Kinetic derivation of a Hamilton-Jacobi traffic flow model

TL;DR

This paper reviews kinetic traffic models and derives macroscopic equations, including modified Aw-Rascle and Hamilton-Jacobi types, supported by microscopic models and numerical experiments for highway traffic.

Contribution

It introduces new Hamilton-Jacobi traffic equations from kinetic models, expanding the range of macroscopic traffic flow descriptions.

Findings

Derived modified Aw-Rascle equations for traffic flow

Found new Hamilton-Jacobi type traffic equations

Compared models through numerical experiments

Abstract

Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow equations leads to different types of equations: in certain situations modified Aw-Rascle equations are obtained. On the other hand, for several choices of kinetic parameters new Hamilton-Jacobi type traffic equations are found. Associated microscopic models are discussed and numerical experiments are presented discussing several situations for highway traffic and comparing the different models.