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Mathematical Modelling of Traffic Flows

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • Tong Li

    (University of Iowa, Department of Mathematics)

Abstract

We are concerned with mathematical modeHng of of traffic flow. In particular, well-posedness theory of various nonequilibrium continuum models of traffic flow are established. One such a model is an inhomogeneous traffic flow model which allows road situation changes. The road situation changes arise naturally from obstacles, curvature, number of lanes, speed limit and others. Our proposed inhomogeneous model is a system of nonlinear hyperbolic equations in which the flux and the source terms depend on the space variable. We show the global existence of solutions and their convergence to a solution of the equilibrium equation as the relaxation time goes to zero. Furthermore, a traffic flow model with a nonconcave fundamental diagram is studied. The model is a system of nonconcave hyperbolic conservation laws with relaxation. A nonconcave fundamental diagram is observed in real traffic flow. Other more realistic traffic flow models are discussed.

Suggested Citation

  • Tong Li, 2003. "Mathematical Modelling of Traffic Flows," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 695-704, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_65
    DOI: 10.1007/978-3-642-55711-8_65
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