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

Helge Holden; Nils Henrik Risebro; Helge Holden; Nils Henrik Risebro

doi:10.3934/nhm.2018018

Networks and Heterogeneous Media

2018, Volume 13, Issue 3: 409-421. doi: 10.3934/nhm.2018018

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

Helge Holden ^{1
,
,},
Nils Henrik Risebro ^{2
,}

1.
Department of Mathematical Sciences, NTNU Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
2.
Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, NO-0316 Oslo, Norway

Received: 01 September 2017 Revised: 01 January 2018
Primary: 35L02; Secondary: 35Q35, 82B21

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.
- Follow-the-Leader model,
- Lighthill-Whitham-Richards model,
- traffic flow,
- continuum limit
Citation: Helge Holden, Nils Henrik Risebro. Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow[J]. Networks and Heterogeneous Media, 2018, 13(3): 409-421. doi: 10.3934/nhm.2018018

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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.

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