A justification of a LWR model based on a follow the leader description

We investigate the correlations between a macroscopic Lighthill-Whitham and Richards model and a microscopic follow-the-leader model for traffic flow. We prove that the microscopic model tends to the macroscopic one in a sort of kinetic limit, i.e. as the number of individuals tends to infinity, keeping the total mass fixed. Based on this convergence result, we approximately compute the solutions to a conservation law by means of the integration of an ordinary difierential system. From the numerical point of view, the limiting procedure is then extended to the case of several populations, referring to the macroscopic model in [2] and to the natural multi-population analogue of the microscopic one.