Day-to-Day dynamical evolution of network traffic flow under bounded rational view

Li Tao; Guan Hong-Zhi; Liang Ke-Ke

doi:10.7498/aps.65.150502

Abstract

The formation mechanism of network traffic flow and its evolution law are closely related to daily activities of travelers. The current studies indicate that the law of network traffic flow evolution is day-to-day; therefore, using days as the scale unit is an important way to illustrate the evolution of network traffic flow. In previous studies, travelers in the network were tacitly assumed to be entirely rational. When the rationality of travelers is limited, the dynamics of the evolution law needs to be re-examined. This paper presents the utility maximization hypothesis in a logit model by using the bounded rationality hypothesis and develops a bounded rational binary logit (BRBL) model. We apply the BRBL model to a day-to-day network traffic flow distribution and discuss the evolution law of day-to-day network traffic flow under the assumption of the limited rationality of travelers. Through a numerical experiment, this paper analyzes the evolution characteristics of network traffic flow. The results are as follows. Firstly, the final state of the network traffic flow process is not only correlated to the cost-sensitivity of travelers and dependence on actual cost, but also strongly related to the degree of the nationality of travelers. Secondly, the system will be either bifurcated or chaotic when either cost-sensitivity increases or dependence on actual cost increases. Moreover, within the group of travelers whose rationality level is low, no matter what the cost-sensitivity of travelers and the dependence on actual cost are, the evolution results are asymptotically stable. Finally, in particular, in certain circumstances, it is easy to achieve stability when the rationallty degree of travelers is very high or very low, while it is not easy to achieve stability when the rationality degree of travelers is medium.

Keywords:

Authors and contacts

1.
Beijing Key Laboratory of Transportation Engineering, Beijing University of Technology, Beijing 100124, China

Corresponding author: Li Tao, jiaowo87@emails.bjut.edu.cn

Funds: Project supported by the National Basic Research Program of China (Grant No. 2012CB725403), the National Natural Science Foundation of China (Grant No. 51338008), the National Natural Science Foundation of China (Grant No. 51378036) and the National Natural Science Foundation of China (Grant No. 51308018).

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Cited By

[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 物理学报 61 090506]
[2]	Cascetta E, Cantarella G E {1991 Transp. Res. B 18 13
[3]	Cantarella G E, Cascetta E 1995 Transp. Sci. 29 305
[4]	Nakayama S, Kitamura R, Fujii S 1999 Trans. Res. Rec. 1676 30
[5]	Nakayama S, Kitamura R 2000 Transp. Res. Rec. 1725 63
[6]	Nakayama S, Kitamura R, Fujii S 2001 Transp. Res. Rec. 1752 62
[7]	Klgl F, Bazzan A L C 2002 Proc. of the First Int. Joing Conf. on Autonomous Agents and Multi-angent Systems Bologna, Italy, July 15-19, 2002 p217
[8]	Klgl F, Bazzan A L C {2004 J. Artific. Soc. Soc. Simulat. 7 1
[9]	Klgl F, Bazzan A L C 2004 J. Intellig. Transp. Syst. 8 223
[10]	Liu T L, Huang H J {2005 Intellig. Transp. Syst. 4 17 (in Chinese) [刘天亮, 黄海军 2005 通讯 4 17]
[11]	Liu T L, Huang H J 2007 Acta Phys. Sin. 56 6321 (in Chinese) [刘天亮, 黄海军 2007 物理学报 56 6321]
[12]	Kim H, Oh J S, Jayakrishnan R 2009 KSCE J. Civil Engineer. 13 117
[13]	Smith M J 1984 Transp. Sci. 18 245
[14]	Friesz T L, Bemstein D, Mehta N J, Tobin R L, Ganjalizadeh S 1994 Oper. Res. 42 1120
[15]	Zhang D, Nagumey A 1996 Transp. Res. B 30 245
[16]	Nagumey A, Zhang D 1997 Transp. Sci. 31 147
[17]	Watling D 1999 Transp. Res. B 33 281
[18]	Cho H J, Hwang M C 2005 Math. Comput. Model. 41 501
[19]	Mounce R 2006 Transp. Res. B 40 779
[20]	Guo R Y, Huang H J {2008 J. Managem. Sci. China 11 12 (in Chinese) [郭仁拥, 黄海军 2008 管理科学学报 11 12]
[21]	Horowitz J L {1984 Transp. Res. B 18 13
[22]	Cascetta E, Cantarella G E 1991 Transp. Res. A 25 277
[23]	Cantarella G E, Cascetta E 1995 Transp. Sci. 29 305
[24]	Watling D, Hazelton M L 2003 Netw. Spat. Econ. 3 349
[25]	Bie J, Lo H K 2010 Transp. Res. B 44 90
[26]	Nakayama S 2004 The 83rd Annual Meeting of the Transportation Research Board Washington, D.C., January 11-15, 2004
[27]	Simon H A {1995 Quart. J. Economics 69 343
[28]	Huang Z W, Zhou J Z, He H, Zhang X Y, Wang C Q {2011 J. Mech. Engineer. 47 59 (in Chinese) [黄志伟, 周建中, 贺徽, 张孝远, 王常青 2011 机械工程学报 47 59]
[29]	Wang X Y, Wang M J 2008 Physica A 387 3751
[30]	Zhang L S, Cai L, Feng C W 2010 Acta Electron. Sin. 38 1 (in Chinese) [张立森, 蔡理, 冯朝文 2010 电子学报 38 1]
[31]	Tang Y, Fang B, Zhang Y W, Li Q F 2011 J. Vib. Shock 30 269 (in Chinese) [唐冶, 方勃, 张业伟, 李庆芬 2011 振动与冲击 30 269]
[32]	Ma C, Wang X Y 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 721
[33]	Zhang W, Song C Z 2007 Int. J. Bifurcat. Chaos 17 1637
[34]	Hu J, Chung K W, Chan C L 2007 Appl. Dyn. Syst. 6 29
[35]	Jiang J, Ulbrich H 2005 ASME J. Vib. Acoust. 127 594
[36]	Chen L Q 2005 ASME, Appl. Mech. Reviews 58 91
[37]	Mahmassani H S, Chang G L 1986 Transp. Res. Part B 20 297
[38]	Mahmassani H S, Chang G L 1987 Transp. Sci. 21 89
[39]	Mahmassani H S, Jou R C {2000 Transp. Res. Part A 34 243
[40]	Lou Y, Yin Y, Lawphongpanich S 2010 Transp. Res. Part B 44 15
[41]	Avineri E, Prashker J N 2003 Transp. Res. Record 1854 90
[42]	Avineri E 2004 J. Intellig. Transp. Syst. 8 195
[43]	Avineri E, Prashker J N {2005 Transp. Res. Part C 13157
[44]	Liu Z H 2006 Fundamentals and Applications of Chaotic Dynamic (Beijing: Higher Education Press) pp9-14, 60 (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9-14, 60页]
[45]	Di X, Liu H X, Pang J S, Ban X G 2013 Transp. Res. Part B 57 300

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Vol. 65, Issue 15 - 2016-08-05

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