# From heterogeneous microscopic traffic flow models to macroscopic models

## TL;DR

This paper rigorously derives macroscopic traffic flow models from heterogeneous microscopic follow-the-leader models with random driver and vehicle types, establishing convergence and linking to the LWR model.

## Contribution

It provides a rigorous mathematical derivation of macroscopic traffic models from heterogeneous microscopic models, including convergence results and connections to the LWR model.

## Key findings

- Cumulative distribution functions converge to macroscopic solutions
- Established link between microscopic models and LWR model
- Validated macroscopic model derivation from heterogeneous microscopic dynamics

## Abstract

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 converge to the solution of a macroscopic model. We also make the link between this macroscopic model and the so-called LWR model.