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Chin. Phys., 2002, Vol. 11(11): 1128-1134    DOI: 10.1088/1009-1963/11/11/007
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Analysis of the stability and density waves for traffic flow

Xue Yu
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Department of Physics, Guangxi University, Nanning 530003, China
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.
Keywords:  traffic flow      density wave      car-following model      relative velocity  
Received:  29 March 2002      Revised:  18 June 2002      Published:  12 June 2005
PACS:  05.45.Yv (Solitons)  
  05.45.Pq (Numerical simulations of chaotic systems)  
  02.60.-x (Numerical approximation and analysis)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 19932020).

Cite this article: 

Xue Yu Analysis of the stability and density waves for traffic flow 2002 Chin. Phys. 11 1128

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