复杂交通运输网络上的拥挤与效率问题研究

肖尧; 郑建风

doi:10.7498/aps.62.178902

摘要

本文研究复杂交通运输网络上的拥挤与效率问题. 在无标度网络、随机网络以及小世界网络等不同拓扑结构中, 探讨了不同的能力分配方式和不同的OD (Origin-Destination) 交通需求分布对网络拥挤度和效率的影响. 随着平均交通需求的增加, 分析无标度网络、随机网络以及小世界网络从自由流状态到交通拥堵状态的变化规律. 为便于比较, 本文侧重研究网络拥挤度的倒数, 并将其定义为通畅度. 研究发现网络中的通畅度与效率之间存在线性相关关系, 并且不同网络中的线性比例系数 (或斜率)是不同的, 从而体现了不同网络具有不同的运输性能.

关键词:

复杂网络 /
拥挤 /
效率

Abstract

This paper investigates the congestion and efficiency in complex traffic and transportation networks. Effects of different distributions of capacity and origin-destination traffic demand on the degree of congestion and efficiency are explored in different network topologies including scale-free networks, random networks and small-world networks. According to the increase of average traffic demand, the transition from free flow state to congested state is analyzed. For easy comparison, we discuss the reciprocal of the congestion degree, which is defined as the network unobstructedness. A linear relation between the degree of unobstructedness and efficiency in different networks is uncovered, and the linear proportional coefficients are different in scale-free networks, random networks and small-world networks. These coefficients can also be used to describe the different transport performance in different networks.

Keywords:

作者及机构信息

肖尧¹,
郑建风^{1 2}

1.
北京交通大学交通运输学院, 北京 100044;

2.
北京交通大学城市交通复杂系统理论与技术教育部重点实验室, 北京 100044

基金项目: 国家重点基础研究发展计划(批准号: 2012CB725400)和国家自然科学基金(批准号: 71131001, 71222101)资助的课题.

Authors and contacts

Xiao Yao¹,
Zheng Jian-Feng^{1 2}

1.
School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China;

2.
MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China

Funds: Project supported by the National Basic Research of China (Grant No. 2012CB725400), and the National Natural Science Foundation of China (Grant Nos. 71131001, 71222101).

参考文献

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[2]	Watts D J, Strogatz S H 1998 Nature 393 440
[3]	Barabási A L, Albert R 1999 Science 286 509
[4]	Latora V, Marchiori M 2002 Physica A 314 109
[5]	Wu J J, Gao Z Y, Sun H J, Huang H J 2004 Mod. Phys. Lett. B 18 1043
[6]	Amaral L A N, Scala A, Barthelemy M, Stanley H E 2000 Proc. Natl. Acad. Sci. 97 11149
[7]	Chi L P, Wang R, Su H, Xu X P, Zhao J S, Li W, Cai X 2003 Chin. Phys. Lett. 20 1393
[8]	Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106 (in Chinese) [刘宏鲲, 周涛 2007 物理学报 56 106]
[9]	Hu Y, Zhu D 2009 Physica A 388 2061
[10]	Echenique P, Gomez-Gardenes J, Moreno Y 2004 Phys. Rev. E 70 056105
[11]	Wang W X, Wang B H, Yin C Y, Xie Y B, Zhou T 2006 Phys. Rev. E 73 026111
[12]	Yan G, Zhou T, Hu B, Fu Z Q, Wan B H 2006 Phys. Rev. E 73 046108
[13]	Wang D, Yu H, Jing Y W, Jiang N, Zhang S Y 2009 Acta Phys. Sin. 58 6802 (in Chinese) [王丹, 于灏, 井元伟, 姜囡, 张嗣瀛 2009 物理学报 58 6802]
[14]	Wu J J, Gao Z Y, Sun H J, Huang H J 2006 Europhys. Lett. 74 560
[15]	Wu J J, Gao Z Y, Sun H J 2008 Physica A 387 1025
[16]	Wu J J, Gao Z Y, Sun H J 2008 Journal of Transportation Systems Engineering and Information Technology 4 69 (in Chinese) [吴建军, 高自友, 孙会君 2008 交通运输系统工程与信息 4 69]
[17]	Zhao X M, Gao Z Y 2007 Phys. lett. 24 283
[18]	O’Kelly M E, Bryan D L 1998 Transp. Res. B 32 605
[19]	Alumur S A, Kara B Y 2008 Euro. J. Oper. Res. 190 1
[20]	Sheffi Y 1985 Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods (Prentice Hall, Englewood Cliffs, New Jersey)
[21]	Wardrop J G 1952 Proceedings of the Institute of Civil Engineers Part II 1 325
[22]	Beckmann M, Mcguire C B, Winsten C B 1956 Studies in the Economics of Transportation (New Haven: Yale University Press) p325
[23]	Kim T J 1990 Advanced Transport and Spatial Systems Model (New York: Springer Verlag)
[24]	Latora V, Marchiori M 2001 Phys. Rev. Lett. 87 198701

