地理学多视角研究方法——Braess网络车流分配过程的理论分析与数值计算

doi:10.11821/yj2008060016

地理研究 ›› 2008, Vol. 27 ›› Issue (6): 1367-1380.doi: 10.11821/yj2008060016

地理学多视角研究方法——Braess网络车流分配过程的理论分析与数值计算

陈彦光

北京大学城市与环境学院,北京100871

收稿日期:2008-04-20 修回日期:2008-07-11 出版日期:2008-11-25 发布日期:2008-11-25
作者简介:陈彦光(1965-),男,河南罗山人,副教授,理学博士。从事地理分形和空间复杂性研究,重点研究自组织城市网络。E-mail:chenyg@pku.edu.cn
基金资助:
国家科技部科技基础工作专项重点资助项目"地理研究方法"的综合集成部分(2007FY140800);国家自然科学基金资助项目(40771061)

An integrated analytical process oftraffic assignment problems of Braess' network

CHEN Yan-guang

College of Urban and Environmental Sciences, Peking University, Beijing 100871, China

Received:2008-04-20 Revised:2008-07-11 Online:2008-11-25 Published:2008-11-25
Supported by:
国家科技部科技基础工作专项重点资助项目"地理研究方法"的综合集成部分(2007FY140800);国家自然科学基金资助项目(40771061)

摘要/Abstract

摘要：

对复杂的地理系统采用多种方法从不同的视角开展分析,可以降低错误结论的概率。本文以Braess交通网络为例,提出一个地理系统多视角分析的研究案例。首先借助La氏乘数法预测奇对称Braess网络的车流优化分配的结果。然后采用数值计算和模拟方法论证,在该网络中,车流会通过自组织过程自动向着优化分配的方向演化,并且利用Markov链预测各个阶段的车流分配数值。最后借助最大熵原理从理论上证明,上述最优化过程的本质是地理系统的熵最大化;运用对偶规划和对称思想揭示,熵最大化的实质是车流运行的耗时总量最小。不同的方法给出的结果殊途同归、互相印证。这一套研究方法可以推广到多维不对称的交通网络,进而推广应用于地理学其他方面的理论分析和应用研究。

关键词: 地理研究方法, 理论演绎, 数值模拟, Braess网络, 最大熵方法

Abstract:

Braess' network can be regarded as a significant metaphor of human geographical phenomena. By means of this simple model, we can reveal many important geographical principles. Based on the problem of traffic assignment in Braess' network, an integrated analytical process is propounded in this paper for efficiently exploring complex geographical systems. For simplicity, only the linear Braess' network without the third expressway is taken into consideration. The question is as follows: how the traffic flow is assigned between the two routes which have odd symmetric structure.Six methods are exerted to solve this problem, including Lagrange multiplier method (LMM), linear dynamical analysis, numerical simulation, numerical computation, Markov chain, and entropy-maximizing method. In the first place, Lagrange multiplier method is employed to give a preliminary solution. Secondly, a pair of linear dynamic equations is constructed for making deep analysis.The dynamic equations are utilized to make numerical computation and simulation. Further, Markov chain is used to make a prediction analysis.All the five kinds of analysis reach the same conclusion by different routes: the traffic flow should be averagely allocated in the two roads.Finally, the method of entropy-maximizing is employed to bring to light the theoretical foundation of average assignment of traffic flow in the Braess’ network.The entropy-maximization of geographical systems suggests the most equity for individuals and efficiency on the whole.All the six methods can be integrated to solve a problem from multifarious views of angles.If the conclusions drawn by different approaches are consistent with each other, the question is clear.However, in practice, some conclusions are not very clear, or even a conclusion based on one method may come into conflict with another one based on a different method.In this instance , the analytical process of multi-views of angles will help us solve the problem more efficiently and rapidly.

Key words: geographical methods, theoretical derivation, numerical simulation, Braess’s network, e ntropy-maximization

陈彦光. 地理学多视角研究方法——Braess网络车流分配过程的理论分析与数值计算[J]. 地理研究, 2008, 27(6): 1367-1380.

CHEN Yan-guang. An integrated analytical process oftraffic assignment problems of Braess' network[J]. GEOGRAPHICAL RESEARCH, 2008, 27(6): 1367-1380.

参考文献

[1] Gleick J. Chaos: Making a New Science. New York: Viking Penguin Inc., 1988.

[2] Waldrop M. Complexity: The Emerging of Science at the Edge of Order and Chaos.NY: Simon and Schuster, 1992.

[3] Bak P. How Nature Works: The Science of Self-organized Criticality. New York: Springer-Verlag, 1996.

