# The Aw-Rascle traffic model: Enskog-type kinetic derivation and generalisations

## TL;DR

This paper derives the Aw-Rascle traffic model from kinetic theory, revealing the multiscale physics involved and generalizing it to a broader class of second order macroscopic traffic models.

## Contribution

It provides a novel Enskog-type kinetic derivation of the Aw-Rascle model and introduces generalizations that satisfy the no-wave-speed-exceeding condition.

## Key findings

- Derived the Aw-Rascle model as a hydrodynamic limit of kinetic equations.
- Unveiled the multiscale physics behind the traffic model.
- Generalized the model to new second order macroscopic models.

## 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.