弹性需求下的网络交通流逐日动态演化

刘诗序; 陈文思; 池其源; 严海

doi:10.7498/aps.66.060501

摘要

在现实交通系统中，网络的交通需求是可变的，随交通运行状态而改变.针对需求可变情形，以含两条路径的简单路网为例，建立了弹性需求下的网络交通流逐日动态演化模型，基于非线性动力学理论，证明了动态演化模型的不动点存在且唯一，并且推导出了弹性需求下网络交通流动态演化的稳定性条件.通过数值实验，分析了网络交通流演化特征.研究发现：在一定条件下流量演化会出现分岔和混沌现象，并且出行者的出行需求对费用越敏感，系统演化越可能稳定；出行者路径选择的随机性越小，系统演化越不可能稳定；出行者对前一天实际费用的依赖程度越小，系统演化越可能稳定.

关键词:

Abstract

Network traffic flow is an aggregated result of a huge number of travelers' route choices, which is influenced by the travelers' choice behaviors. So day-to-day traffic flow is not static, but presents a complex and tortuous day-to-day dynamic evolution process. Studying day-to-day dynamic evolution of network traffic flow, we can not only know whether the traffic network equilibrium can be reached and how the process is achieved, but also can know what phenomenon will occur in the evolution of network traffic flow if the equilibrium is not reached. In a real traffic system, taking day as scale unit, the day-to-day network traffic demand is variable and changes with everyday's traffic network state. The travelers' route choices are also influenced by the previous day's behaviors and network state. Then, will the day-to-day network traffic flow evolution be stable? If it is unstable, when will bifurcation and chaos occur? In this paper we discuss the day-to-day dynamic evolution of network traffic flow with elastic demand in a simple two-route network. The dynamic evolution model of network traffic flow with elastic demand is formulated. Based on a nonlinear dynamic theory, the existence and uniqueness of the fixed point of dynamic evolution model are proved, and an equilibrium stability condition for the dynamic evolution of network traffic flow with elastic demand is derived. Then, the evolution of network traffic flow is investigated through numerical experiments by changing the three parameters associated with travelers, which are the sensitivity of travelers' travel demand to travel cost, the randomness of travelers' route choices, and travelers' reliance on the previous day's actual cost. Our findings are as follows. Firstly, there are three kinds of final states in the evolution of network traffic flow: stability and convergence to equilibrium, periodic motion and chaos. The final state of the network traffic flow evolution is related to the above three parameters. It is found that under certain conditions the bifurcation diagram of the network traffic flow evolution reveals a complicated phenomenon of period doubling bifurcation to chaos, and then period-halving bifurcation. Meanwhile, the chaotic region is interspersed with odd periodic windows. Moreover, the more sensitive to cost the travelers' travel demand the more likely the system evolution is to be stable. The smaller the randomness of travelers' route choices, the less likely the system evolution is to be stable. The lower the degree of travelers' reliance on the previous day's actual cost, the more likely the system evolution is to be stable.

Keywords:

作者及机构信息

1.
福州大学土木工程学院, 福州 350116;

2.
北京工业大学北京城市交通协同创新中心, 北京 100124

通信作者: 刘诗序, liushixu@fzu.edu.cn

基金项目: 国家自然科学基金（批准号：51308126，51378036，51308018）资助的课题.

Authors and contacts

1.
School of Civil Engineering, Fuzhou University, Fuzhou 350116, China;

2.
Beijing Collaborative Innovation Center for Metropolitan Transportation, Beijing University of Technology, Beijing 100124, China

Corresponding author: Liu Shi-Xu, liushixu@fzu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51308126, 51378036, 51308018).

