中国物理B ›› 2002, Vol. 11 ›› Issue (11): 1128-1134.doi: 10.1088/1009-1963/11/11/307

• GENERAL • 上一篇    下一篇

Analysis of the stability and density waves for traffic flow

薛郁   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Department of Physics, Guangxi University, Nanning 530003, China
  • 收稿日期:2002-03-29 修回日期:2002-06-18 出版日期:2005-06-12 发布日期:2005-06-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 19932020).

Analysis of the stability and density waves for traffic flow

Xue Yu (薛郁)   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Department of Physics, Guangxi University, Nanning 530003, China
  • Received:2002-03-29 Revised:2002-06-18 Online:2005-06-12 Published:2005-06-12
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 19932020).

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摘要： In this paper, the optimal velocity model of traffic is extended to take into account the relative velocity. The stability and density waves for traffic flow are investigated analytically with the perturbation method. The stability criterion is derived by the linear stability analysis. It is shown that the triangular shock wave, soliton wave and kink wave appear respectively in our model for density waves in the three regions: stable, metastable and unstable regions. These correspond to the solutions of the Burgers equation, Korteweg－de Vries equation and modified Korteweg－de Vries equation. The analytical results are confirmed to be in good agreement with those of numerical simulation. All the results indicate that the interaction of a car with relative velocity can affect the stability of the traffic flow and raise critical density.

Abstract: In this paper, the optimal velocity model of traffic is extended to take into account the relative velocity. The stability and density waves for traffic flow are investigated analytically with the perturbation method. The stability criterion is derived by the linear stability analysis. It is shown that the triangular shock wave, soliton wave and kink wave appear respectively in our model for density waves in the three regions: stable, metastable and unstable regions. These correspond to the solutions of the Burgers equation, Korteweg－de Vries equation and modified Korteweg－de Vries equation. The analytical results are confirmed to be in good agreement with those of numerical simulation. All the results indicate that the interaction of a car with relative velocity can affect the stability of the traffic flow and raise critical density.

Key words: car-following model, traffic flow, density wave, relative velocity

中图分类号:  (Solitons)

  • 05.45.Yv
05.45.Pq (Numerical simulations of chaotic systems) 02.60.-x (Numerical approximation and analysis)