施引文献

[1]	Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[2]	Watts D J, Strogatz S H 1998 Nature 393 440
[3]	Barabási A L, Albert R 1999 Science 286 509
[4]	Latora V, Marchiori M 2002 Physica A 314 109
[5]	Wu J J, Gao Z Y, Sun H J, Huang H J 2004 Mod. Phys. Lett. B 18 1043
[6]	Amaral L A N, Scala A, Barthelemy M, Stanley H E 2000 Proc. Natl. Acad. Sci. 97 11149
[7]	Chi L P, Wang R, Su H, Xu X P, Zhao J S, Li W, Cai X 2003 Chin. Phys. Lett. 20 1393
[8]	Liu H K, Zhou T 2007 Acta Phys. Sin. 56 106 (in Chinese) [刘宏鲲, 周涛 2007 物理学报 56 106]
[9]	Hu Y, Zhu D 2009 Physica A 388 2061
[10]	Echenique P, Gomez-Gardenes J, Moreno Y 2004 Phys. Rev. E 70 056105
[11]	Wang W X, Wang B H, Yin C Y, Xie Y B, Zhou T 2006 Phys. Rev. E 73 026111
[12]	Yan G, Zhou T, Hu B, Fu Z Q, Wan B H 2006 Phys. Rev. E 73 046108
[13]	Wang D, Yu H, Jing Y W, Jiang N, Zhang S Y 2009 Acta Phys. Sin. 58 6802 (in Chinese) [王丹, 于灏, 井元伟, 姜囡, 张嗣瀛 2009 物理学报 58 6802]
[14]	Wu J J, Gao Z Y, Sun H J, Huang H J 2006 Europhys. Lett. 74 560
[15]	Wu J J, Gao Z Y, Sun H J 2008 Physica A 387 1025
[16]	Wu J J, Gao Z Y, Sun H J 2008 Journal of Transportation Systems Engineering and Information Technology 4 69 (in Chinese) [吴建军, 高自友, 孙会君 2008 交通运输系统工程与信息 4 69]
[17]	Zhao X M, Gao Z Y 2007 Phys. lett. 24 283
[18]	O’Kelly M E, Bryan D L 1998 Transp. Res. B 32 605
[19]	Alumur S A, Kara B Y 2008 Euro. J. Oper. Res. 190 1
[20]	Sheffi Y 1985 Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods (Prentice Hall, Englewood Cliffs, New Jersey)
[21]	Wardrop J G 1952 Proceedings of the Institute of Civil Engineers Part II 1 325
[22]	Beckmann M, Mcguire C B, Winsten C B 1956 Studies in the Economics of Transportation (New Haven: Yale University Press) p325
[23]	Kim T J 1990 Advanced Transport and Spatial Systems Model (New York: Springer Verlag)
[24]	Latora V, Marchiori M 2001 Phys. Rev. Lett. 87 198701

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