基于元胞自动机的交通流研究
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摘要
随着我国国民经济的迅速发展和城市化进程的加快，城市交通堵塞日益严重。如何采取措施改善交通状况是一项亟待解决的问题，而交通流规律的研究和交通本质的认识可以为我们提供理论依据和参考。高速公路修建的指数增长更加需要精确和可靠的方法进行交通流的建模和预测，交通流的建模和仿真提供了对交通流的微观和宏观的观测，因而成为交通工程中的重要分析工具。
本文首先介绍了元胞自动机理论的理论，元胞自动机模型把复杂系统量化为简单的个体。在元胞自动机模型中，空间、时间都被离散化，每一个相互作用的单元仅为有限的状态。以元胞自动机理论为基础，把车辆在路段上运动的变化规律表述为元胞自动机的演化规则，建立了基于元胞自动机理论的交通流模拟模型，标定了元胞长度和最大速度等参数，继而提出反映车辆在路段上自由行驶、跟驰行驶减速行驶等交通行为的元胞自动机规则，并对各种规则进行了详细说明。在元胞自动机交通NaSch模型和FI模型的基础上，基于交通流中实际车辆的慢起动行为，进一步提出一种新的一维交通流元胞自动机模型，在临界密度附近，存在着亚稳态和滞后现象。利用面向对象的JAVA语言，设计实现了CATS仿真系统，模拟了各种一维周期性边界条件下高速公路上车流运动，显示了交通流的各种现象。例如从自由相到堵塞相的相变行为、临界性和自组织临界性、亚稳态和相分离等。采用统计物理的分析方法进行了分析，其中应用平均场理论对交通流的流量、密度和速度间的基本关系进行了求解。最后，对拥挤交通的交通堵塞进行了分析，从交通崩溃的角度，例如交通从自由流线型交通到堵塞交通的过程，得到结论为：当堵塞流出量的车头时距大于高密度时的车头时距时，堵塞稳定存在。另外，对交通流的自组织的可能性进行了讨论，对交通流的分形和耗散进行了初步的研究。
本论文的研究对交通组织和管理均具有重要的理论和实践意义。
As the national economics rapid developing and cities scale becoming larger and larger, it has became more and more serious that the problems of urban transportation block. How to improve the traffic state is a issue that must be dealed with, the studies and the nature of traffic flow can help solve it. The exponential rate of increase in freeway traffic is expanding the need for accurate and realistic methods to model and predict traffic flow. Traffic modeling and simulation facilitates an examination of both microscopic and macroscopic views of traffic flows and is therefore considered one of the most important analytical tools in traffic engineering.
This paper presents some cellular automata models for traffic flow simulation. Firstly, the celluar automata theory was introduced, cellular autoata models quantize complex behavior into simple individual components. In general, CA are idealization of physical systems in which both space and time are assumed to be discrete and each of the interacting units can have only a finite number of discrete states. Based on the cellular automata theory, this paper describes the moving character of vehicles as changing rules of cellular automata, thus traffic flow simulation models based on cellular automata are presented. After calibrating the basic parameters such as cellular length, maximum speed and so on, the traffic behaviors such as free moving, following, decelerating are described by the special changing rules of cellular automata. All the rules are also explained in great detail including a minimal model of NaSch and FI which reproduce the basic features of real traffic. An improved one-dimensional CA traffic model was proposed to describe the freeway traffic under the periodic boundary conditions. This model was based on the NaSch model, it can describe stop-and-go traffic, which gives a better description of the phenomena observed on highways with a slow-to-start rule. It is found that there exists the metastability and hysteresis effect of traffic flow in the neighborhood of critical density under different initial conditions. A computer simulation system named CATS was fulfilled with all celluar automata models in JAVA language. It proved some of these phenomena, observed in vehicular traffic under different
circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. Anslytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Mean field theory is proposed for analysis the relation of traffic flow density and speed. In the last, traffic jams in the congested traffic flow are investigated by the computer simulation and the analytical method, this paper looks at this question in particular from the perspective of breakdown behavior, i.e. the transtion from free, "laminar" traffic to congested traffic. The typical traffic jam instability is intuitively explained via the insight that stable jams exist once time headways at jam outflow are larger than time headway in dense traffic. In addition, the feasibility and rationality to apply self-organization theory on traffic flow study are discussed, fractality and dissipation in traffic flow are studied preliminary.
