Analysis of the stability and density waves for traffic flow
Xue Yu (薛郁)
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.
Received: 29 March 2002
Revised: 18 June 2002
Accepted manuscript online:
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