道路交通流元胞自动机模型中的相变现象研究
|
摘要
交通输运能力是制约一个国家城市化现代化进程快慢的关键因素,对国民经济的发展起重要的支撑作用。较高的交运能力可以降低人们的出行时间,提高工作效率,促进物资和人力资源更好更便捷的流通。在现代社会,一个国家或城市的交通运输状况已是衡量此地区增长潜力的重要指标。虽然一直以来世界各国对交通改善非常重视且投入了巨资,但是交通拥堵现象还是常有发生,从而成为困扰政府的重大难题。在世界范围内,每年因交通拥塞、事故频发和尾气过量排放污染环境等问题,都直接或间接地对当地造成了巨大的经济损失。以我国为例,“十一五”时期是我国交通运输事业发展最快、成绩最突出的五年,不论是交通设施总量、规模,还是运输能力供给等方面都取得了巨大成就。但是由于私家车保有量以爆发式的速度增长,还是造成了车多路少、道路供不应求的现状,致使在大城市上下班高峰时段,动辄几小时的堵车情形屡见不鲜,每年由于交通拥堵带来的经济损失可达数千亿人民币。
为了解决我国城市的交通问题,改善城市交通系统的性能,一方面需要通过改造路网系统、拓宽路面、增添交通设施以及道路建设等城市交通所必须的硬件建设来实现,另一方面还需要通过采用科学的管理手段,把现代高新技术引入到交通管理中来提高现有路网的交通性能,从而改善整个道路交通的管理效率,提高道路设施的利用率,实现城市交通管理的科学性和有效性。这两个方面是相辅相成、缺一不可的。而交通流作为一门先进的科学理论,就是要研究城市交通中的各种复杂现象及其成因,以求对交通问题的本质加以理解,来最优化地解决道路交通问题。归根结底,能充分地利用现有的交通设施,有计划地开发有限的交通资源,以科学的理论来管理、指导以及控制交通,才是缓解迅速增长的交通需求压力,彻底解决城市发展中的各种交通问题的根本途径。交通流理论研究作为二十世纪末一门新兴的交叉性学科便是由此而产生的,特别是近年来更是受到许多学科领域研究人员的关注,涵盖了流体力学、系统科学、非线性科学、理论物理学、应用数学、交通工程学、计算机信息科学、统计学等等。
交通流理论研究的宗旨是,利用现代科学知识正确地描述与实测数据相符的交通特性,对其建立恰当的数学模型和理论解析,依靠参数识别和计算机数值模拟揭示出各种交通流现象的本质特征,为实际的交通规划以及交通管理策略提供可靠的科学理论依据,并研制出适用的程序和软件包,最终达到能够对交通系统实时监控优化的目的。而且,交通流理论研究除了具有上述重要的工程实用价值,其还具有深远的科学意义。因为,交通系统是由大量离散的车辆在复杂的道路网络中运动而构成的,车辆与车辆及道路间存在着相互制约关系,可以将其看做一种自我演化驱动的非线性复杂非平衡系统。对这类系统的运行规律的描述目前还没有严格成熟的基本理论,所以对其研究可以提供一个角度来加深对复杂性科学的认识,并且能够促进多学科的交叉融合和发展。
本文作者充分调研了国内外交通流理论的大量文献,在前人研究的基础上,提出了一些更为符合实际交通状况的二维和一维道路交通元胞自动机模型。并进一步对改进模型做了广泛细致的计算机模拟和理论解析,最终发现和解释了一些新结果,比如新的稳定平衡态和相变现象等。这一系列工作期望可以实现从交通问题的表面现象深入到本质规律认识,而后再次从理论上升到指导实际的城市或高速道路交通管理、规划和设计的实践过程中去。本论文的主要内容可以分如下三个方面展开。
(一)考虑交通灯周期影响的城市交通模型。此模型在二维城市道路交通流元胞自动机经典模型的基础上,考虑了延长了交通灯的周期,也即红绿灯的持续时间,对城市交通系统带来的影响。模型的模拟结果显示,除了发现以往模型中已有的平衡态,还发现了以前文献所没有报道过的一种新的中间态,此稳定平衡的中间态由自由流态和阻塞态两部分组成,对应的密度区间介于高速相和低速相的临界相变点附近。并且进一步指出,系统的临界密度与交通灯周期有非单调关系,后者存在使系统通行能力最大化所对应的最优值。最后,我们定性地解释了此自由阻塞分离相的形成和动态稳定性,并用平均场近似方法给出了不同交通灯周期下系统的平均速度与车辆密度关系的理论解,以及系统临界密度与交通灯周期关系的理论解。此解析解和计算机模拟结果符合的很好,但在较短的交通灯周期条件下显得仍不够精确,我们讨论了误差产生的原因。此工作的意义在于,通过揭示城市中交通灯周期变化对整体交通系统带来的影响,来因地制宜地根据车辆密度情况设计最优的交通灯策略,在不改变城市路网结构的前提下,使得系统中可顺利通行的车辆数目达到最大。
(二)引入车辆间博弈行为的二维道路交通模型。此模型在经典模型的基础上,加入了实际交通中驾驶员微观心理层面的相互作用。设想现实生活中可能发生的情况,如果十字路口没有安装交通灯,两交叉方向行驶的车辆又同时试图进入路口时,结果总会有至少一辆车为避免发生相撞和冲突,而停下来让过。这一情形可以用驾驶员的博弈行为来模拟,套用博弈理论的术语,可将驾驶员分为两种状态,一种称为“合作者”,另一种称为“背叛者”。合作者是指当要与另一辆车发生抢道冲突时,此驾驶员会首先选择减速,试图进行“协商”交流而后决定何方先行。而背叛者是指当两车遇到冲突时,不管对方行为如何,自己总是选择加速试图抢先通过。此耦合了博弈行为的模型,模拟时发现了一种近自由流随机相,此相介于完全自由流和堵塞相之间,是系统车辆能达到的一种较高平均速度水平的新平衡态。并且发现系统中如果加入一部分背叛者,反而可能提高临界车辆密度,使交通总体更有效率,如果鼓励和加大背叛者向合作者转变的概率,则可以更好地促进车辆运行通畅。此工作的意义在于,将实际交通中存在的车辆间行为博弈这一微观模型引入到道路交通流建模中,并发现在一定的车辆密度和博弈策略转变概率下,系统的整体平均速度会随着合作者比例的增加而增大,给现实交通中鼓励驾驶员间多多相互谦让这一现象提供了科学依据和理论支持。
(三)基于前车信息速度优化的混合智能交通模型。此模型的建立根植于现代智能交通系统中高新通讯技术的不断发展成熟,实践中所带来的对交通基础理论研究的需要。目前已有在汽车上获得应用的自适应巡航控制系统,能够通过设备搜集道路中车辆的位置和速度,可以根据这一车辆信息,来设计能达到系统最大车流的速度优化模型。基于这一思想,我们提出的模型采用任意车辆前方行驶的若干辆车的车距和速度作为输入参数,以此来分析此智能车允许达到的最大即时速度。此模型的模拟结果同样发现了相变现象的存在,即随着车辆密度的增大,系统的车流量先是线性增大,而后在大于临界密度处开始线性减小至零。并且还发现在智能车和普通手动车混合行驶情况下,道路中的车辆密度如果低于一定阈值,对应于有最优的智能车比例值,其刚好能使系统达到最大车流量,且再增大也不会有所改善。最后,我们还对系统相变时临界密度与智能车视野和比例之间的关系进行了精确的理论解析。此工作意义在于,提出了一种基于道路车辆信息智能优化车速的混合交通流模型,理论上论证了增加带有智能系统的车辆从而改善道路交通状况的可行性。另外,还指导我们在进行实际交通规划时,要准确把握系统的运行现状,针对不同情况来设计最有效的策略。
Traffic transport capacity is a key factor restricting the speed of a country’s urbanization and modernization, and has played an important role in supporting the development of the national economy. The high transport ability can reduce people’s travel time, improve work efficiency, and promote convenient circulation of the materials and human resources. In the modern society, the transportation situation of a country or city has already been an important index to measure the region’s growth potential. Although the global governments have paid much attention to the transportation improvement and spent enormous amounts on it, the traffic jams phenomena still appear quite often and become one of the major problems troubling governments. Around the world, the frequent traffic congestion, traffic accidents and problem of exhaust gas emission polluting environment have directly or indirectly caused a huge economic loss. For example in the "11th five-year plan" period of China, the transportation development has gotten the outstanding achievement and been the fastest among past periods, regardless of traffic facilities amount, scale, or transportation capacity supply etc. But due to the amounts of private cars maintaining the even more tremendous growth speed, the roads supply is still not enough comparing to the vehicles demand. Hence in big cities during the rush time, it is common to see hours of traffic jams. Every year the economic losses caused by traffic congestions can reach to hundreds of billions Yuan.
