structure for the exchange of information between the network and intersections

  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 Programming. Each vehicle is considered individually. The vehicle can exchange information with the intersection by the connection of V2I. Accordingly, the rightof-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.

  T D(n 1 , ..., n l , ..., n L , ..., n 8 , L) = min L ∈{1,8} {T D(n 1 , ..., n l , ..., n L , ..., n 8 , L ) + T D (n L ,L) } (3.1) where n l = n l for l L, otherwise n L = n L -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). T D(n 1 , ..., n l , ..., n L , ..., n 8 , L) = min{T D(n 1 , ..., n l , ..., n L -1, ..., n 8 , 1) + T D (n L ,L) ; T D(n 1 , ..., n l , ..., n L -1, ..., n 8 , 2) + T D (n L ,L) ; T D(n 1 , ..., n l , ..., n L -1, ..., n 8 , 3) + T D (n L ,L) ; T D(n 1 , ..., n l , ..., n L -1, ..., n 8 , 4) + T D (n L ,L) ; T D(n 1 , ..., n l , ..., n L -1, ..., n 8 , 5) + T D (n L ,L) ; T D(n 1 , ..., n l , ..., n L -1, ..., n 8 , 6) + T D (n L ,L) ; T D(n 1 , ..., n l , ..., n L -1, ..., n 8 , 7) + T D (n L ,L) ; T D(n 1 , ..., n l , ..., n L -1, ..., n 8 , 8) + T D (n L ,L) ; } (3.2)

Figure 3 . 1 :

 31 Figure 3.1: Example of recursion formula

  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 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 ET 3 f is 18s. Then its allowed entrance time to pass the intersection ET 3 a 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 ET 3 a 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 ET 3 a should be 26s.

  * w l ) + (L * 1); (3.5) 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).

3- 9 , 4 :

 94 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 Algorithm Optimal process based on the algorithm of DP Count the total number of new vehicles in the first segment from each input lane N l ; Calculate and index each initial sub-problems; for n 1 , ..., n 8 from 0 to N 1 , ..., N 8 respectively do for L from 1 to 8 do Number current sub-problem; Find his eight previous sub-problems; Calculate the ET 3 a for the last vehicle according to previous 8 sub-problems, respectively; Calculate the time delay of the last vehicle and the current sub-problem on the basis of previous sub-problems, respectively;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;Comparing the time delay in the 8 final sub-problems to find the best solution; 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 thecurrent sub-problem is T D(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 subproblems: T D(0, 2, 2, 1, 1, 2, 1, 3, 1) , ..., T D(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 ET 3 a for Vehicle (n L , L) under the various previous sub-problems. In the line 8, as shown in Chapter 2, the maximal EV3 a is calculated based on the ET 3 a , referring to the Fig. 2.11. Then the T T 3 a can be calculated also, as shown in the Eq.

7Figure 3 . 2 :

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

Figure 3 . 3 :

 33 Figure 3.3: Example of SO operation

Figure 3 . 4 :

 34 Figure 3.4: Example of SS operation

4. 2 . 1 /

 21 EXAMPLE OF APPLYING THE DYNAMIC PROGRAMMING IN 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:

Figure 4 . 1 :

 41 Figure 4.1: Phase configuration in FT control

Tab. 4 . 2 .

 42 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

Figure 4 . 2 :

 42 Figure 4.2: Schedule in FT control

4. 2 . 1 . 3 /

 213 SOME VEHICLES' SPEED PROFILES IN THE FIRST OPTIMAL PROCESSOF DPThe 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-

Figure 4 . 3 :Figure 4 . 4 :Figure 4 . 5 :

 434445 Figure 4.3: Example of achieving the optimal solution

4. 2 . 1 . 5 /Figure 4 . 6 :Figure 4 . 7 :

 2154647 Figure 4.6: Comparison of average time delay under the different traffic volumes

Figure 4 . 9 :Fig. 4 . 8 . 4 . 8 .

 494848 Figure 4.9: Comparison of time delay between ABC and DP under different traffic volumes

Figure 4 . 10 :

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

Figure 4 . 11 :

 411 Figure 4.11: Comparison of speed profiles for the second vehicle

  .6, and their basic input data and the simulation results are given in the Tab. 4.6. Another case of simulation is 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 2 nd veh and the 3 rd veh are shown in Fig. 4.11.

