The analyses of kinematic wave properties of a new dynamics model for traffic flow are carried out. The model does not exhibit the problem that one characteristic speed is always greater than macroscopic traffic speed, and therefore satisfies the requirement that traffic flow is anisotropic. Linear stability analysis shows that the model is stable under certain condition and the condition is obtained. The analyses also indicate that the model has a hierarchy of first and second order waves, and allows the existence of both smooth traveling wave and shock wave. However, the model has a distinctive criterion of shock wave compared with other dynamics models, and the distinction makes the model more realistic in dealing with some traffic problems such as wrong-way travel analysis.
Payne H J.Models of freeway traffic and control[A].In:G A Behey Ed.Proc Simulation Council Mathematical Models of Public Systems[C].La Jolla:Simulation Council,1971,1(1):51-61.
[3]
Daganzo C F.Requiem for second-order fluid approximations of traffic flow[J].Transp Res B,1995,29(4):277-286.
[4]
Whitham G B.Linear and Nonlinear Wave[M].New York:John Wiley and Sons,Inc,1974.
[5]
Zhang H M.Analyses of the stability and wave properties of a new continuum traffic theory[J].Transp Res B,1999,33(6):399-415.
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