In order to solve the urban traffic problems and improve the performance of the transportation system in our country, on the one hand, it needs to transform road network system, widen the roads and traffic facilities, and add the constructions such as hardware. On the other hand, it also needs to adopt scientific traffic management and the modern high technology for improving the existing road traffic performance, the whole road management efficiency, and realizing the rationality and validity of urban traffic management. Above two respects are complementing each other and can be both equal important. The traffic flow as an advanced scientific theory is just to investigate various complex phenomena and their causes in urban or highway transportation, understand the nature of traffic problems and solve them optimistically. In one words, sufficiently utilizing the existing traffic facilities, rationally using the limited traffic resources, and scientifically managing and controlling traffic is the only way to relieve the pressure of rapidly increasing traffic demand, and eventually solve the traffic problems during the country development. For this reason, the traffic flow theory is emerging at the end of last twentieth century, and especially in recent years has attracted many researchers’attention of various disciplines, covering the fluid mechanics, system science, nonlinear science, theoretical physics, applied mathematics, traffic engineering, computer information science, statistics, and so on.
The objective of traffic flow theory research is using modern scientific knowledge with measured data, accurately describing the traffic characteristics, establishing and proposing proper mathematical model and theoretical analysis, revealing the essence of traffic flow phenomena through numerical simulation and parameter identification, providing reliable transportation management strategy, developing the applicable procedures and computer packages, and eventually achieving real-time monitoring and optimization of the transport system. And besides above important practical value, traffic flow theory study also has profound scientific significance. The transportation system is composed of a number of discrete vehicles moving in complex road network. The relations of vehicles and roads can be regard as a kind of complicated nonlinear evolution in unbalanced self-driven system. Until now there has not been a strict and mature fundamental theory to describe such complex system. Therefore, the research of traffic flow theory can provide an angle to deepen the understanding of complex science and promote the multidisciplinary development.
After studying the extensive literature about traffic flow theory and based on previous researchers’work, the authors of this paper propose some more realistic two-dimensional and one-dimensional traffic flow cellular automata model, and then give detailed computer simulations and theoretical analyses. These modified models have shown some new results, such as new stable equilibrium and phase transition phenomenon etc. This series work is expected to establish the theory to understand the essence rule behind the traffic surface phenomenon, and then in turn guide the practice of urban or highway traffic management, planning and design process. The main content of this paper includes three aspects of research work as follows.
(1) We introduce the urban traffic flow model considering the impact of traffic lights period, which is on the basis of the classical two-dimensional traffic flow cellular automata model. The simulation results of the new model show that besides the equilibrium phases which have been found in previous literature, there is another stable equilibrium state which has not been reported. This new phase consists of the free flow pattern and congestion area, and appears near the density region corresponding to the critical phase transition from high speed to low speed phase. And further we find that the system critical densities have non-monotonous relation with the traffic light periods, indicating there is an optimal traffic light period maximizing the traffic capacity for certain system. Finally, we qualitatively explain the formation and dynamic stability of the free flow and jam separation phase, and give the theoretical relations of the system average velocity to vehicle density and the critical density to traffic light period using the mean-field approximation method. The analytical solutions accord with the computer simulation results very well, except in the short traffic light period condition. Then we have discussed the reason of relative errors. The significance of this work is for designing the optimal traffic light period strategy through revealing the impact of period change, and making the system to contain the maximum number of vehicles without changing the urban road network structure.
(2) We introduced the two-dimensional traffic flow model taking into account the drivers’game behaviors. This model is also on the basis of the classical model, and then considers the actual drivers’micro psychology. Supposing two cross directional driving cars encounter in the crossroad without installing traffic lights, finally there must be at least one car stopping in order to avoid crash. This situation can be simulated through the drivers’game behaviors, which can be called cooperator and defector in term of game theory. The cooperator means the driver whom will decelerate and consult when meeting another direction car. And the defector means the driver whom will accelerate and try to pass through when encountering another car. The simulation of this traffic flow model finds a near free flow random phase locating between free flow and jammed phases. It is a new equilibrium state with high average vehicles velocity just below one. And further, it is found that adding some defector drivers and increasing transform probability of defector to cooperator could increase the system critical vehicle density and make the transportation more efficiency. The significance of this work is for introducing the game behaviors to the traffic flow model and finding that the more cooperator drivers the smoother of transportation, which provides the scientific support of encouraging the drivers to be mutual amicable.
(3) We introduce the hybrid intelligent traffic flow model with vehicle speed optimization based on leading vehicles’information. This model is proposed for the practical need of the modern intelligent transportation system with the development of high communication technology. Recently there have been cars equipping adaptive cruise control system, which can collect the information of the positions and velocities of vehicles in the road. Thus it is possible to calculate the optimal velocity for each car based on vehicles’information. From this idea, we design the model to analyze the permitted instant maximum speed of the traffic system according to the leading cars’information as input parameters. Through numerical simulation, this model also finds the phase transition phenomenon, of which the traffic flux first increases linearly with the increasing vehicle density and then decreases until to zero after critical density. And then it is found that there is an optimal intelligent cars ratio just according to the maximum traffic flux in the condition that the vehicle density is below the certain threshold of the hybrid system. Finally, we give the accurate theoretical analysis of the relationship of critical density to the sight and ratio of the intelligent vehicles. The significance of this work is for proposing a hybrid intelligent traffic flow model with vehicle speed optimization and certifying the feasibility of adding the intelligent cars for improving the transportation ability. And in addition, it properly instructs us to design the right most effective traffic strategy according to the present actual road situation.
为了解决我国城市的交通问题,改善城市交通系统的性能,一方面需要通过改造路网系统、拓宽路面、增添交通设施以及道路建设等城市交通所必须的硬件建设来实现,另一方面还需要通过采用科学的管理手段,把现代高新技术引入到交通管理中来提高现有路网的交通性能,从而改善整个道路交通的管理效率,提高道路设施的利用率,实现城市交通管理的科学性和有效性。这两个方面是相辅相成、缺一不可的。而交通流作为一门先进的科学理论,就是要研究城市交通中的各种复杂现象及其成因,以求对交通问题的本质加以理解,来最优化地解决道路交通问题。归根结底,能充分地利用现有的交通设施,有计划地开发有限的交通资源,以科学的理论来管理、指导以及控制交通,才是缓解迅速增长的交通需求压力,彻底解决城市发展中的各种交通问题的根本途径。交通流理论研究作为二十世纪末一门新兴的交叉性学科便是由此而产生的,特别是近年来更是受到许多学科领域研究人员的关注,涵盖了流体力学、系统科学、非线性科学、理论物理学、应用数学、交通工程学、计算机信息科学、统计学等等。
交通流理论研究的宗旨是,利用现代科学知识正确地描述与实测数据相符的交通特性,对其建立恰当的数学模型和理论解析,依靠参数识别和计算机数值模拟揭示出各种交通流现象的本质特征,为实际的交通规划以及交通管理策略提供可靠的科学理论依据,并研制出适用的程序和软件包,最终达到能够对交通系统实时监控优化的目的。而且,交通流理论研究除了具有上述重要的工程实用价值,其还具有深远的科学意义。因为,交通系统是由大量离散的车辆在复杂的道路网络中运动而构成的,车辆与车辆及道路间存在着相互制约关系,可以将其看做一种自我演化驱动的非线性复杂非平衡系统。对这类系统的运行规律的描述目前还没有严格成熟的基本理论,所以对其研究可以提供一个角度来加深对复杂性科学的认识,并且能够促进多学科的交叉融合和发展。
本文作者充分调研了国内外交通流理论的大量文献,在前人研究的基础上,提出了一些更为符合实际交通状况的二维和一维道路交通元胞自动机模型。并进一步对改进模型做了广泛细致的计算机模拟和理论解析,最终发现和解释了一些新结果,比如新的稳定平衡态和相变现象等。这一系列工作期望可以实现从交通问题的表面现象深入到本质规律认识,而后再次从理论上升到指导实际的城市或高速道路交通管理、规划和设计的实践过程中去。本论文的主要内容可以分如下三个方面展开。
(一)考虑交通灯周期影响的城市交通模型。此模型在二维城市道路交通流元胞自动机经典模型的基础上,考虑了延长了交通灯的周期,也即红绿灯的持续时间,对城市交通系统带来的影响。模型的模拟结果显示,除了发现以往模型中已有的平衡态,还发现了以前文献所没有报道过的一种新的中间态,此稳定平衡的中间态由自由流态和阻塞态两部分组成,对应的密度区间介于高速相和低速相的临界相变点附近。并且进一步指出,系统的临界密度与交通灯周期有非单调关系,后者存在使系统通行能力最大化所对应的最优值。最后,我们定性地解释了此自由阻塞分离相的形成和动态稳定性,并用平均场近似方法给出了不同交通灯周期下系统的平均速度与车辆密度关系的理论解,以及系统临界密度与交通灯周期关系的理论解。此解析解和计算机模拟结果符合的很好,但在较短的交通灯周期条件下显得仍不够精确,我们讨论了误差产生的原因。此工作的意义在于,通过揭示城市中交通灯周期变化对整体交通系统带来的影响,来因地制宜地根据车辆密度情况设计最优的交通灯策略,在不改变城市路网结构的前提下,使得系统中可顺利通行的车辆数目达到最大。
(二)引入车辆间博弈行为的二维道路交通模型。此模型在经典模型的基础上,加入了实际交通中驾驶员微观心理层面的相互作用。设想现实生活中可能发生的情况,如果十字路口没有安装交通灯,两交叉方向行驶的车辆又同时试图进入路口时,结果总会有至少一辆车为避免发生相撞和冲突,而停下来让过。这一情形可以用驾驶员的博弈行为来模拟,套用博弈理论的术语,可将驾驶员分为两种状态,一种称为“合作者”,另一种称为“背叛者”。合作者是指当要与另一辆车发生抢道冲突时,此驾驶员会首先选择减速,试图进行“协商”交流而后决定何方先行。而背叛者是指当两车遇到冲突时,不管对方行为如何,自己总是选择加速试图抢先通过。此耦合了博弈行为的模型,模拟时发现了一种近自由流随机相,此相介于完全自由流和堵塞相之间,是系统车辆能达到的一种较高平均速度水平的新平衡态。并且发现系统中如果加入一部分背叛者,反而可能提高临界车辆密度,使交通总体更有效率,如果鼓励和加大背叛者向合作者转变的概率,则可以更好地促进车辆运行通畅。此工作的意义在于,将实际交通中存在的车辆间行为博弈这一微观模型引入到道路交通流建模中,并发现在一定的车辆密度和博弈策略转变概率下,系统的整体平均速度会随着合作者比例的增加而增大,给现实交通中鼓励驾驶员间多多相互谦让这一现象提供了科学依据和理论支持。
