中国物理B ›› 2009, Vol. 18 ›› Issue (4): 1322-1327.doi: 10.1088/1674-1056/18/4/005

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Lattice models of traffic flow considering drivers' delay in response

祝会兵   

  1. Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo 315211, China
  • 收稿日期:2008-07-24 修回日期:2008-09-02 出版日期:2009-04-20 发布日期:2009-04-20
  • 基金资助:
    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

Lattice models of traffic flow considering drivers' delay in response

Zhu Hui-Bing(祝会兵)†   

  1. Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo 315211, China
  • Received:2008-07-24 Revised:2008-09-02 Online:2009-04-20 Published:2009-04-20
  • Supported by:
    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

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摘要： 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.

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.

Key words: lattice hydrodynamic model, traffic jams, analytical method, drivers' delay in response

中图分类号:  (Lattice theory and statistics)

  • 05.50.+q
05.45.Yv (Solitons) 45.70.Vn (Granular models of complex systems; traffic flow) 02.30.Jr (Partial differential equations) 89.40.-a (Transportation)