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

• 经济与区域发展 • 上一篇    下一篇

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   

  1. 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   

  1. 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:

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