2

 2

. 4 .

 4 The criteria to be compared are the time delay, fuel consumption, average waiting time, etc.

Figure 4 . 12 :

 412 Figure 4.12: Illustration of speed profile of the work[START_REF] Katsaros | Performance study of a green light optimized speed advisory (glosa) application using an integrated cooperative its simulation platform[END_REF]

Figure 4 . 13 :

 413 Figure 4.13: Comparison of average stop time before the intersection

Figure 4 . 14 :Figure 4 . 15 :

 414415 Figure 4.14: Comparison of average entrance speed in the intersection

  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.[START_REF] Vine | Autonomous cars: The tension between occupant experience and intersection capacity[END_REF]. This means that, in the optimization of time delay, the proposed model meets the realtime 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.

Figure 4 . 16 :Figure 4 . 17 :

 416417 Figure 4.16: Comparison of calculation time for the optimization of time delays

Figure 4 . 18 :

 418 Figure 4.18: Comparison of Average time delay

4. 3 . 2 /

 32 COMPARISON BETWEEN ABC AND DP IN A NETWORK OF 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),

Figure 4 . 19 :Figure 4 . 20 :

 419420 Figure 4.19: Comparison of average fuel consumption

Figure 4 . 21 :

 421 Figure 4.21: Comparison of calculation time in a network of intersections

Figure 4 . 22 :

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

105 food.

 105 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.

56 3 Proposed control approaches 57 3

  . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 .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 Optimization process for the passing sequence according to the DP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Limitations of DP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Approximate method -Artificial Bee Colony (ABC) . . . . . . . . 3.4.1 Code of solution . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Operator of evolution . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Selection based on the roulette wheel . . . . . . . . . . . . 3.4.4 Process of applying ABC to optimize the passing sequence 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . on DP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2.3 Initialization of DP . . . . . . . . . . . . . . . . . . . . . . . 65 3.2.4 Index of sub-problems . . . . . . . . . . . . . . . . . . . . . 66 CONTENTS xi 3.2.5 4 Simulation and results 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Simulation case in an isolated intersection . . . . . . . . . . . . . . 4.2.1 Example of applying the Dynamic Programming in optimizing the passing sequence in detail . . . . . . . . . . . . . .

Table 2 .

 2 1: Definition of notation in the second chapter Notation Definition l

Table 2 .

 2 3: relationship between the ET 3 and the maximal EV3 aInterval of ET 3 a Range of the maximal EV3 a Formulation of EV3 a 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. First of all, the length MD should be calculated. MD means the minimal distance needed by the vehicle to accelerate from EV3 to V Imax with Amax. If the L3 i is longer than MD, the vehicle accelerates to V Imax and keeps it to finish the remainder L3 i . Otherwise, it keeps acceleration in L3 i .

	[ET 3 f , KP1]	V Imax	V Imax
	(KP1, KP2]	[Vmin, V Imax)	Eq. (2.12)
	(KP2, KP3)	(0, Vmin]	Eq. (2.13)
	(KP3, ∞)	0	0

Table 2 .

 2

	Coefficients v 0	4: Coefficients for the model VT-Micro v 1 v 2 v 3
	positive (a)
	a 0	-7.73452	2.799E-2	-2.228E-4	1.09E-06
	a 1	0.22946	6.8E-3	-4.402E-05 4.80E-08
	a 2	-5.61E-3	-7.7221E-4 7.90E-07	3.27E-08
	a 3	9.77E-05	8.38E-6	8.17E-07	-7.79E-09
	negative (a)
	a 0	-7.73452	2.804E-2	-2.1988E-4 1.08E-06
	a 1	-1.799E-2 7.72E-3	-5.219E-5	2.47E-07
	a 2	-4.27E-3	8.3744E-4 -7.44E-06	4.87E-08
	a 3	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:

Table 2 .

 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
		3	N p
		FUEL =
		p=1

h=1 MOE(v (p,h) , a p ) * t (p,h) (2.22)

  [START_REF] Shanker | Autonomous cars, self-driving the new auto industry paradigm[END_REF][START_REF] Musso | Sidt scientific seminar 2013 automated vehicles and the rethinking of mobility and cities[END_REF][START_REF] Mauro | Utopia[END_REF], 10 and V I 2 = 2322 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.

