Preprint 1999-008

Resurrection of "Second Order" Models of Car Traffic ?

A. Aw and M. Rascle

Abstract: We introduce a new ``second order'' model - i.e. a continuum model with two equations ! - of traffic flow. As noted in \cite{dag}, the previous "second order" models i.e models with two equations (mass and ``momentum'') lead to nonphysical effects, probably because they try to mimic the gas dynamics equations, with an unrealistic dependence of the acceleration with respect to the space derivative of the ``pressure''. We simply replace this space derivative by a {\em convective} derivative, and we show that this very simple repair completely resolves the inconsistencies of these models. Moreover, our model nicely predicts instabilities nearby the vacuum i.e. for a very light traffic.

Available as PostScript.
A. Aw , <>
M. Rascle, <>
Publishing information:
To appear in SIAM Appl. Math.
Submitted by:
<> March 29 1999.

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