In a word, the studies of this paper have a profound function to traffic control and management.
本文首先介绍了元胞自动机理论的理论，元胞自动机模型把复杂系统量化为简单的个体。在元胞自动机模型中，空间、时间都被离散化，每一个相互作用的单元仅为有限的状态。以元胞自动机理论为基础，把车辆在路段上运动的变化规律表述为元胞自动机的演化规则，建立了基于元胞自动机理论的交通流模拟模型，标定了元胞长度和最大速度等参数，继而提出反映车辆在路段上自由行驶、跟驰行驶减速行驶等交通行为的元胞自动机规则，并对各种规则进行了详细说明。在元胞自动机交通NaSch模型和FI模型的基础上，基于交通流中实际车辆的慢起动行为，进一步提出一种新的一维交通流元胞自动机模型，在临界密度附近，存在着亚稳态和滞后现象。利用面向对象的JAVA语言，设计实现了CATS仿真系统，模拟了各种一维周期性边界条件下高速公路上车流运动，显示了交通流的各种现象。例如从自由相到堵塞相的相变行为、临界性和自组织临界性、亚稳态和相分离等。采用统计物理的分析方法进行了分析，其中应用平均场理论对交通流的流量、密度和速度间的基本关系进行了求解。最后，对拥挤交通的交通堵塞进行了分析，从交通崩溃的角度，例如交通从自由流线型交通到堵塞交通的过程，得到结论为：当堵塞流出量的车头时距大于高密度时的车头时距时，堵塞稳定存在。另外，对交通流的自组织的可能性进行了讨论，对交通流的分形和耗散进行了初步的研究。
本论文的研究对交通组织和管理均具有重要的理论和实践意义。
As the national economics rapid developing and cities scale becoming larger and larger, it has became more and more serious that the problems of urban transportation block. How to improve the traffic state is a issue that must be dealed with, the studies and the nature of traffic flow can help solve it. The exponential rate of increase in freeway traffic is expanding the need for accurate and realistic methods to model and predict traffic flow. Traffic modeling and simulation facilitates an examination of both microscopic and macroscopic views of traffic flows and is therefore considered one of the most important analytical tools in traffic engineering.
This paper presents some cellular automata models for traffic flow simulation. Firstly, the celluar automata theory was introduced, cellular autoata models quantize complex behavior into simple individual components. In general, CA are idealization of physical systems in which both space and time are assumed to be discrete and each of the interacting units can have only a finite number of discrete states. Based on the cellular automata theory, this paper describes the moving character of vehicles as changing rules of cellular automata, thus traffic flow simulation models based on cellular automata are presented. After calibrating the basic parameters such as cellular length, maximum speed and so on, the traffic behaviors such as free moving, following, decelerating are described by the special changing rules of cellular automata. All the rules are also explained in great detail including a minimal model of NaSch and FI which reproduce the basic features of real traffic. An improved one-dimensional CA traffic model was proposed to describe the freeway traffic under the periodic boundary conditions. This model was based on the NaSch model, it can describe stop-and-go traffic, which gives a better description of the phenomena observed on highways with a slow-to-start rule. It is found that there exists the metastability and hysteresis effect of traffic flow in the neighborhood of critical density under different initial conditions. A computer simulation system named CATS was fulfilled with all celluar automata models in JAVA language. It proved some of these phenomena, observed in vehicular traffic under different
circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. Anslytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Mean field theory is proposed for analysis the relation of traffic flow density and speed. In the last, traffic jams in the congested traffic flow are investigated by the computer simulation and the analytical method, this paper looks at this question in particular from the perspective of breakdown behavior, i.e. the transtion from free, "laminar" traffic to congested traffic. The typical traffic jam instability is intuitively explained via the insight that stable jams exist once time headways at jam outflow are larger than time headway in dense traffic. In addition, the feasibility and rationality to apply self-organization theory on traffic flow study are discussed, fractality and dissipation in traffic flow are studied preliminary.
In a word, the studies of this paper have a profound function to traffic control and management.
