The continuum limit of Follow-the-Leader models - a short proof

TL;DR

This paper provides a straightforward proof demonstrating that Follow-the-Leader models mathematically converge to the classical traffic flow model, Lighthill-Whitham-Richards, in the continuum limit.

Contribution

It offers a simple, self-contained proof establishing the convergence of discrete Follow-the-Leader models to a well-known macroscopic traffic flow model.

Findings

Proof of convergence to the Lighthill-Whitham-Richards model

Simplification of existing convergence proofs

Clarification of the continuum limit process

Abstract

We offer a simple and self-contained proof that the Follow-the-Leader model converges to the Lighthill-Whitham-Richards model for traffic flow.