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, for example the model by Illner et. al. (2003). New Fokker--Planck models are also given and their differences to existing equations are highlighted. Finally, numerical computations of steady--states are given.
Fokker-Planck asymptotics for traffic flow models
PARESCHI, Lorenzo;HERTY, Michael Matthias
2010
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, for example the model by Illner et. al. (2003). New Fokker--Planck models are also given and their differences to existing equations are highlighted. Finally, numerical computations of steady--states are given.File in questo prodotto:
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