	Algorithm 2: Algorithm for choosing the route for each vehicles entering the in-
	tersections from the east
	Data: IID sou (x,y) , IID des (x,y) ;
	Result: M sou ;
	if (IID des x ≥ IID sou x -1)&&(IID des y > IID sou y ) then
	Turn left;
	else if (IID des x ≥ IID sou x -1)&&(IID des y < IID sou y ) then
	Turn right;
	else if (IID sou y = IID des y )||
	(IID sou y = 1)&&(IID des y = 0)&&(IID sou x > IID des x + 1)||
	(IID sou y = I row )&&(IID des y = I row + 1)&&(IID sou x > IID des x + 1) then
	Turn right;
	else
	if (IID sou y > IID des y ) then
	if (T V sou (x-1,y-1) > T V sou (x-1,y) ) then
	Go straight;
	else
	Turn right ;
	else
	if (IID sou y < IID des y ) then
	if (T V sou (x-1,y+1) > T V sou (x-1,y) ) then
	Go straight;
	else
	Turn left ;
	Simulation completed;
	Table 2.6: Example to choose the route
		Input			Output
	Vehicles IID sou IID cur IID des	Operation IID nex
	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

Table 3 .

 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
	ET 3 lc 20 16 18 14 17 9	15 21

Table 3 .

 3 2: Weight for each item in T D(n 1 , ..., n l , ..., n L , ..., n 8 , L)In order to index each sub-problem, a weight w l 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 T D(n 1 , ..., n l , ..., n L , ..., n 8 , L) based on the total number of new vehicles on each lane N l , 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.

	element	n 1	n 2	n 3	n 4
	8	8	8	8
	weight (w l ) 8	(N l + 1). 8	(N l + 1). 8	(N l + 1). 8	(N l + 1).
	l=2	l=3	l=4	l=5
	element	n 5	n 6	n 7	n 8	L
	8	8	8
	weight (w l ) 8	(N l + 1). 8	(N l + 1). 8	(N l + 1).	8	1
	l=6	l=7	l=8

Table 3 .

 3

			3: Example of the weight
	element	n 1	n 2	n 3	n 4
	weight (w l )	207360	51840(=6*8640) 8640(=5*1728) 1728(=3*567)
	element	n 5	n 6	n 7	n 8	L
	weight (w l ) 576(=4*144)	144(=6*24)	24(=8*3)	8	1

Table 3 .

 3

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

Table 3 .

 3

		5: Example of coding the solution
	Number	first method	feasible	second method code veh 1 veh 2 veh 3
	1

Table 3 .

 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
	Initialization: (EBS ), (OBS ), limit, cycle, max cycle , etc;
	Generate a random passing sequence for the employed bees;
	for cycle from 0 to max cycle do

Table 4 .

 4

		1: Parameters of simulation in an isolated intersection
	Parameters	V max	V min	A max	D max	TV
	Value	60 (km/h) 10 (km/h) 4 (km/h/s) -4 (km/h/s) 500 (veh/h/l)
	Parameters	L 12	L 23	L 33	HW	T S
	Value	100 (m)	250 (m)	20 (m)	1 (s)	0.1 (s)
	4.2.1.1/ SIMULATION 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
	T D and fuel consumption FC for each vehicle, which is explained by simulation

Table 4 .

 4

			2: Simulation results of all vehicles in the first optimal process
	l	j	S eq DP	FT	ET 1	ET 3 f	ET 3 a DP	FT	T T 3 a DP	FT	EV3 a DP FT	DP	T D a	FT	DP	FC	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
	4	1 2	5 7	5 8	2 4	23 25	23.47 25.41	60 61	0.47 1.2	3.76 6	60 60	0 0	0.47 0.41	44.5 43.5	57.6 58.4	102.1 102.7
	5	1 2	8 9	9 11	4 8	25 29	26.89 29	80 81	1.41 1.41	6.5 6.5	60 60	0 0	1.89 0	62.5 59.5	63.4 57.8	111.2 109.9
	6	1	1	1	2	23	23	23	0.47	0.47	60	60	0			0	56.5	56.5
	7	1 2	6 11	2 4	3 8	24 29	24 30.61	40 41	1.41 1.41	6.5 6.51	60 60	0 0	0 1.61	23.5 19.5	57.8 62.5	94.2 92.4
	8	1 2	2 4	6 7	4 7	25 28	25 28	60 61	0.47 1.2	3.76 6	60 60	0 0	0 0		42.5 40.5	56.5 57.5	101.2 90.2
	4.2.1.2/ METHOD OF CODING THE SOLUTION IN THE FIRST OPTIMAL PROCESS

Table 4 .

