Time-dependent Ginzburg–Landau equation in a car-following model considering the driver’s physical delay

Hong-xia Ge, Xiang-pei Meng, Rong-jun Cheng and Siu-Ming Lo

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 20, 3348-3353

Abstract: In this paper, an extended car-following model considering the delay of the driver’s response in sensing headway is proposed to describe the traffic jam. It is shown that the stability region decreases when the driver’s physical delay in sensing headway increases. The phase transition among the freely moving phase, the coexisting phase, and the uniformly congested phase occurs below the critical point. By applying the reductive perturbation method, we get the time-dependent Ginzburg–Landau (TDGL) equation from the car-following model to describe the transition and critical phenomenon in traffic flow. We show the connection between the TDGL equation and the mKdV equation describing the traffic jam.

Keywords: Traffic flow; Car-following model; Time-dependent Ginzburg–Landau equation; Modified Korteweg–de Vries equation (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:20:p:3348-3353

DOI: 10.1016/j.physa.2011.04.033

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