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

2017/02/06 by Helge Holden, Holden, Helge, Nils Henrik Risebro +1 · 2 citations
Engineering · #Traffic control and management

paper · pdf · doi:10.48550/arxiv.1702.01718

Abstract

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

Cited by

• The Follow-the-Leader scheme with non-monotone velocity
• Relaxation and stability analysis of a third-order multiclass traffic flow model

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