拥挤交通网络的Braess’ 悖论现象

交通运输系统工程与信息 ›› 2012, Vol. 12 ›› Issue (4): 155-160.

拥挤交通网络的Braess’ 悖论现象

赵春雪¹，傅白白²，王天明^*1

1. 大连理工大学数学科学学院，辽宁大连 116024；2. 山东建筑大学建筑城规学院，济南 250101

收稿日期:2012-03-28 修回日期:2012-05-13 出版日期:2012-08-25 发布日期:2012-09-07
作者简介:赵春雪（1985- ），女，山东聊城人，博士生.
基金资助:
国家自然科学基金（71171124，10871219）.

Braess’ Paradox Phenomenon of Congested Traffic Networks

ZHAO Chun-xue¹, FU Bai-bai², WANG Tian-ming¹

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024，Liaoning, China; 2. School of Architecture and Urban Planning, Shandong Jianzhu University, Jinan 250101, China

Received:2012-03-28 Revised:2012-05-13 Online:2012-08-25 Published:2012-09-07

摘要/Abstract

摘要：

在拥挤交通网络中，路段阻抗不仅与本路段车流量有关，也受其它路段车流量影响.本文讨论拥挤交通网络中同时考虑本路段和其它路段流量影响时Braess’悖论的性质及在系统最优分配下新增路段的作用.利用用户平衡(UE)和系统最优(SO)条件,计算得出Braess’悖论发生时交通需求具体范围及SO分配下新增路段有意义的交通需求具体范围，研究其它路段车流量对悖论产生概率影响及对SO分配下新增路段是否起作用的影响，讨论其它路段对UE分配和SO分配网络总阻抗差距的影响.结果表明,悖论发生概率，SO分配下新增路段起作用的概率及两种交通分配网络总阻抗的差距都受其它路段不同程度的影响，这为城市交通网络规划拓宽了思路.

关键词: 城市交通；Braess&rsquo, 悖论；解析方法；交通网络；用户平衡；系统最优

Abstract:

In the congested traffic networks, the link congestion is related to the flow on this link, as well as to that on other links. This paper investigates the properties of Braess’ paradox and whether the adding link makes sense under the system optimal in the congested traffic networks. Using the user equilibrium (UE) and system optimal (SO), it gives the explicit ranges of the total demand that the Braess’ paradox occurs and the adding link makes sense under SO, respectively. In addition, we investigate the influence of other links on the probability that the paradox occurs and the adding link works under SO, subsequently, we discuss the influence of other links on the difference between the total congestion under UE and that under SO. The results show the probability that the paradox occurs and the adding link works under SO, the difference of total congestion under two assignment methods are both influenced by the extent on other links, which widens theoretical ideas for the assignment of the urban transportation networks.

Key words: urban traffic, Braess&rsquo, paradox, analytical approach, traffic network, user equilibrium, system optimization

中图分类号:

U116.2

赵春雪, 傅白白, 王天明. 拥挤交通网络的Braess’ 悖论现象[J]. 交通运输系统工程与信息, 2012, 12(4): 155-160.

ZHAO Chun-Xue, FU Bai-Bai, WANG Tian-Ming. Braess’ Paradox Phenomenon of Congested Traffic Networks[J]. Journal of Transportation Systems Engineering and Information Technology, 2012, 12(4): 155-160.

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http://www.tseit.org.cn/CN/Y2012/V12/I4/155

参考文献

[1] Braess D. ber Ein Paradoxon Der Verkehrsplanung[J]. Unternehmensforschung, 1968, 12:258–268.
[2] Dafermos S, Nagurney A. On Some Traffic Equilibrium Theory Paradoxes[J]. Transpn Res. B, 1984, 18:101–110.
[3] Calvert B, Keady G. Braess Paradox and Power-law Nonlinearities in Networks[J]. J. Ausy. Math.Soc. Ser. B–Appl. Math, 1993, 35:1–22.
[4] Steinberg R, Zangwill W I. The Prevalent of Braess’ Paradox[J]. Transpn Science, 1983, 17:301–318.
[5] Akamatsu T, Heydecker B. Detecting Dynamic Traffic Assignment Capacity Paradoxes in Saturated Networks[J]. Transportation Science, 2003, 37(2):123–138.
[6] Braess D, Nagurney A, Wakolbinger T. On a Paradox of Traffic Planning[J]. Transportation Science, 2005, 39(4):446–450.
[7] Roughgarden T. Selfish Routing and the Price of Anarchy[J]. Optima Mathematical Programming Society Newsletter, 2006, 74:1–14.
[8] Yang H, Bell M G H. A Capacity Paradox in Network Design and How to Avoid It[J]. Transportation Research Part A, 1998, 32(7):539–545.
[9] Arnott R, Palma A D, Lindsey R. Properties of Dynamic Traffic Equilibrium Involving Bottlenecks, Including a Paradox and Metering[J]. Transportation Science, 1993, 27:148–160.
[10] Hallefjord A, Jornsten K, Storoy S. Traffic Equilibrium Paradoxes When Travel Demand is Elastic[J]. Asia-Pacific Journal of Operational Trsearch, 1994, 11:41–50.
[11] Pas E, Principio S. Braess’Paradox: Some New Insight[J]. Transpn Res. B, 1997, 31(3): 265–276.
[12] Dafermos S C, Sparrow F T. The Traffic Assignment Problem for a General Network[J]. Journal of Research of the National Bureau of Standards, 1969, 73B:91–118.
[13] Smith M. Existence, Uniqueness and Stability of Traffic Equilibria[J]. Transportation Research B, 1979, 13: 259–304.
[14] Dafermos S C. Traffic Equilibrium and Variational Inequalities[J]. Transportation Science, 1980, 14(1):42–54. [15] Joseph N P., Shlomo B. Some Observations on Stochastic User Equilibrium and System Optimum of Traffic Assignment[J]. Transportation Research B, 2000, 34: 277–291.