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.

Paper:
Available as PostScript.
Author(s):
A. Aw , <aaw@math.unice.fr>
M. Rascle, <rascle@math.unice.fr>
Publishing information:
To appear in SIAM Appl. Math.