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

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.