The KdV-Burgers equation in modified speed gradient continuum model

doi:10.1088/1674-1056/22/6/060511

Abstract Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micro-macro linkage. In this paper, the Taylor expansion is adopted to modify the model. The backward travel problem is overcome by our model, which exists in many higher-order continuum models. The neutral stability condition of the model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves. Moreover, the Korteweg-de Vries-Burgers (KdV-Burgers) equation is derived to describe the traffic flow near the neutral stability line and the corresponding solution for traffic density wave is derived. The numerical simulation is carried out to investigate the local cluster effects. The results are consistent with the realistic traffic flow and also further verify the results of nonlinear analysis.

Keywords: traffic flow the speed gradient model KdV-Burgers equation

Received: 12 November 2012
Revised: 27 December 2012
Accepted manuscript online:

PACS:	05.70.Fh	(Phase transitions: general studies)
	05.60.-k	(Transport processes)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11072117), the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6110007), the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. Z201119278), the Natural Science Foundation of Ningbo City (Grant Nos. 2012A610152 and 2012A610038), and K.C. Wong Magna Fund in Ningbo University.

Corresponding Authors: Ge Hong-Xia
E-mail: gehongxia@nbu.edu.cn

Cite this article:

Lai Ling-Ling (赖玲玲), Cheng Rong-Jun (程荣军), Li Zhi-Peng (李志鹏), Ge Hong-Xia (葛红霞) The KdV-Burgers equation in modified speed gradient continuum model 2013 Chin. Phys. B 22 060511

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