(三)基于前车信息速度优化的混合智能交通模型。此模型的建立根植于现代智能交通系统中高新通讯技术的不断发展成熟,实践中所带来的对交通基础理论研究的需要。目前已有在汽车上获得应用的自适应巡航控制系统,能够通过设备搜集道路中车辆的位置和速度,可以根据这一车辆信息,来设计能达到系统最大车流的速度优化模型。基于这一思想,我们提出的模型采用任意车辆前方行驶的若干辆车的车距和速度作为输入参数,以此来分析此智能车允许达到的最大即时速度。此模型的模拟结果同样发现了相变现象的存在,即随着车辆密度的增大,系统的车流量先是线性增大,而后在大于临界密度处开始线性减小至零。并且还发现在智能车和普通手动车混合行驶情况下,道路中的车辆密度如果低于一定阈值,对应于有最优的智能车比例值,其刚好能使系统达到最大车流量,且再增大也不会有所改善。最后,我们还对系统相变时临界密度与智能车视野和比例之间的关系进行了精确的理论解析。此工作意义在于,提出了一种基于道路车辆信息智能优化车速的混合交通流模型,理论上论证了增加带有智能系统的车辆从而改善道路交通状况的可行性。另外,还指导我们在进行实际交通规划时,要准确把握系统的运行现状,针对不同情况来设计最有效的策略。
Traffic transport capacity is a key factor restricting the speed of a country’s urbanization and modernization, and has played an important role in supporting the development of the national economy. The high transport ability can reduce people’s travel time, improve work efficiency, and promote convenient circulation of the materials and human resources. In the modern society, the transportation situation of a country or city has already been an important index to measure the region’s growth potential. Although the global governments have paid much attention to the transportation improvement and spent enormous amounts on it, the traffic jams phenomena still appear quite often and become one of the major problems troubling governments. Around the world, the frequent traffic congestion, traffic accidents and problem of exhaust gas emission polluting environment have directly or indirectly caused a huge economic loss. For example in the "11th five-year plan" period of China, the transportation development has gotten the outstanding achievement and been the fastest among past periods, regardless of traffic facilities amount, scale, or transportation capacity supply etc. But due to the amounts of private cars maintaining the even more tremendous growth speed, the roads supply is still not enough comparing to the vehicles demand. Hence in big cities during the rush time, it is common to see hours of traffic jams. Every year the economic losses caused by traffic congestions can reach to hundreds of billions Yuan.
In order to solve the urban traffic problems and improve the performance of the transportation system in our country, on the one hand, it needs to transform road network system, widen the roads and traffic facilities, and add the constructions such as hardware. On the other hand, it also needs to adopt scientific traffic management and the modern high technology for improving the existing road traffic performance, the whole road management efficiency, and realizing the rationality and validity of urban traffic management. Above two respects are complementing each other and can be both equal important. The traffic flow as an advanced scientific theory is just to investigate various complex phenomena and their causes in urban or highway transportation, understand the nature of traffic problems and solve them optimistically. In one words, sufficiently utilizing the existing traffic facilities, rationally using the limited traffic resources, and scientifically managing and controlling traffic is the only way to relieve the pressure of rapidly increasing traffic demand, and eventually solve the traffic problems during the country development. For this reason, the traffic flow theory is emerging at the end of last twentieth century, and especially in recent years has attracted many researchers’attention of various disciplines, covering the fluid mechanics, system science, nonlinear science, theoretical physics, applied mathematics, traffic engineering, computer information science, statistics, and so on.
The objective of traffic flow theory research is using modern scientific knowledge with measured data, accurately describing the traffic characteristics, establishing and proposing proper mathematical model and theoretical analysis, revealing the essence of traffic flow phenomena through numerical simulation and parameter identification, providing reliable transportation management strategy, developing the applicable procedures and computer packages, and eventually achieving real-time monitoring and optimization of the transport system. And besides above important practical value, traffic flow theory study also has profound scientific significance. The transportation system is composed of a number of discrete vehicles moving in complex road network. The relations of vehicles and roads can be regard as a kind of complicated nonlinear evolution in unbalanced self-driven system. Until now there has not been a strict and mature fundamental theory to describe such complex system. Therefore, the research of traffic flow theory can provide an angle to deepen the understanding of complex science and promote the multidisciplinary development.
After studying the extensive literature about traffic flow theory and based on previous researchers’work, the authors of this paper propose some more realistic two-dimensional and one-dimensional traffic flow cellular automata model, and then give detailed computer simulations and theoretical analyses. These modified models have shown some new results, such as new stable equilibrium and phase transition phenomenon etc. This series work is expected to establish the theory to understand the essence rule behind the traffic surface phenomenon, and then in turn guide the practice of urban or highway traffic management, planning and design process. The main content of this paper includes three aspects of research work as follows.
(1) We introduce the urban traffic flow model considering the impact of traffic lights period, which is on the basis of the classical two-dimensional traffic flow cellular automata model. The simulation results of the new model show that besides the equilibrium phases which have been found in previous literature, there is another stable equilibrium state which has not been reported. This new phase consists of the free flow pattern and congestion area, and appears near the density region corresponding to the critical phase transition from high speed to low speed phase. And further we find that the system critical densities have non-monotonous relation with the traffic light periods, indicating there is an optimal traffic light period maximizing the traffic capacity for certain system. Finally, we qualitatively explain the formation and dynamic stability of the free flow and jam separation phase, and give the theoretical relations of the system average velocity to vehicle density and the critical density to traffic light period using the mean-field approximation method. The analytical solutions accord with the computer simulation results very well, except in the short traffic light period condition. Then we have discussed the reason of relative errors. The significance of this work is for designing the optimal traffic light period strategy through revealing the impact of period change, and making the system to contain the maximum number of vehicles without changing the urban road network structure.
(2) We introduced the two-dimensional traffic flow model taking into account the drivers’game behaviors. This model is also on the basis of the classical model, and then considers the actual drivers’micro psychology. Supposing two cross directional driving cars encounter in the crossroad without installing traffic lights, finally there must be at least one car stopping in order to avoid crash. This situation can be simulated through the drivers’game behaviors, which can be called cooperator and defector in term of game theory. The cooperator means the driver whom will decelerate and consult when meeting another direction car. And the defector means the driver whom will accelerate and try to pass through when encountering another car. The simulation of this traffic flow model finds a near free flow random phase locating between free flow and jammed phases. It is a new equilibrium state with high average vehicles velocity just below one. And further, it is found that adding some defector drivers and increasing transform probability of defector to cooperator could increase the system critical vehicle density and make the transportation more efficiency. The significance of this work is for introducing the game behaviors to the traffic flow model and finding that the more cooperator drivers the smoother of transportation, which provides the scientific support of encouraging the drivers to be mutual amicable.
(3) We introduce the hybrid intelligent traffic flow model with vehicle speed optimization based on leading vehicles’information. This model is proposed for the practical need of the modern intelligent transportation system with the development of high communication technology. Recently there have been cars equipping adaptive cruise control system, which can collect the information of the positions and velocities of vehicles in the road. Thus it is possible to calculate the optimal velocity for each car based on vehicles’information. From this idea, we design the model to analyze the permitted instant maximum speed of the traffic system according to the leading cars’information as input parameters. Through numerical simulation, this model also finds the phase transition phenomenon, of which the traffic flux first increases linearly with the increasing vehicle density and then decreases until to zero after critical density. And then it is found that there is an optimal intelligent cars ratio just according to the maximum traffic flux in the condition that the vehicle density is below the certain threshold of the hybrid system. Finally, we give the accurate theoretical analysis of the relationship of critical density to the sight and ratio of the intelligent vehicles. The significance of this work is for proposing a hybrid intelligent traffic flow model with vehicle speed optimization and certifying the feasibility of adding the intelligent cars for improving the transportation ability. And in addition, it properly instructs us to design the right most effective traffic strategy according to the present actual road situation.
