On the micro-macro limit in traffic flow

Abstract

We investigate the relations between a macroscopic Lighthill-Whitham and Richards model and a microscopic follow-the-leader model for traffic flow. Solutions to the microscopic model are proved to tend to those to the macroscopic one in a sort of kinetic limit, i.e. as the number of individuals tends to $+\infty$ while their total mass is constant. Based on this convergence result, we approximately compute the solutions to a conservation law by means of the integration of an ordinary differential system.