[4] Prigogine I.Stengers I. Order out of Chaos: Man's New Dialogue with Nature. New York: Bantam Book, Inc. , 1984.196~203.

[5] Allen P M. Cities and Regions as Self-Organizing Systems: Models of Complexity. Amsterdam: Gordon and Breach Science Pub. , 1997.

[6] Braess D.Vber ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung, 1968, 12, 258~268

[7] Braess D. On a paradox of traffic planning. Transportation Science, 2005, 39(4): 446~450.

[8] 陈彦光,刘继生.Braess模型与城市网络的空间复杂性探讨.地理科学,2006,26(6):658~663.

[9] 金凤君.我国航空客流网络发展及其地域系统研究.地理研究,2001,20(1):31~39.

[10] 周江评,崔功豪,张京祥,徐建刚.城镇交通网络信息图谱研究刍议.地理研究,2001,20(4):397~406.

[11] 曹小曙,阎小培.经济发达地区交通网络演化对通达性空间格局的影响——以广东省东莞市为例.地理研究,2003,22(3):305~312.

[12] 刘妙龙,黄蓓佩.上海大都市交通网络分形的时空特征演变研究.地理科学,2004,24(2):144~149.

[13] 曹小曙,薛德升,阎小培.中国干线公路网络联结的城市通达性.地理学报,2005,60(6):903~910.

[14] Portugali J. Self-Organization and the City. Berlin: Springer-Verlag, 2000.

[15] 陈彦光.城市化:相变与自组织临界性.地理研究,2004,23(3):301~311.

[16] Benenson I, Torrens P M. Geosimulation: Automata-based Modeling of Urban Phenomena. Chichester: John Wiley & Sons, Ltd. , 2004.

[17] Albeverio S, Andrey D. Giordano P, Vancheri A. The Dynamics of Complex Urban Systems: An Interdisciplinary Approach. Heidelberg: Physica-Verlag, 2008.

[18] 黎夏,叶嘉安,刘小平,杨青生.地理模拟系统:元胞自动机与多智能体.北京:科学出版社,2007.

[19] 陈彦光,刘继生.地理学的主要任务与研究方法——从整个科学体系的视角看地理科学.地理科学,2004,24(3):257~263.

[20] COMAP. Principles and Practice of Mathematics. New York:Springer, 1997.

[21] Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability(2^nd ed.). Cambridge: Cambridge University Press, 2008.

[22] Wilson A G. Complex Spatial Systems: The Modelling Foundations of Urban and Regional Analysis.Singapore: Pearson Education Asia Pte Ltd., 2000.

[23] Wilson A G 著.蔡运龙译.地理学与环境:系统分析方法.北京:商务印书馆,1997.

[24] 陈彦光,刘继生,房艳刚.效用最大化、Logit变换和城市地理学的数量分析模型.地理科学,2002,22(5):581~586.

[25] 陈彦光.分形城市系统:标度、对称和空间复杂性.北京:科学出版社,2008.

[26] Bekenstein J D. Information in the holographic universe. Scientific American, 2003, 289(2): 48~55.

[27] Diebold F X. Elements of Forecasting (3^rd ed.). Mason, Ohio:Thomson/South-Western,2004.

[28] Rao D N, Karmeshu Jain V P. Dynamics of urbanization: The empirical validation of the replacement hypothesis. Environment and Planning B: Planning and Design, 1989, 16: 289~295.

[29] 周一星.城市化水平与国民生产总值关系的规律性探讨.人口与经济,1982,(1):28~33.

[30] Couclelis H. From cellular automata to urban models: New principles for model development and implementation. Environment and Planning B: Planning and Design, 1997, 24: 165~174.

[31] Holland J H. Emergence: From Chaos to Order. Cambridge, Massachusetts: Perseus Books, 1998.

[32] 陈彦光,罗静.城市化水平与城市化速度的关系探讨——中国城市化速度和城市化水平饱和值的初步推断.地理研究,2006,25(6):1063~1072.

[33] Helbing D, Keltsch J, Molnar P. Modelling the evolution of human trail systems. Nature, 1997, 388: 47~50.

[34] Makse H A, Andrade Jr. J S, Batty M, Havlin S, Stanley H E. Modeling urban growth patterns with correlated percolation. Physical Review E, 1998, 58(6): 7054~7062.

[35] Zanette D, Manrubia S. Role of intermittency in urban development: A model of large-scale city formation. Physical Review Letters, 1997, 79(3): 523~526.

[36] Manrubia S, Zanette D. Intermittency model for urban development. Physical Review E, 1998, 58(1): 295~302.

地理学多视角研究方法——Braess网络车流分配过程的理论分析与数值计算

An integrated analytical process oftraffic assignment problems of Braess' network

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