固定需求网络中多用户类随机均衡的效率损失

交通运输系统工程与信息 ›› 2009, Vol. 9 ›› Issue (4): 83-89 .

固定需求网络中多用户类随机均衡的效率损失

余孝军^* ^1,2;黄海军¹ ;刘天亮³

1北京航空航天大学经济管理学院，北京 100191; 2 贵州财经学院数学与统计分院，贵阳 550004；3 清华大学经济管理学院，北京 100084

收稿日期:2009-03-09 修回日期:2009-05-26 出版日期:2009-08-25 发布日期:2009-08-25
通讯作者: 余孝军
作者简介:余孝军(1974-)，男，湖南新邵人，副教授，博士生.
基金资助:
国家重大基础科学研究“973”计划资助课题（2006CB705503）；国家自然科学基金资助项目（70521001）；中国博士后科学基金资助项目（20080440357）

Efficiency Loss of the Multi-Class Stochastic Traffic Equilibrium Assignment with Fixed Demand

YU Xiao-jun ^1,2;HUANG Hai-jun ¹; LIU Tian-liang ³

1. School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China; 2. School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004, China; 3. School of Economics and Management, Tsinghua University, Beijing 100084, China

Received:2009-03-09 Revised:2009-05-26 Online:2009-08-25 Published:2009-08-25
Contact: YU Xiao-jun

摘要/Abstract

摘要： 用户均衡同系统最优之间通常存在效率损失，它已吸引很多学者来研究这种效率损失问题，但现有文献大多数局限于研究单用户类、确定性均衡的效率损失，而对多用户类随机均衡的效率损失研究得比较少．本文研究了固定需求网络中多用户类随机均衡的效率损失上界问题．通过利用变分不等式的方法，解析推导了固定需求网络中多用户类随机均衡分配分别在时间度量和费用度量两种出行决策准则下的效率损失上界．研究结果表明：时间度量下，其效率损失上界值同路段出行时间函数、网络复杂程度、网络需求以及用户对网络熟悉程度等因素相关；费用度量下，其效率损失上界值除了和上述因素有关之外，还与出行者的时间价值系数有关．

关键词: 随机交通均衡, 变分不等式, 效率损失, 固定需求

Abstract: There exists efficiency loss when introducing a user equilibrium traffic assignment in comparison with the system optimization assignment. Seeking the upper bound of the efficiency loss has attracted many scholars’ attentions. The existing researches mainly focus on single user class and deterministic traffic assignment, few on stochastic user equilibrium (SUE) assignment with multiple user classes. In this paper, the authors investigate the upper bound of this SUE’s inefficiency. Two decision making criteria are used in the SUE, namely, time-based and monetary-based. It is shown that the upper bound of efficiency loss caused by the time-based SUE depends on the type of link travel time function, the network complexity, the travel demand, and the degree of users’ perception error to travel cost. The upper bound of efficiency loss caused by the monetary-based SUE depends on the value of time of user classes besides the aforementioned factors.

Key words: stochastic equilibrium traffic assignment, variational inequality, efficiency loss, fixed demand

中图分类号:

U491

余孝军,黄海军,刘天亮. 固定需求网络中多用户类随机均衡的效率损失[J]. 交通运输系统工程与信息, 2009, 9(4): 83-89 .

YU Xiao-jun,HUANG Hai-jun, LIU Tian-liang . Efficiency Loss of the Multi-Class Stochastic Traffic Equilibrium Assignment with Fixed Demand[J]. Journal of Transportation Systems Engineering and Information Technology, 2009, 9(4): 83-89 .

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参考文献

[1] Yang H, Huang H J. Mahematical and economic theory of road pricing [M]. Oxford: Elsevier, 2005.

[2] Koutsoupias E, Papadimitriou C. Worst-case equilibria [C]//Proceeding of the 16th Symposium on Theoretical Aspects of Computer Science, NCS 1563, 1999: 404-413.

[3] Roughgarden T, Tardos E. How bad is selfish routing? [J]. Journal of the ACM, 2002, 49 (2): 236-259.

[4] Roughgarden T, Tardos E. The price of anarchy is independent of the network topology [J]. Journal of Computer and System Science, 2003, 67 (2): 341-364.

[5] Roughgarden T, Tardos E. Bounding the inefficiency of equilibria in non-atomic congestion games [J]. Games and Economic Behavior, 2004, 47 (2): 389-403.

[6] Chau C K, Sim K M. The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands [J].Operations Research Letter, 2003, 31 (5): 327-334.

[7] Correa J R, Schulz A S, Stier-Moses NS. Selfish routing in capacitated networks[J]. Mathematics of Operations Research, 2004, 29 (4): 961-976.

[8] Correa J R, Schulz A S, Stier-Moses NS. On the inefficiency of equilibria in congestion games [C]// Proceedings of the 11th Conference on Integer Programming and Combinatorial Optimaztion(Lecture Notes in Computer Science 3509). Berlin: Springer, 2005:167-181.

[9] 黄海军, 欧阳恋群, 刘天亮. 交通网络中用户均衡行为的效率损失上界[J]. 北京航空航天大学学报, 2006, 32 (10): 1215-1219.[HUANG H J, OUYANG L Q, LIU T L. Upper bounds of efficiency loss for equilibrium behavior in traffic networks [J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32 (10): 1215-1219.]

[10] 吴建军, 高自友, 孙会君. 城市交通网络上个体选择行为的统计动力学特性研究 [J]. 交通运输系统工程与信息, 2008, 8 (2): 69-74. [WU J J, GAO Z Y, SUN H J. Statistical properties of individual choice behaviors on urban traffic networks [J]. Journal of Transportation Systems Engineering and Information Technology, 2008, 8 (2): 69-74.]

[11] 刘天亮, 欧阳恋群, 黄海军. ATIS作用下的混合交通行为网络与效率损失上界[J].系统工程理论与实践, 2007, 27 (4): 154-159．[LIU T L, OUYANG L Q, HUANG H J. Mixed travel behavior in networks with ATIS and upper bound of efficiency loss [J]. Systems Engineering - Theory & Practice, 2007, 27 (4): 154-159.]

[12] Han D R, Yang H. The multi-class,multi-criterion traffic equilibrium and the efficiency of congestion pricing [J]. Transportation Research Part E, 2008, 44 (5): 753–773.

[13] Guo X L, Yang H. The price of anarchy of stochastic user equilibrium in traffic networks [C]// Proceeding of the 10th HKSTS Conference, Hong Kong, 2005.

[14] Huang H J, Liu T L, Guo X L, et al. Efficiency loss of a stochastic user equilibrium in a traffic network with ATIS market penetration [C]// Proceedings of the Fifth International Conference on Traffic and Transportation Studies, 2006: 709-719

[15] 黄海军．城市交通网络平衡分析理论与实践[M]. 北京：人民交通出版社, 1994．[HUANG H J. Urban transportation network equilibrium analysis: theory and practice [M]. Beijing: China Communications Press, 1994. ]

[16] 徐兵, 朱道立. 多用户多准则固定需求随机交通均衡变分模型 [J]．公路交通科技，2007, 24 (4) : 129-133.[XU B, ZHU D L. A multiclass and multicriteria stochastic traffic network equilibrium variational inequality model with fixed demand[J]. Journal of Highway and Transportation Research and Development, 2007, 24 (4): 129-133.]