引文
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5 Ihor Lub Towards the fundamental of car following theory, e-print:Cond-mat/0212382
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26 D J.Dailey, N Taiyab,acellular automata model for use with real freeway data,ITS Research program,final research report,January 2002
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2 交通工程手册[M]．交通工程委员会．北京：人民交通出版社．1998
3 [美]丹尼尔L．鸠洛夫、马休丁．休伯著．交通流理论．蒋璜、任福田、肖秋生等译．北京：人民交通出版社．1983
4 Nathan Gartner, Carroll J.Messer, Ajay K.Rathi,Monograph on Traffic Flow Theory[M]. US, 1996
5 Ihor Lub Towards the fundamental of car following theory, e-print:Cond-mat/0212382
6 冯蔚东等：交通流理论评述．系统工程学报，1998；13(3)：71-82
7 冯苏苇等：交通流的动力学模型与数值模拟．上海大学学报(自然科学版)，1997；3(4)：443-452
8 宫晓燕等：高速公路交通流建模综述．交通运输工程学报，2002；2(1)：74-79
9 Mark Brackstone and Mike McDonald,car following:a historical review, T. Res F.2(4)pp 181-196.2000
10 C.F. Daganzo,Remarks on traffic flow modeling and its applications, ", in Traffic and Mobility, Proc. Traffic and Mobility Simulation, Economics and Environment Conference (Brilon, Huber, Schreckenberg and Wallentowitz, eds.),pp. 105-115,Aachen, Germany, Springer-Verlag, New York, N.Y., 1999
11 M.Waldrop著，陈玲译，复杂：诞生于秩序与混沌边缘的学科，三联书店，1997
12 谢惠民，非线性科学丛书：复杂性与动力系统[M]，上海科技教育出版社，1994
13 Algers, S., Bernauer, E., Boero, M., Breheret, L., di Taranto, C., Dougherty, M., Fox, K., and Gabard, J. (1997) Review of micro-simulation models. Smartest Project deliverable D3. Leeds.
14 W. Knospe, L. Santen, A. Schadschneider, and M. Schreckenberg. Towards a realistic microscopic description of highway traffic. Journal of Physics A,33:L477, 2000.
15 D. Wolf. Cellular automata for traffic simulations. Physica A,263:438-451,1999.
16 P. Wagner, K. Nagel, and D. E.Wolf. Realistic multi-lane traffic rules for cellular automata. Physica A, 234:687-698, 1997.
17 A.Schadschneider and M. Schreckenberg. Cellular automaton models and traffic flow J.phys A,26,1993
18 王雷、汪秉宏、决定论性逐步加速交通流模型的渐近稳态行为[J]．物理学报 1999，48(5)：808-815
19 汪秉宏、王雷、徐伯铭、胡斑比．高速车随机延迟逐步加速交通流元胞自动机模型[J]．物理学报，2000，49(10)：1926-1932
20 汪秉宏等，逐步加速交通流模型的渐近稳态行为[J]．深圳大学学报1999，16(2-3)：36-41
21 Matti Pursula,simulation of traffic systems-an overview J.GIDA 3(1999)pp. 1-8
22 王殿海等，对交通流理论的再认识[J]．交通运输工程学报，1(4)：54-59，2001
23 周成虎等著，地理元胞自动机研究[M]，北京，科学出版社，1999
24 史忠植，高级人工智能，北京：科学出版社，1998
25 R. Barlovic,online traffic simulation with cellular automata,traffic and mobility:simulation-economics-environment,pp: 117-134,july 1999
26 D J.Dailey, N Taiyab,acellular automata model for use with real freeway data,ITS Research program,final research report,January 2002
27 J.Wahle,L.Neubert,M. Schreckenberg,modeling and simulation of traffic flow, computer physics communications 121-122(1999)402-404
28 丁爱玲等，城市交通的计算机仿真设计[J]西安公路交通大学学报，20(3)：70-74，2000
29 邹智军等，道路交通仿真研究综述．[J]交通运输工程学报，1(2)：88-91，2001
30 邹智军等，动态交通状态微观仿真技术初探，[J]同济大学学报，27(3)：305-308，1999
31 张安胜等，城市道路交通流仿真算法研究，[J]计算机工程，28(8)：102-104，2002
32 K.Nagel,Particle hopping models and traffic flow theory, Los Alamos Unclassified Report 95:2908(1995),phys. Rev. E
33 Kai Nagel and steel Rasmussen,traffic at the edge of chaos,ARTIFICIAL LIFE ,pp.222-235,1994
34 K.Nagel.From particle hopping models to traffic flow theory. Transportation Research Records, 1644:1-9, 1999.
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