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Networks and Spatial Economics

, Volume 1, Issue 1–2, pp 167–177 | Cite as

The Mathematical Theory of an Enhanced Nonequilibrium Traffic Flow Model

  • T. Li
  • H. M. ZhangEmail author
Article

Abstract

This paper establishes the mathematical theory of an enhanced nonequilibrium traffic flow model. The innovation of the model is that it addresses the anisotropic feature of traffic flows. We show rigorously that this new theory reduces to the celebrated LWR theory when the relaxation time goes to zero, that global solutions for this theory exist for initial data of bounded total variation under certain mild conditions, and that the solutions approach the equilibrium solutions exponentially fast. The results justify rigorously the asymptotic equivalence of the relaxation model and the equilibrium equation. Our analysis is based on a generalized Glimm scheme which incorporates the effect of the relaxation source.

non-equilibrium traffic flow global existence large-time behavior Glimm scheme 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IowaIowa City
  2. 2.Department of Civil and Environmental EngineeringThe University of CaliforniaDavis

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