From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models

The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the microscopic models, we consider follow-the-leader type models with different types of drivers and vehicles which are distributed randomly on the road. After a rescaling, we show that the cumulative distribution function converges to the solution of a macroscopic model. We also establish a connection between this macroscopic model and the so-called Lighthill--Whitham--Richards model.