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Density waves in traffic flow model with relative velocity

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  • L. Yu
  • Z.-K. Shi

Abstract

The car-following model of traffic flow is extended to take into account the relative velocity. The stability condition of this model is obtained by using linear stability theory. It is shown that the stability of uniform traffic flow is improved by considering the relative velocity. From nonlinear analysis, it is shown that three different density waves, that is, the triangular shock wave, soliton wave and kink-antikink wave, appear in the stable, metastable and unstable regions of traffic flow respectively. The three different density waves are described by the nonlinear wave equations: the Burgers equation, Korteweg-de Vries (KdV) equation and modified Korteweg-de Vries (mKdV) equation, respectively. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • L. Yu & Z.-K. Shi, 2007. "Density waves in traffic flow model with relative velocity," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(1), pages 115-120, May.
    • Handle: RePEc:spr:eurphb:v:57:y:2007:i:1:p:115-120
    DOI: 10.1140/epjb/e2007-00160-1
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    Cited by:

    1. Yu, Lei, 2020. "A new continuum traffic flow model with two delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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