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施引文献

[1]	Liu S X, Guan H Z, Yan H 2012 Acta Phys. Sin. 61 090506 (in Chinese) [刘诗序, 关宏志, 严海 2012 61 090506]
[2]	Sheffi Y 1985 Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods (Englewood Cliffs: Prentice-Hall, Inc.) pp59-61, 309
[3]	Kim H, Oh J S, Jayakrishnan R 2009 KSCE J. Civil Engineer. 13 117
[4]	Nakayama S, Kitamura R, Fujii S 1999 Transp. Res. Rec. 1676 30
[5]	Klgl F, Bazzan A L C 2004 J. Artificial Societies and Social Simulation 7 1
[6]	Wei F F, Ma S F, Jia N 2014 Math. Probl. Eng. 204 1
[7]	Kusakabe T, Nakano Y 2015 Transp. Res. C 59 278
[8]	Liu T L, Huang H J 2007 Acta Phys. Sin. 56 6321 (in Chinese) [刘天亮, 黄海军 2007 56 6321]
[9]	Liu S X, Guan H Z 2013 China Civil Eng. J. 46 136 (in Chinese) [刘诗序, 关宏志 2013 土木工程学报 46 136]
[10]	Iida Y, Akiyama T, Uchida T 1992 Transp. Res. B 26 17
[11]	Selten R, Chmura T, Pitz T, Kubec S, Schreckenberg M 2007 Game Econ. Behav. 58 394
[12]	Rapoport A, Gisches E J, Daniel T 2014 Transp. Res. B 68 154
[13]	Smith M J 1984 Transp. Sci. 18 245
[14]	Smith M J, Watling D P 2016 Transp. Res. B 85 132
[15]	Nagurney A, Zhang D 1997 Transp. Sci. 31 147
[16]	Watling D 1999 Transp. Res. B 33 281
[17]	Cho H J, Hwang M C 2005 Math. Comput. Model. 41 501
[18]	Kumar A, Peeta S 2015 Transp. Res. B 80 235
[19]	Tan Z, Yang H, Guo R Y 2015 Transp. Res. C 61 87
[20]	Di X, Liu H X, Ban X X, Yu J W 2015 Netw. Spat. Econ. 15 537
[21]	He X Z, Peeta S 2016 Transp. Res. B 84 237
[22]	Iryo T 2016 Transp. Res. B 92 88
[23]	Xiao F, Yang H, Ye H B 2016 Transp. Res. B 86 86
[24]	Guo R Y, Huang H J 2008 J. Manag. Sci. in China 11 12 (in Chinese) [郭仁拥, 黄海军 2008 管理科学学报 11 12]
[25]	Guo R Y, Yang H, Huang H J, Tan Z J 2015 Transp. Res. B 71 248
[26]	Zhang B, Juan Z C, Ni A N 2014 J. Ind. Eng. Eng. Manag. 28 164
[27]	Horowitz J L 1984 Transp. Res. B 18 13
[28]	Cascetta E, Cantarella G E 1991 Transp. Res. A 25 277
[29]	Cantarella G E, Cascetta E 1995 Transp. Sci. 29 305
[30]	Cantarella G E 2013 Transp. Res. C 29 117
[31]	Watling D, Hazelton M L 2003 Netw. Spat. Econ. 3 349
[32]	Bie J, Lo H K 2010 Transp. Res. B 44 90
[33]	He X, Liu H X 2012 Transp. Res. B 46 50
[34]	Han L, Du L 2012 Transp. Res. B 46 72
[35]	Zhao X, Orosz G 2014 Physica D 275 54
[36]	Di X, Liu H X 2016 Transp. Res. B 85 142
[37]	Li T, Guan H Z, Liang K K 2016 Acta Phys. Sin. 65 150502 (in Chinese) [李涛, 关宏志, 梁科科 2016 65 150502]
[38]	Guo R Y, Yang H, Huang H J 2013 Transp. Res. C 34 121
[39]	Guo R Y, Huang H J 2016 Transp. Res. C 71 122
[40]	Yang W J, Guo R Y, Li Q 2015 Syst. Eng. Theory Pract. 35 3192 (in Chinese) [杨文娟, 郭仁拥, 李琦 2015 系统工程理论与实践 35 3192]
[41]	Xu H L, Yu X L, Zhou J 2015 J. Manag. Sci. China 18 39 (in Chinese) [徐红利, 于新莲, 周晶 2015 管理科学学报 18 39]
[42]	Cantarella G E, Watling D P 2016 Euro. J. Transp. Logist. 5 69
[43]	Dafermos S 1982 Networks 12 57
[44]	Cantarella G E 1997 Transp. Sci. 31 107
[45]	Yu Q, Fang D B, Du W 2014 Eur. J. Oper. Res. 239 112
[46]	Zhou J 2001 J. Syst. Engineer. 16 88 (in Chinese) [周晶 2001 系统工程学报 16 88]
[47]	Nagurney A 1999 Network Economics: A Variational Inequality Approach (Boston: Kluwer Academic Publishers) pp17-19
[48]	Liu Z H 2006 Fundamentals and Applications of Chaotic Dynamic (Beijing: Higher Education Press) pp24-29, 60-61 (in Chinese) [刘宗华 2006 混沌动力学基础及其应用 (北京: 高等教育出版社) 第2429, 6061页]
[49]	Stone L 1993 Nature 365 617
[50]	Yu W B, Wei X P 2006 Acta Phys. Sin. 55 3969 (in Chinese) [于万波, 魏小鹏 2006 55 3969]
[51]	Peng M S 2005 Chaos Solitons Fract. 25 1123

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