A justification of a LWR model based on a follow the leader description

Elena Rossi

doi:10.3934/dcdss.2014.7.579

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2014, Volume 7, Issue 3: 579-591. Doi: 10.3934/dcdss.2014.7.579

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A justification of a LWR model based on a follow the leader description

Elena Rossi^1,

1.
Department of Mathematics and Applications, University of Milano-Bicocca, Via Cozzi, 53, 20125 Milano

Received: April 30, 2013

Revised: June 30, 2013

Published: May 2014

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Abstract

We investigate the correlations between a macroscopic Lighthill--Whitham and Richards model and a microscopic follow-the-leader model for traffic flow. We prove that the microscopic model tends to the macroscopic one in a sort of kinetic limit, i.e. as the number of individuals tends to infinity, keeping the total mass fixed. Based on this convergence result, we approximately compute the solutions to a conservation law by means of the integration of an ordinary differential system. From the numerical point of view, the limiting procedure is then extended to the case of several populations, referring to the macroscopic model in [2] and to the natural multi--population analogue of the microscopic one.

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Mathematics Subject Classification: Primary: 35L65; Secondary: 90B20.

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References

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