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 models, we consider follow-the-leader type with different types drivers and vehicles which are distributed randomly on road. After a rescaling, show that cumulative distribution function converges solution model. We also establish connection between model so-called Lighthill--Whitham--Richards