 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(0,0,1,2,1,1,1,2,5)		T(1,0,1,2,2,1,1,2,1)
	1379		1820			2276			2565
									T(0,0,1,2,2,1,1,2,5)

Table 4 .

 4

	4: Performance under different traffic volumes
	TV (veh/h/l)	100	500
	Time delay (s)	DP 0.042 0.2531 FT 27.58 33.97
	Fuel consumption (ml)	DP 57.7 FC 90.3	59.4 94.9
	Average EV3 (km/h)	DP 60 FC 14.8	60 8.8
	Average T T 3 (s)	DP 1.12 FC 4.46	1.12 4.88
	Calculation time for optimizing time delay (ms)	DP 1.1 FC 10-4	117.8 10-4
	Calculation time for optimizing fuel consumption (ms)	DP 6 FC 2	19 2
	4.2.2/ COMPARISON BETWEEN ABC AND DP IN AN ISOLATED IN-

  The variable limit equals to 3. The 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					ABC	117.8
							DP
		100
	Calculation time (ms)	40 60 80					64.9
		20					24.2	14.7	20
		0	100 2.3 1.1	200 5.3 8.2	300 9.3	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
		250					243.4	253.1
	Time delay (ms)	150 200					165.9	150.3	215.8
		100			101.5	94.5
		50	44.4	42.2
		0	100	200	300	400	500
							Traffic volume (veh/h/l)

Table 4 .

 4

	5: Simulation parameters in a network of intersections
	V max V min	V I lt max	V I rt max	V I gs max	T V
	14	4	0.8V max 0.6V max V max 500
	L 1	L 2	L 3	L 4	T HW t step
	100 200	10	300	1	0.1
	I cow I column	A max	D max
	2	2	2	-2
	introduce briefly the traffic control method in the work [87]. Next, an example is

Table 4 .

 4

	6: Comparison of simulation results between the work [87] and the pro-
	posed 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
	ET 3 stop	Work [87] 24.9	27.9	26.9	28.9	31.9
	ET 3 f	DP	21.4	24.4	23.4	25.4	28.4
	TT3	Work [87] DP	3.2 0.7	3.2 0.7	3.2 0.7	3.2 0.7	3.2 0.7
	Sequence	Work [87] DP	1 1	2 3	3 2	4 4	5 5
	ET 3 a	Work [87] 24.9 DP 21.4	27.9 24.4	31.1 23.4	32.1 25.4	31.9 28.4
	EV3	Work [87] DP	0 14	0 14	0 14	0 14	0 14
	TT	Work [87] 50.8 DP 43.6	50.8 43.6	55 43.6	54 43.6	50.8 43.6
	TD	Work [87] DP	7.2 0	7.2 0	11.4 0	10.4 0	7.2 0
	According to the above simulation examples, the method proposed in this paper

Table 4 .

 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

Execute an optimal process based on DP (refering to Algorithm. 4) or ABC (refering to Algorithm. 5) to achieve a passing sequence; 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; Mark all new vehicles as older vehicles; 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

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. Furthermore 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 Dynamic Programming (DP) because the optimization of passing sequence satisfies 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. Therefore, 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 Ls: The length of s th segment of lane.

V max , V min : The maximum and minimum allowed speed on the road except for the intersection.

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

I row , I column : The row and the column of the network intersections.

T D, FC: The time delay and fuel consumption for one vehicle or a sequence of 129 vehicles in the entire trip.

HW:

The headway between two successive vehicles in the same lane.

T S : The time step in the simulation.

A max , D max : The maximal acceleration and deceleration for each vehicle.

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

CS : The code (label) of each sub-problem.

w l : 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.

T PP: The total number of passing sequence.

Document generated with L AT E X and: the L AT E X 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 Vehicleto-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 realtime 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: