March  2010, 3(1): 165-179. doi: 10.3934/krm.2010.3.165

Fokker-Planck asymptotics for traffic flow models

1. 

RWTH Aachen University, D-52056 Aachen, Germany

2. 

Department of Mathematics & CMCS, University of Ferrara, I-44100 Ferrara

Received  October 2009 Revised  November 2009 Published  January 2010

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.
Citation: Michael Herty, Lorenzo Pareschi. Fokker-Planck asymptotics for traffic flow models. Kinetic & Related Models, 2010, 3 (1) : 165-179. doi: 10.3934/krm.2010.3.165
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