引文
[1]贾斌,高自友,李克平,李新刚,基于元胞自动机的交通系统建模与模拟,科学出版社北京(2007).
[2]徐东云,张雷,兰荣娟,城市交通拥堵的背景变换分析,城市问题164 (2009) 46-49.
[3]李瑞敏,城市交通信号控制系统相关理论模型研究及软件开发,Ph.D thesis,清华大学(2005).
[4]唐孝威,张训生,陆坤权(Ed.),交通流与颗粒流,浙江大学出版社, 2004.
[5] D. Chowdhury, L. Santen, A. Schadschneider, Statistical physics of vehicular traffic and some related systems, Phys. Rep. 329 (2000) 199–329.
[6]高坤,从基本图方法到三相交通流理论---交通流元胞自动机模型理论研究,Ph.D thesis,中国科学技术大学(2009).
[7] TRANSIMS. Transportation Analysis and Simulation System. Los Alamos National Laboratory, Los Alamos, http://transims.tsasa.lanl.gov.
[8] D. Helbing, A. Hennecke, V. Shvetsov, et al. MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model. Transp. Res. B 35 (2001) 183-211.
[9]孙晓燕,交通流复杂动态特性的交通流元胞自动机模型研究,Ph.D thesis,中国科学技术大学(2010).
[10]姜锐,交通流复杂动态特征的微观和宏观模式研究,Ph.D thesis,中国科学技术大学(2002).
[11] D. L. Gerlough, and M. J. Huber, Traffic Flow Theory, Transportation Research Board, Washington, DC (1975) 165. D. L. Gerlough, and M. J. Huber, Traffic Flow Theory, Transportation Research Board, Washington, DC (1975) 165.
[12] M. Koshi, Iwasaki M., and I. Ohkura, in Proceedings of the 8th International Symposium on Transportation and Traffic Flow Theory, University of Toronto, Toronto (1983) 403.
[13] A. D. May, Traffic Flow Fundamentals, Prentice Hall, Englewood Cliffs, NJ, (1990).
[14] C. F. Daganzo, Fundamentals of Transportation and Traffic Operations, Pergamon Elsevier, Oxford, England (1997).
[15] B. S. Kerner, in Proceedings of the 3rd International Symposium on Highway Capacity edited by R. Rysgaard, Road Directorate, Denmark, Vol. 2 (1998) 621.
[16] B. S. Kerner, in Traffic and Granular Flow’97, edited by M. Schreckenberg and D. E. Wolf, Springer, New York (1998) 239.
[17] C. F. Daganzo, A Behavioral Theory of Multi-lane Traffic Flow. I: Long HomogeneousFreeway Sections. Research Report UCB-ITS-RR-99-5, Institute of Transportation Studies, University of California, Berkeley, CA, (1999).
[18] C. F. Daganzo, A Behavioral Theory of Multi-lane Traffic Flow. II: Merges and the Onset of Congestion. Research Report UCB-ITS-RR-99-6, Institute of Transportation Studies, University of California, Berkeley, CA (1999).
[19] B. S. Kerner, Phys. World 12 (8) (1999) 25.
[20] B. S. Kerner, Transp. Res. Rec. 1678, (1999) 160.
[21] B. S. Kerner, Transp. Res. Rec. 1710 (2000) 136.
[22] B. S. Kerner, in Traffic and Granular Flow’99: Social, Traffic, and Granular Dynamics, edited by D. Helbing, H. J. Herrmann, M. Schreckenberg, and D. E. Wolf, Springer, Berlin, (2000) 253.
[23] K. Nagel, P. Wagner and R. Woesler, Still flowing: Approaches to traffic flow and traffic jam modeling, Oper. Res. 51(5) (2003) 681-710.
[24] D. Helbing, Traffic and related self-driven many-particle systems, Rev. Mod. Phys., 73 (2001).
[25] L. C. Edie, Car-following and steady-state theory for non-congested traffic, Oper. Res. 9 (1961) 66-77.
[26] F. L. Hall and K. Agyemang-Duah, Freeway capacity drop and the definition of capacity, Transp. Res. Rec. 1320 (1991) 91-98.
[27] B. S. Kerner and H. Rehborn, Experimental features and characteristics of traffic jams, Phys. Rev. E (1996) R1297-1230.
[28] J. R. Windover and M. J. Cassidy, Some observed details for freeway traffic evolution, Transp. Res. A 35 (2001) 881-894.
[29] B. S. Kerner, Experimental features of self-organization in traffic flow. Phys. Rev. Lett. 81(17) (1998) 3797-3800.
[30] S. A. Paul and J. L. David, A novel nonlinear car-following model, chaos 8 (1998) 791-799.
[31] L. A. Safonov, Delay-induced chaos with multifractal attractor in a traffic flow model. Euro. Phys. Lett. 57 (2002) 151-157.
[32] K. P. Li and Z. Y. Gao, Nonlinear dynamics analysis of traffic times series, Mod. Phys. Letts. B 18 (2004) 1395-1402.
[33] K. P. Li and Z. Y. Gao, Controlling the states of traffic flow at the intersections, Int. J. Mod. Phys. C 15 (2004) 553-562.
[34] K. P. Li and Z. Y. Gao, tranisition from disorder to order in traffic flow, Chin. Phys. Lett.21 (2004) 1212-1215.
[35] K. P. Li and Z. Y. Gao, Order moving states in traffic flow, Physica A 348 (2005) 553-560.
[36] K. P. Li and Z. Y. Gao, Controlling the vehicle states in two lane traffic, Int. J. Mod. Phys. C 16(3) (2005) 501-512.
[37] D. A. Kurtz, Traffic jam, granular flow and soliton selection, Phys. Rev. E 52 (1993) 5574-5582.
[38] D. Helbing, Jams, waves and clusters, Science 282 (1998) 2001-2003.
[39] T. Nagatani, Density wave in traffic flow, Phys. Rev. E 60 (1999) 6395-6401.
[40] D. Helbing, Master: macroscopic traffic simulation based on a gas-kinetic nonlocal traffic model. Trasp. Res. B 35 (2001) 180-211.
[41] Y. Xue, Analysis of the stability and density waves for traffic flow, Chin. Phys. 11(11) (2002) 1128-1134.
[42] J. P. Kinzer, Application of the theory of probability to problem of highway traffic, B. C. E thesis, Politech. Inst. Brooklyn (1933).
[43] M. J. Lighthill, G. B. Whitham, On kinematic waves: II. a theory of traffic flow on long crowded roads, Proceedings of the Royal Society, Ser. A 229 (1955) 317-345.
[44] P. I. Richards, Shock waves on the highway, Oper. Res. 4 (1956) 42-51.
[45] H. J. Payne Models of freeway traffic and control, In: Bekey, G.A. (Ed.), Mathematical Models of Public Systems 1, Simulation Council, La Jolla, (1971) 51-61.
[46] R. D. Kühne, Macroscopic freeway model for dense traffic stop-start waves and incident detection, In: Proceedings of the Ninth International Symposium on Transportation and Traffic Theory (1984) 20-42.
[47] P. Ross, Traffic dynamics, Transp. Res. B 22 (1988) 421-435.
[48] M. Papageorgiou, J.M. Blosseville, H. Hadj-Salem, Macroscopic modeling of traffic flow on the Boulevard Peripherique in Paris, Transp. Res. B 23 (1989) 29-47.
[49] P. G. Michalopoulos, P. Yi, A.S. Lyrintzis, Continuum modeling of traffic dynamics for congested freeways, Transp. Res. B 27 (1993) 315-332.
[50] B. S. Kerner, P. Konh?auser, Cluster effect in initially homogeneous traffic flow, Phys. Rev. E 48 (1993) R2335-2338.
[51] B. S. Kerner, P. Konh?user, Structure and parameters of clusters in traffic flow, Phys. Rev. E 50 (1994) 54-83.
[52] H. Y. Lee, H.W. Lee, D. Kim, Origin of synchronized traffic flow on highways and its dynamic phase transition, Phys. Rev. Lett. 81 (1998) 1130-1133.
[53] H. Y. Lee, H.W. Lee, D. Kim, Dynamic states of a continuum traffic equation withon-ramp, Phys. Rev. E 59 (1999) 5101-5111.
[54] H. M. Zhang, A theory of nonequilibrium traffic flow, Transp. Res. B 32 (1998) 485-498.
[55] A. Aw, M. Rascle, Resurrection of "second order" models of traffic flow, SIAM Journal on Appl. Math. 60 (2000) 916-938.
[56] R. Jiang, Q. S. Wu, Z. J. Zhu, A new continuum model for traffic flow and numerical tests, Transp. Res. B 36 (2002) 405-419.
[57] Y. Xue, S. Q. Dai, Continuum traffic model with the consideration of two delay time scales, Phys. Rev. E 68 (2003) 066123.
[58] F. Siebel, W. Mauser, On the fundmental diagram of traffic flow, SIAM Journal on Appl. Math. 66 (2006) 1150-1162.
