The Aw–Rascle Traffic Model: Enskog-Type Kinetic Derivation and Generalisations

Abstract

We study the derivation of second order macroscopic traffic models from kinetic descriptions. In particular, we recover the celebrated Aw–Rascle model as the hydrodynamic limit of an Enskog-type kinetic equation out of a precise characterisation of the microscopic binary interactions among the vehicles. Unlike other derivations available in the literature, our approach unveils the multiscale physics behind the Aw–Rascle model. This further allows us to generalise it to a new class of second order macroscopic models complying with the Aw–Rascle consistency condition, namely the fact that no wave should travel faster than the mean traffic flow.