# Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow

## TL;DR

This paper demonstrates that Follow-the-Leader models serve as a numerical approximation to the Lighthill-Whitham-Richards traffic flow model, providing a convergence proof based on conservation law analysis techniques.

## Contribution

It establishes a rigorous connection between FtL models and the LWR model, showing convergence in dense traffic conditions with a novel proof approach.

## Key findings

- FtL models approximate the LWR model in dense traffic
- A simple proof of convergence is provided
- Techniques from numerical schemes for conservation laws are used

## Abstract

We show how to view the standard Follow-the-Leader (FtL) model as a numerical method to compute numerically the solution of the Lighthill--Whitham--Richards (LWR) model for traffic flow. As a result we offer a simple proof that FtL models converge to the LWR model for traffic flow when traffic becomes dense. The proof is based on techniques used in the analysis of numerical schemes for conservation laws, and the equivalence of weak entropy solutions of conservation laws in the Lagrangian and Eulerian formulation.