[59] F. Siebel, W. Mauser, Synchronized flow and wide moving jams from balanced vehicular traffic, Phys. Rev. E 73 (2006) 066108.
[60] I. Prigogine, R. Herman, Kinetic theory of vehicular traffic, American Elsevier, New York 1971.
[61] S. L. Paveri-Fontana, On Boltzmann-like treatments for traffic flow. A critical review of the basic model and an alternative proposal for dilute traffic analysis. Tranpn. Res. 9 (1975) 225-235.
[62] D. Helbing, Derivation and empirical validation of a refined traffic flow model, Physica A 233 (1996) 253-282.
[63] T. Nagatani, Kinetic segregation in a multilane highway traffic flow, Physica A 237 (1997) 67-74.
[64] D. Helbing, A. Greiner, Modeling and simulation of multilane traffic flow, Phys. Rev. E 55 (1997) 5498-5508.
[65] V. Shvetsov, D. Helbing, Macroscopic dynamics of multilane traffic, Phys. Rev. E 59 (1999) 6382-6339.
[66] S. P. Hoogendoorn, P. H. L. Bovy, Continuum modeling of multiclass traffic flow, Transp. Res. B 34 (2000) 123-146.
[67] M. Treiber, A. Hennecke, D. Helbing, Derivation, properties and simulation of a gas-kinetic-based nonlocal traffic model, Phys. Rev. E 59 (1999) 239-253.
[68] D. Helbing et al., MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model, Transp. Res. B 35 (2001) 183-211.
[69] S. P. Hoogendoorn, P. H. L. Bovy, Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow, Transp. Res. B 35 (2001) 317-336.
[70] A. Reuschel, Vehicle movements in a platoon. Oesterreichisches Ingenieur-Archir 4 (1950)193-215.
[71] L. A. Pipes, An operational analysis of traffic dynamics. J. Appl. Phys. 24 (1953) 274-287.
[72] G. F. Newell, Nonlinear effects in the dynamics of car following, Oper. Res. 9 (1961) 209-229.
[73] M. Bando et al., Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51 (1995) 1035-1042.
[74] D. Helbing, B. Tilch, Generalized force model of traffic dynamics, Phys. Rev. E 58 (1998) 133-138.
[75] R. Jiang, Q. S. Wu, Z. J. Zhu, Full velocity difference model for car-following theory, Phys. Rev. E 64 (2001) 017101.
[76] H. Lenz, Multi-anticipative car-following model, Eur. J. Phys. B 7 (1999) 331-335.
[77] T. Nagatani, Stabilization and enhancement of traffic flow by the next-nearest-neighbor interaction, Phys. Rev. E 60 (1999) 6395-6401.
[78] A. Nagayama et al., Effect of looking at the car that follows in an optimal velocity model of traffic flow, Phys. Rev. E 65 (2002) 016112.
[79] M. Treiber, A. Hennecke, D. Helbing, Congested traffic states in empirical observations and microscopic simulations, Phys. Rev. E 62 (2000) 1805-1824.
[80] E. Tomer et al., Presence of many stable nonhomogeneous states in an inertial car-following model, Phys. Rev. Lett. 84 (2000) 382-385.
[81] D. Helbing et al., Modelling widely scattered states in 'synchronized' traffic flow and possible relevance for stock market dynamics, Physica A 303 (2002) 251-260.
[82] S. Yukwa et al., Dynamical phase transition in one dimensional traffic flow model with blockage, J. Phys. Soc. Jpn. 63 (1994) 3609-3618.
[83] S. Krauss et al., Metastable states in a microscopic model of traffic flow, Phys. Rev. E 55 (1997) 5597-5602.
[84] S. Tadaki et al., Coupled map traffic flow simulator based on optimal velocity functions, J. Phys. Soc. Jpn. 67 (1998) 2270-2276.
[85] B. S. Kerner, S.L. Klenov, A microscopic model for phase transitions in traffic flow, J. Phys. A 35 (2002) L31-L43.
[86] M. Cremer, J. Ludwig, A fast simulation model for traffic flow on the basis of Boolean operations, J. Math. Comp. Simul. 28 (1986) 297-303.
[87] M. R. Evans, D. P. Foster, C. Godreche and D Mukamel, Spontaneous Symmetry Breaking in a One-Dimensional Driven Diffusive System, Phys. Rev. Lett. 74 (1995) 208-211.
[88] M. R. Evans, D. P. Foster, C. Godrecher and D. Mukamel, Asymmetric Exclusion Modelwith Species: Spontaneous Symmetry Breaking, J. Stat. Phys. 80 (1995) 69-102.
[89] S. Wolfram, A New Kind of Science, Champaign Illinois: Wolfram Media (2002).
[90] B. Chopard and M. Droz, Cellular Automata Modeling of Phyaical Systems.祝玉学,赵学龙(译),物理系统的元胞自动机模型,北京清华大学出版社(2003).
[91] A. Reggia, S. L. Armentrout, H. H. Chou and Y. Peng, Simple systems that exhibit self-directed replication, Science 259 (1993) 1282-1287.
[92] E. F. Godd, Cellular Automata, New York: Academic Press (1968).
[93] C. G. Langton, Self-reproduction in cellular automata, Physica D 10 (1984) 135-144.
[94] J. Byl, Self-reproduction in small cellular automata, Physica D 34 (1989) 259-299.
[95] S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys. 55 (1983) 601–644.
[96] S. Wolfram, Theory and application of cellular automata, World Scientific Singapore, 1986.
[97] K. Nagel, M. Schreckenberg, A cellular automaton model for freeway traffic, J. DE Phys. I 2 (1992) 2221–2229.
[98] M. Takayasu and H. Takayasu, 1/f noise in a traffic model, Fractals 1 (1993) 860-866.
[99] R. Barlovic, L. Santen, A. Schadschneider, M. Schreckenberg, Metastable states in cellular automata for traffic flow, Eur. Phys. J. B 5 (1998) 793–800.
[100] S. C. Benjamin, N. F. Johnson and P. M. Hui, Cellular automaton models of traffic flow along a highway containing a junction, J. Phys. A 29, (1996) 3119-3127.
[101] X. B. Li, Q. S. Wu and R. Jiang, Cellular automaton model considering the velocity effect of a car on the successive car. Phys. Rev. E 64 (2001) 066128.
[102] T. Nagatani, Self-organization and phase-transition in traffic-flow model of a 2-lane roadway, J. Phys. A 26 (1993) L781-L787.
[103] T. Nagatani, Dynamical jamming transition induced by a car accident in traffic-flow model of a 2-lane roadway, Physica A 202 (1994) 449-458.
[104] M. Rickert, K. Nagel and M. Schreckenberg, Two lane traffic simulation using cellular automata, Physica A 231 (1996) 534-550.
[105] D. Chowdhury, D. E. Wolf and M. Schreckenberg, Particle hopping models for two-lane traffic with two kinds of vehicles: effects of lane changing rules. Physica A 235 (1997) 417-439.
[106] P. Wagner, K. Nagel and D. E. Wolf, Realistic multi-lane traffic rules for cellular automata, Physica A 234 (1997) 687-698.
[107] K. Nagel, D. E. Wolf and P. Wagner, Two-lane traffic rules for cellular automata: A systematic approach. Phys. Rev. E 58 (1998) 1425-1437.
[108] W. Knospe, L. Santen and A Schadschneider, Disorder effects in cellular automata for two-lane traffic. Physica A 265 (1999) 614-633.
[109] W. Knospe, L. Santen and A Schadschneider, A realistic two-lane traffic model for high-way traffic, J. Phys. A 35 (2002) 3369-3388.
[110] B. Jia, R. Jiang and Q. S. Wu, Honk effect in the two-lane cellular automation model for traffic flow. Physica A 348 (2005) 544-552.
[111] M. M. Pederson and P. T. Ruhoff, Entry ramps in the Nagel-Schrekenberg model, Phys. Rev. E 65 (2002) 056705.
[112] A. K. Daoudia and N. Moussa, Numerical simulations of a three-lane traffic model using cellular automata, Chin. J. Phys., 41(6) (2003) 671-681.
[113] O. Biham, A. A. Middleton, D. A. Levine, Self-organization and a dynamical transition in traffic flow models, Phys. Rev. A 46 (1992) R6124–R6127.
[114] T. Nagatani, Jamming transition in the traffic-flow model with two-level crossings, Phys. Rev. E 48 (1993) 3290-3294.
[115] Y. Ishibashi and M. Fukui, Temporal variations of traffic flow in the Biham-Middleton- Levine model, J. Phys. Soc. Japan 63 (1994) 2882-2885.
[116] K. H. Chung, P. M. Hui and G. Q. Gu, Two-dimensional traffic flow problems with faulty traffic lights, Phys. Rev. E 51 (1995) 772-774.
[117] T. Nagatani, Anisotropic effect on jamming transition in traffic flow, J. Phys. Soc. Japan 62 (1993) 2656-2662.
