The continuum limit of non-local Follow-the-Leader models

TL;DR

This paper proves that a generalized non-local Follow-the-Leader traffic model converges to the classical Lighthill-Whitham-Richards model in dense traffic conditions, demonstrating the robustness of the classical model.

Contribution

It introduces a generalized model considering multiple vehicles ahead and behind, and proves its convergence to the classical traffic flow model in dense traffic.

Findings

The generalized model converges to the Lighthill-Whitham-Richards model as traffic density increases.

The classical model's robustness is confirmed through this convergence.

The model accounts for finite vehicle interactions in traffic flow.

Abstract

We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model converges to the classical Lighthill-Whitham-Richards model for traffic flow when traffic becomes dense. This also underscores the robustness of the Lighthill-Whitham-Richards model.