Communications in Mathematical Sciences

Volume 11 (2013)

Number 3

Kinetic derivation of a Hamilton-Jacobi traffic flow model

Pages: 739 – 756

DOI: http://dx.doi.org/10.4310/CMS.2013.v11.n3.a4

Authors

Raul Borsche (Fachbereich Mathematik, Technische Universität Kaiserslautern, Germany)

Marc Kimathi (Fachbereich Mathematik, Technische Universität Kaiserslautern, Germany)

Axel Klar (Fachbereich Mathematik, Technische Universität Kaiserslautern, Germany)

Abstract

Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow equations leads to different types of equations; in certain situations modified Aw-Rascle equations are obtained. On the other hand, for several choices of kinetic parameters new Hamilton-Jacobi type traffic equations are found. Associated microscopic models are discussed and numerical experiments are presented discussing several situations for highway traffic and comparing the different models.

Keywords

traffic flow, macroscopic equations, kinetic derivation, Hamilton-Jacobi equations

2010 Mathematics Subject Classification

60K15, 76P05, 90B20

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