[118] J. A. Cuesta, F. C. Martines and J. M. Molera, Phase transition in two-dimensional traffic-flow models, Phys. Rev. E 48 (1993) R4175-R4178.
[119] T. Nagatani, Effect of jam-avoiding turn on jamming transition in two-dimensional traffic flow model, J. Phys. Soc. Japn. 63(4) (1994) 1228-1231.
[120] G. Q. Gu, K. H. Chung, P. M. Hui, two-dimensional traffic flow model problems in inhomogeneous lattice, Physica A 217 (1995) 339-347.
[121] M. Fukui, H. Oikawa and Y. Ishibashi, Flow of cars crossing with unequal velocities in a two-dimensional cellular automaton model. J. Phys. Soc. Japn. 65 (1996) 2514-2517.
[122] B. H. Wang, Y. F. Woo and P. M. Hui, Improved mean-field theory of two-dimensional traffic flow models, J. Phys. A 29 (1996) L31-L35.
[123] B. H. Wang, Y. F. Woo and P. M. Hui, Mean field theory of traffic flow problems with overpasses and asymmetric distributions of cars, J. Phys. Soc. Jpn 65 (1996) 2345-2348.
[124] H. F. Chau, P. M. Hui and Y. F. Woo, Upper bounds for the critical car densities in traffic flow problems, J. Phys. Soc. Japan 64 (1995) 3570-3572.
[125] J. M. Molera, F. C. Martinez, J. A. Cuesta and R. Brito, Theoretical approach to two- dimensional traffic flow models, Phys. Rev. E 51 (1995) 175-187.
[126] T. Nagatani and T. Seno, Traffic jam induced by a crosscut road in traffic-flow model, Physica A 207 (1994) 574-583.
[127] T. Horiguchi and T. Sakakibara, Numerical simulations for traffic-flow models on a decorated square lattice, Physica A 207 (1998) 388-404.
[128] B. Chopard, P. O. Luthi and P. A. Queloz, Cellular automata model of car traffic in two-dimensional street networks, J. Phys. A 29 (1996) 2325-2336.
[129] D. Chowdhury and A. Schadschneider, Self-organization of traffic jams in cities: Effects of stochastic dynamics and signal periods, Phys. Rev. E 59 (1999) R1311-R1214.
[130] Raissa M. D’Souza, Coexisting phases and lattice dependence of a cellular automaton model for traffic flow, Phys. Rev. E 71(2005) 066112.
[131] J. T?r?k and J. Kertész, The green wave model of two-dimensional traffic: transitions in the flow properties and in the geometry of the traffic jam, Physica A 231 (1996) 515-533.
[132] J. Weibull, Evolutionary Game Theory, Cambridge: MIT Press (1995).
[133] J. Hofbauer and K.Sigmund, Evolutionary Games and Population Dynamics, Cambridge: Cambridge University Press (1998).
[134] J. V. Neuman and O. Morgenstern, Theory of games and economic behavior, Princeton: Princeton University Press (1953).
[135] R. Axelrod, The Evolution of Cooperation, NewYork: Basic Books (1984).
[136] G. Szabóand and C. T?ke, Evolutionary prisoner’s dilemma game on a square lattice, Phys. Rev. E 58 (1998) 69-73.
[137] C. Hauert and G. Szabó, Game theory and physics, American Journal of Physics 73 (2005) 405- 414.
[138] Matja? Perc, Premature seizure of traffic flow due to the introduction of evolutionary games, New Journal of Physics 9 (2007) 3-17.
[139]百度百科、维基百科:智能交通、智能交通系统等。
[140] X. B. Li, R. Jiang and Q. S. Wu, Cellular automata model simulating complex spatiotemporal structure of wide jams, Phys. Rev. E 68 (2003) 016117.
[141] M. E. Lárraga, J. A. del Río and A. Schadschneider, New kind of phase separation in a CA traffic model with anticipation, J. Phys. A 37 (2004) 3769-3781.
[142] R. L. Wang, R. Jiang, Q. S. Wu and M. Z. Liu, Synchronized flow and phase separations in single-lane mixed traffic flow, Physica A 378 (2007) 475-484.
[143] M. Barthélemy, and A. Flammini, Modeling Urban Street Patterns, Physical ReviewLetters 100 (2008) 138702.
[144] H. Youn, M. T. Gastner and H. Jeong, Price of Anarchy in Transportation Networks: Efficiency and Optimality Control, Physical Review Letters 101 (2008) 128701.
[145] N. Rajewsky, L. Santen, A. Schadschneider and M. Schreckenberg, The asymmetric exclusion process: comparison of update procedures, Journal of statistical physics 92 (1998) 151-194.
[146] Z. J. Ding, R. Jiang and B. H. Wang, Traffic flow in the Biham-Middleton-Levine model with random update rule, Phys. Rev. E 83 (2001) 047101.
[2]徐东云,张雷,兰荣娟,城市交通拥堵的背景变换分析,城市问题164 (2009) 46-49.
[3]李瑞敏,城市交通信号控制系统相关理论模型研究及软件开发,Ph.D thesis,清华大学(2005).
[4]唐孝威,张训生,陆坤权(Ed.),交通流与颗粒流,浙江大学出版社, 2004.
[5] D. Chowdhury, L. Santen, A. Schadschneider, Statistical physics of vehicular traffic and some related systems, Phys. Rep. 329 (2000) 199–329.
[6]高坤,从基本图方法到三相交通流理论---交通流元胞自动机模型理论研究,Ph.D thesis,中国科学技术大学(2009).
[7] TRANSIMS. Transportation Analysis and Simulation System. Los Alamos National Laboratory, Los Alamos, http://transims.tsasa.lanl.gov.
[8] D. Helbing, A. Hennecke, V. Shvetsov, et al. MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model. Transp. Res. B 35 (2001) 183-211.
[9]孙晓燕,交通流复杂动态特性的交通流元胞自动机模型研究,Ph.D thesis,中国科学技术大学(2010).
[10]姜锐,交通流复杂动态特征的微观和宏观模式研究,Ph.D thesis,中国科学技术大学(2002).
[11] D. L. Gerlough, and M. J. Huber, Traffic Flow Theory, Transportation Research Board, Washington, DC (1975) 165. D. L. Gerlough, and M. J. Huber, Traffic Flow Theory, Transportation Research Board, Washington, DC (1975) 165.
[12] M. Koshi, Iwasaki M., and I. Ohkura, in Proceedings of the 8th International Symposium on Transportation and Traffic Flow Theory, University of Toronto, Toronto (1983) 403.
[13] A. D. May, Traffic Flow Fundamentals, Prentice Hall, Englewood Cliffs, NJ, (1990).
[14] C. F. Daganzo, Fundamentals of Transportation and Traffic Operations, Pergamon Elsevier, Oxford, England (1997).
[15] B. S. Kerner, in Proceedings of the 3rd International Symposium on Highway Capacity edited by R. Rysgaard, Road Directorate, Denmark, Vol. 2 (1998) 621.
[16] B. S. Kerner, in Traffic and Granular Flow’97, edited by M. Schreckenberg and D. E. Wolf, Springer, New York (1998) 239.
[17] C. F. Daganzo, A Behavioral Theory of Multi-lane Traffic Flow. I: Long HomogeneousFreeway Sections. Research Report UCB-ITS-RR-99-5, Institute of Transportation Studies, University of California, Berkeley, CA, (1999).
[18] C. F. Daganzo, A Behavioral Theory of Multi-lane Traffic Flow. II: Merges and the Onset of Congestion. Research Report UCB-ITS-RR-99-6, Institute of Transportation Studies, University of California, Berkeley, CA (1999).
[19] B. S. Kerner, Phys. World 12 (8) (1999) 25.
[20] B. S. Kerner, Transp. Res. Rec. 1678, (1999) 160.
[21] B. S. Kerner, Transp. Res. Rec. 1710 (2000) 136.
[22] B. S. Kerner, in Traffic and Granular Flow’99: Social, Traffic, and Granular Dynamics, edited by D. Helbing, H. J. Herrmann, M. Schreckenberg, and D. E. Wolf, Springer, Berlin, (2000) 253.
[23] K. Nagel, P. Wagner and R. Woesler, Still flowing: Approaches to traffic flow and traffic jam modeling, Oper. Res. 51(5) (2003) 681-710.
[24] D. Helbing, Traffic and related self-driven many-particle systems, Rev. Mod. Phys., 73 (2001).
[25] L. C. Edie, Car-following and steady-state theory for non-congested traffic, Oper. Res. 9 (1961) 66-77.
[26] F. L. Hall and K. Agyemang-Duah, Freeway capacity drop and the definition of capacity, Transp. Res. Rec. 1320 (1991) 91-98.
[27] B. S. Kerner and H. Rehborn, Experimental features and characteristics of traffic jams, Phys. Rev. E (1996) R1297-1230.
[28] J. R. Windover and M. J. Cassidy, Some observed details for freeway traffic evolution, Transp. Res. A 35 (2001) 881-894.
[29] B. S. Kerner, Experimental features of self-organization in traffic flow. Phys. Rev. Lett. 81(17) (1998) 3797-3800.
[30] S. A. Paul and J. L. David, A novel nonlinear car-following model, chaos 8 (1998) 791-799.
