An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model

Authors:
M. Rascle
Affiliations:
Laboratoire de Mathématiques U.M.R. C.N.R.S. No. 6621 Université de Nice, Parc Valrose B.P. 71 F06108 Nice Cedex 2, France
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2002

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Abstract

We first recall a macroscopic model with two equations, that we have introduced in [1], and which completely resolves the severe inconsistencies of the class of Payne-Whitham models. In this short paper, we describe the effects of adding a relaxation term in the anticipation equation, and the main steps and mathematical difficulties to show rigorously the convergence to the Lighthill-Whitham model when the relaxation time tends to 0.