JAMMING TRANSITION IN EXTENDED COOPERATIVE DRIVING LATTICE HYDRODYNAMIC MODELS INCLUDING BACKWARD-LOOKING EFFECT ON TRAFFIC FLOW

Xingli Li (), Zhipeng Li (), Xianglin Han () and Shiqiang Dai ()
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Xingli Li: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
Zhipeng Li: College of Electronics and Information Engineering, Tongji University, Shanghai 201804, China
Xianglin Han: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
Shiqiang Dai: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

International Journal of Modern Physics C (IJMPC), 2008, vol. 19, issue 07, 1113-1127

Abstract: Two extended cooperative driving lattice hydrodynamic models are proposed by incorporating the intelligent transportation system and the backward-looking effect in traffic flow under certain conditions. They are the lattice versions of the hydrodynamic model of traffic: one (model A) is described by the differential-difference equation where time is a continuous variable and space is a discrete variable, and the other (model B) is the difference-difference equation in which both time and space variables are discrete. In light of the real traffic situations, the appropriate forward and backward optimal velocity functions are selected, respectively. Then the stability conditions for the two models are investigated with the linear stability theory and it is found that the new consideration leads to the improvement of the stability of traffic flow. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations. Moreover, the anisotropy of traffic flow is further discussed through examining the negative propagation velocity as the effect of following vehicle is involved.

Keywords: Traffic flow; looking backward; phase transition; mKdV equation; anisotropy; 45.70.Vn; 89.40.-a; 02.60.Cb; 05.70.Fh (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0129183108012698

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