[31] L. A. Safonov, Delay-induced chaos with multifractal attractor in a traffic flow model. Euro. Phys. Lett. 57 (2002) 151-157.
[32] K. P. Li and Z. Y. Gao, Nonlinear dynamics analysis of traffic times series, Mod. Phys. Letts. B 18 (2004) 1395-1402.
[33] K. P. Li and Z. Y. Gao, Controlling the states of traffic flow at the intersections, Int. J. Mod. Phys. C 15 (2004) 553-562.
[34] K. P. Li and Z. Y. Gao, tranisition from disorder to order in traffic flow, Chin. Phys. Lett.21 (2004) 1212-1215.
[35] K. P. Li and Z. Y. Gao, Order moving states in traffic flow, Physica A 348 (2005) 553-560.
[36] K. P. Li and Z. Y. Gao, Controlling the vehicle states in two lane traffic, Int. J. Mod. Phys. C 16(3) (2005) 501-512.
[37] D. A. Kurtz, Traffic jam, granular flow and soliton selection, Phys. Rev. E 52 (1993) 5574-5582.
[38] D. Helbing, Jams, waves and clusters, Science 282 (1998) 2001-2003.
[39] T. Nagatani, Density wave in traffic flow, Phys. Rev. E 60 (1999) 6395-6401.
[40] D. Helbing, Master: macroscopic traffic simulation based on a gas-kinetic nonlocal traffic model. Trasp. Res. B 35 (2001) 180-211.
[41] Y. Xue, Analysis of the stability and density waves for traffic flow, Chin. Phys. 11(11) (2002) 1128-1134.
[42] J. P. Kinzer, Application of the theory of probability to problem of highway traffic, B. C. E thesis, Politech. Inst. Brooklyn (1933).
[43] M. J. Lighthill, G. B. Whitham, On kinematic waves: II. a theory of traffic flow on long crowded roads, Proceedings of the Royal Society, Ser. A 229 (1955) 317-345.
[44] P. I. Richards, Shock waves on the highway, Oper. Res. 4 (1956) 42-51.
[45] H. J. Payne Models of freeway traffic and control, In: Bekey, G.A. (Ed.), Mathematical Models of Public Systems 1, Simulation Council, La Jolla, (1971) 51-61.
[46] R. D. Kühne, Macroscopic freeway model for dense traffic stop-start waves and incident detection, In: Proceedings of the Ninth International Symposium on Transportation and Traffic Theory (1984) 20-42.
[47] P. Ross, Traffic dynamics, Transp. Res. B 22 (1988) 421-435.
[48] M. Papageorgiou, J.M. Blosseville, H. Hadj-Salem, Macroscopic modeling of traffic flow on the Boulevard Peripherique in Paris, Transp. Res. B 23 (1989) 29-47.
[49] P. G. Michalopoulos, P. Yi, A.S. Lyrintzis, Continuum modeling of traffic dynamics for congested freeways, Transp. Res. B 27 (1993) 315-332.
[50] B. S. Kerner, P. Konh?auser, Cluster effect in initially homogeneous traffic flow, Phys. Rev. E 48 (1993) R2335-2338.
[51] B. S. Kerner, P. Konh?user, Structure and parameters of clusters in traffic flow, Phys. Rev. E 50 (1994) 54-83.
[52] H. Y. Lee, H.W. Lee, D. Kim, Origin of synchronized traffic flow on highways and its dynamic phase transition, Phys. Rev. Lett. 81 (1998) 1130-1133.
[53] H. Y. Lee, H.W. Lee, D. Kim, Dynamic states of a continuum traffic equation withon-ramp, Phys. Rev. E 59 (1999) 5101-5111.
[54] H. M. Zhang, A theory of nonequilibrium traffic flow, Transp. Res. B 32 (1998) 485-498.
[55] A. Aw, M. Rascle, Resurrection of "second order" models of traffic flow, SIAM Journal on Appl. Math. 60 (2000) 916-938.
[56] R. Jiang, Q. S. Wu, Z. J. Zhu, A new continuum model for traffic flow and numerical tests, Transp. Res. B 36 (2002) 405-419.
[57] Y. Xue, S. Q. Dai, Continuum traffic model with the consideration of two delay time scales, Phys. Rev. E 68 (2003) 066123.
[58] F. Siebel, W. Mauser, On the fundmental diagram of traffic flow, SIAM Journal on Appl. Math. 66 (2006) 1150-1162.
[59] F. Siebel, W. Mauser, Synchronized flow and wide moving jams from balanced vehicular traffic, Phys. Rev. E 73 (2006) 066108.
[60] I. Prigogine, R. Herman, Kinetic theory of vehicular traffic, American Elsevier, New York 1971.
[61] S. L. Paveri-Fontana, On Boltzmann-like treatments for traffic flow. A critical review of the basic model and an alternative proposal for dilute traffic analysis. Tranpn. Res. 9 (1975) 225-235.
[62] D. Helbing, Derivation and empirical validation of a refined traffic flow model, Physica A 233 (1996) 253-282.
[63] T. Nagatani, Kinetic segregation in a multilane highway traffic flow, Physica A 237 (1997) 67-74.
[64] D. Helbing, A. Greiner, Modeling and simulation of multilane traffic flow, Phys. Rev. E 55 (1997) 5498-5508.
[65] V. Shvetsov, D. Helbing, Macroscopic dynamics of multilane traffic, Phys. Rev. E 59 (1999) 6382-6339.
[66] S. P. Hoogendoorn, P. H. L. Bovy, Continuum modeling of multiclass traffic flow, Transp. Res. B 34 (2000) 123-146.
[67] M. Treiber, A. Hennecke, D. Helbing, Derivation, properties and simulation of a gas-kinetic-based nonlocal traffic model, Phys. Rev. E 59 (1999) 239-253.
[68] D. Helbing et al., MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model, Transp. Res. B 35 (2001) 183-211.
[69] S. P. Hoogendoorn, P. H. L. Bovy, Generic gas-kinetic traffic systems modeling with applications to vehicular traffic flow, Transp. Res. B 35 (2001) 317-336.
[70] A. Reuschel, Vehicle movements in a platoon. Oesterreichisches Ingenieur-Archir 4 (1950)193-215.
[71] L. A. Pipes, An operational analysis of traffic dynamics. J. Appl. Phys. 24 (1953) 274-287.
[72] G. F. Newell, Nonlinear effects in the dynamics of car following, Oper. Res. 9 (1961) 209-229.
[73] M. Bando et al., Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51 (1995) 1035-1042.
[74] D. Helbing, B. Tilch, Generalized force model of traffic dynamics, Phys. Rev. E 58 (1998) 133-138.
[75] R. Jiang, Q. S. Wu, Z. J. Zhu, Full velocity difference model for car-following theory, Phys. Rev. E 64 (2001) 017101.
[76] H. Lenz, Multi-anticipative car-following model, Eur. J. Phys. B 7 (1999) 331-335.
[77] T. Nagatani, Stabilization and enhancement of traffic flow by the next-nearest-neighbor interaction, Phys. Rev. E 60 (1999) 6395-6401.
[78] A. Nagayama et al., Effect of looking at the car that follows in an optimal velocity model of traffic flow, Phys. Rev. E 65 (2002) 016112.
[79] M. Treiber, A. Hennecke, D. Helbing, Congested traffic states in empirical observations and microscopic simulations, Phys. Rev. E 62 (2000) 1805-1824.
[80] E. Tomer et al., Presence of many stable nonhomogeneous states in an inertial car-following model, Phys. Rev. Lett. 84 (2000) 382-385.
[81] D. Helbing et al., Modelling widely scattered states in 'synchronized' traffic flow and possible relevance for stock market dynamics, Physica A 303 (2002) 251-260.
[82] S. Yukwa et al., Dynamical phase transition in one dimensional traffic flow model with blockage, J. Phys. Soc. Jpn. 63 (1994) 3609-3618.
[83] S. Krauss et al., Metastable states in a microscopic model of traffic flow, Phys. Rev. E 55 (1997) 5597-5602.
[84] S. Tadaki et al., Coupled map traffic flow simulator based on optimal velocity functions, J. Phys. Soc. Jpn. 67 (1998) 2270-2276.
[85] B. S. Kerner, S.L. Klenov, A microscopic model for phase transitions in traffic flow, J. Phys. A 35 (2002) L31-L43.
[86] M. Cremer, J. Ludwig, A fast simulation model for traffic flow on the basis of Boolean operations, J. Math. Comp. Simul. 28 (1986) 297-303.
[87] M. R. Evans, D. P. Foster, C. Godreche and D Mukamel, Spontaneous Symmetry Breaking in a One-Dimensional Driven Diffusive System, Phys. Rev. Lett. 74 (1995) 208-211.
[88] M. R. Evans, D. P. Foster, C. Godrecher and D. Mukamel, Asymmetric Exclusion Modelwith Species: Spontaneous Symmetry Breaking, J. Stat. Phys. 80 (1995) 69-102.
[89] S. Wolfram, A New Kind of Science, Champaign Illinois: Wolfram Media (2002).
