Fokker-Planck asymptotics for traffic flow models

Michael Herty; Lorenzo Pareschi

doi:10.3934/krm.2010.3.165

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2010, Volume 3, Issue 1: 165-179. Doi: 10.3934/krm.2010.3.165

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Fokker-Planck asymptotics for traffic flow models

Michael Herty^1, and
Lorenzo Pareschi^2,

1.
RWTH Aachen University, D-52056 Aachen
2.
Department of Mathematics & CMCS, University of Ferrara, I-44100 Ferrara

Received: September 30, 2009

Revised: October 31, 2009

Published: February 2010

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Abstract

Starting from microscopic interaction rules we derive kinetic models of Fokker-Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the corresponding Boltzmann model. As particular cases, the derived models comprise existing models. New Fokker-Planck models are also given and their differences to existing models are highlighted. Finally, we report on numerical experiments.

Keywords:

Traffic Flow Modeling,
Fokker-Planck Equations.

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

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