Abstract This paper proposes two lattice traffic models by taking into account the drivers' delay in response. The lattice versions of the hydrodynamic model are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained by using the linear stability theory. The modified KdV equation near the critical point is derived to describe the traffic jam by using the reductive perturbation method, and the kink--antikink soliton solutions related to the traffic density waves are obtained. The results show that the drivers' delay in sensing headway plays an important role in jamming transition.
Received: 24 July 2008
Revised: 02 September 2008
Accepted manuscript online:
Fund: Project supported by the National
Basic Research Program of China (Grant No 2006CB705500), the
National Natural Science Foundation of China (Grant No 10532060),
the Natural Science Foundation of Ningbo (Grant Nos 2008A610022 and
2007A610050), and K. C. Wa
Cite this article:
Zhu Hui-Bing(祝会兵) Lattice models of traffic flow considering drivers' delay in response 2009 Chin. Phys. B 18 1322
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