[90] B. Chopard and M. Droz, Cellular Automata Modeling of Phyaical Systems.祝玉学,赵学龙(译),物理系统的元胞自动机模型,北京清华大学出版社(2003).
[91] A. Reggia, S. L. Armentrout, H. H. Chou and Y. Peng, Simple systems that exhibit self-directed replication, Science 259 (1993) 1282-1287.
[92] E. F. Godd, Cellular Automata, New York: Academic Press (1968).
[93] C. G. Langton, Self-reproduction in cellular automata, Physica D 10 (1984) 135-144.
[94] J. Byl, Self-reproduction in small cellular automata, Physica D 34 (1989) 259-299.
[95] S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys. 55 (1983) 601–644.
[96] S. Wolfram, Theory and application of cellular automata, World Scientific Singapore, 1986.
[97] K. Nagel, M. Schreckenberg, A cellular automaton model for freeway traffic, J. DE Phys. I 2 (1992) 2221–2229.
[98] M. Takayasu and H. Takayasu, 1/f noise in a traffic model, Fractals 1 (1993) 860-866.
[99] R. Barlovic, L. Santen, A. Schadschneider, M. Schreckenberg, Metastable states in cellular automata for traffic flow, Eur. Phys. J. B 5 (1998) 793–800.
[100] S. C. Benjamin, N. F. Johnson and P. M. Hui, Cellular automaton models of traffic flow along a highway containing a junction, J. Phys. A 29, (1996) 3119-3127.
[101] X. B. Li, Q. S. Wu and R. Jiang, Cellular automaton model considering the velocity effect of a car on the successive car. Phys. Rev. E 64 (2001) 066128.
[102] T. Nagatani, Self-organization and phase-transition in traffic-flow model of a 2-lane roadway, J. Phys. A 26 (1993) L781-L787.
[103] T. Nagatani, Dynamical jamming transition induced by a car accident in traffic-flow model of a 2-lane roadway, Physica A 202 (1994) 449-458.
[104] M. Rickert, K. Nagel and M. Schreckenberg, Two lane traffic simulation using cellular automata, Physica A 231 (1996) 534-550.
[105] D. Chowdhury, D. E. Wolf and M. Schreckenberg, Particle hopping models for two-lane traffic with two kinds of vehicles: effects of lane changing rules. Physica A 235 (1997) 417-439.
[106] P. Wagner, K. Nagel and D. E. Wolf, Realistic multi-lane traffic rules for cellular automata, Physica A 234 (1997) 687-698.
[107] K. Nagel, D. E. Wolf and P. Wagner, Two-lane traffic rules for cellular automata: A systematic approach. Phys. Rev. E 58 (1998) 1425-1437.
[108] W. Knospe, L. Santen and A Schadschneider, Disorder effects in cellular automata for two-lane traffic. Physica A 265 (1999) 614-633.
[109] W. Knospe, L. Santen and A Schadschneider, A realistic two-lane traffic model for high-way traffic, J. Phys. A 35 (2002) 3369-3388.
[110] B. Jia, R. Jiang and Q. S. Wu, Honk effect in the two-lane cellular automation model for traffic flow. Physica A 348 (2005) 544-552.
[111] M. M. Pederson and P. T. Ruhoff, Entry ramps in the Nagel-Schrekenberg model, Phys. Rev. E 65 (2002) 056705.
[112] A. K. Daoudia and N. Moussa, Numerical simulations of a three-lane traffic model using cellular automata, Chin. J. Phys., 41(6) (2003) 671-681.
[113] O. Biham, A. A. Middleton, D. A. Levine, Self-organization and a dynamical transition in traffic flow models, Phys. Rev. A 46 (1992) R6124–R6127.
[114] T. Nagatani, Jamming transition in the traffic-flow model with two-level crossings, Phys. Rev. E 48 (1993) 3290-3294.
[115] Y. Ishibashi and M. Fukui, Temporal variations of traffic flow in the Biham-Middleton- Levine model, J. Phys. Soc. Japan 63 (1994) 2882-2885.
[116] K. H. Chung, P. M. Hui and G. Q. Gu, Two-dimensional traffic flow problems with faulty traffic lights, Phys. Rev. E 51 (1995) 772-774.
[117] T. Nagatani, Anisotropic effect on jamming transition in traffic flow, J. Phys. Soc. Japan 62 (1993) 2656-2662.
[118] J. A. Cuesta, F. C. Martines and J. M. Molera, Phase transition in two-dimensional traffic-flow models, Phys. Rev. E 48 (1993) R4175-R4178.
[119] T. Nagatani, Effect of jam-avoiding turn on jamming transition in two-dimensional traffic flow model, J. Phys. Soc. Japn. 63(4) (1994) 1228-1231.
[120] G. Q. Gu, K. H. Chung, P. M. Hui, two-dimensional traffic flow model problems in inhomogeneous lattice, Physica A 217 (1995) 339-347.
[121] M. Fukui, H. Oikawa and Y. Ishibashi, Flow of cars crossing with unequal velocities in a two-dimensional cellular automaton model. J. Phys. Soc. Japn. 65 (1996) 2514-2517.
[122] B. H. Wang, Y. F. Woo and P. M. Hui, Improved mean-field theory of two-dimensional traffic flow models, J. Phys. A 29 (1996) L31-L35.
[123] B. H. Wang, Y. F. Woo and P. M. Hui, Mean field theory of traffic flow problems with overpasses and asymmetric distributions of cars, J. Phys. Soc. Jpn 65 (1996) 2345-2348.
[124] H. F. Chau, P. M. Hui and Y. F. Woo, Upper bounds for the critical car densities in traffic flow problems, J. Phys. Soc. Japan 64 (1995) 3570-3572.
[125] J. M. Molera, F. C. Martinez, J. A. Cuesta and R. Brito, Theoretical approach to two- dimensional traffic flow models, Phys. Rev. E 51 (1995) 175-187.
[126] T. Nagatani and T. Seno, Traffic jam induced by a crosscut road in traffic-flow model, Physica A 207 (1994) 574-583.
[127] T. Horiguchi and T. Sakakibara, Numerical simulations for traffic-flow models on a decorated square lattice, Physica A 207 (1998) 388-404.
[128] B. Chopard, P. O. Luthi and P. A. Queloz, Cellular automata model of car traffic in two-dimensional street networks, J. Phys. A 29 (1996) 2325-2336.
[129] D. Chowdhury and A. Schadschneider, Self-organization of traffic jams in cities: Effects of stochastic dynamics and signal periods, Phys. Rev. E 59 (1999) R1311-R1214.
[130] Raissa M. D’Souza, Coexisting phases and lattice dependence of a cellular automaton model for traffic flow, Phys. Rev. E 71(2005) 066112.
[131] J. T?r?k and J. Kertész, The green wave model of two-dimensional traffic: transitions in the flow properties and in the geometry of the traffic jam, Physica A 231 (1996) 515-533.
[132] J. Weibull, Evolutionary Game Theory, Cambridge: MIT Press (1995).
[133] J. Hofbauer and K.Sigmund, Evolutionary Games and Population Dynamics, Cambridge: Cambridge University Press (1998).
[134] J. V. Neuman and O. Morgenstern, Theory of games and economic behavior, Princeton: Princeton University Press (1953).
[135] R. Axelrod, The Evolution of Cooperation, NewYork: Basic Books (1984).
[136] G. Szabóand and C. T?ke, Evolutionary prisoner’s dilemma game on a square lattice, Phys. Rev. E 58 (1998) 69-73.
[137] C. Hauert and G. Szabó, Game theory and physics, American Journal of Physics 73 (2005) 405- 414.
[138] Matja? Perc, Premature seizure of traffic flow due to the introduction of evolutionary games, New Journal of Physics 9 (2007) 3-17.
[139]百度百科、维基百科:智能交通、智能交通系统等。
[140] X. B. Li, R. Jiang and Q. S. Wu, Cellular automata model simulating complex spatiotemporal structure of wide jams, Phys. Rev. E 68 (2003) 016117.
[141] M. E. Lárraga, J. A. del Río and A. Schadschneider, New kind of phase separation in a CA traffic model with anticipation, J. Phys. A 37 (2004) 3769-3781.
[142] R. L. Wang, R. Jiang, Q. S. Wu and M. Z. Liu, Synchronized flow and phase separations in single-lane mixed traffic flow, Physica A 378 (2007) 475-484.
[143] M. Barthélemy, and A. Flammini, Modeling Urban Street Patterns, Physical ReviewLetters 100 (2008) 138702.
[144] H. Youn, M. T. Gastner and H. Jeong, Price of Anarchy in Transportation Networks: Efficiency and Optimality Control, Physical Review Letters 101 (2008) 128701.
[145] N. Rajewsky, L. Santen, A. Schadschneider and M. Schreckenberg, The asymmetric exclusion process: comparison of update procedures, Journal of statistical physics 92 (1998) 151-194.
[146] Z. J. Ding, R. Jiang and B. H. Wang, Traffic flow in the Biham-Middleton-Levine model with random update rule, Phys. Rev. E 83 (2001) 047101.