We study spatially non-homogeneous kinetic models for vehicular traffic ow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by deriving a modified formulation of the BGK-type equation. The new kinetic model allows to reproduce conditionally stable nonequilibrium phenomena in traffic ow. In particular, stop and go waves appear as bounded backward propagating signals occurring in bounded regimes of the density where the model is unstable. The BGK-type model introduced here also offers the mesoscopic description between the microscopic follow-the-leader model and the macroscopic Aw-Rascle and Zhang model.

The BGK approximation of kinetic models for traffic / Herty, M.; Puppo, G.; Roncoroni, S.; Visconti, G.. - In: KINETIC AND RELATED MODELS. - ISSN 1937-5093. - 13:2(2020), pp. 279-307. [10.3934/krm.2020010]

The BGK approximation of kinetic models for traffic

Puppo G.;Visconti G.
2020

Abstract

We study spatially non-homogeneous kinetic models for vehicular traffic ow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by deriving a modified formulation of the BGK-type equation. The new kinetic model allows to reproduce conditionally stable nonequilibrium phenomena in traffic ow. In particular, stop and go waves appear as bounded backward propagating signals occurring in bounded regimes of the density where the model is unstable. The BGK-type model introduced here also offers the mesoscopic description between the microscopic follow-the-leader model and the macroscopic Aw-Rascle and Zhang model.
2020
BGK models; Chapman-enskog expansion; kinetic equations; multiscale models; vehicular traffic
01 Pubblicazione su rivista::01a Articolo in rivista
The BGK approximation of kinetic models for traffic / Herty, M.; Puppo, G.; Roncoroni, S.; Visconti, G.. - In: KINETIC AND RELATED MODELS. - ISSN 1937-5093. - 13:2(2020), pp. 279-307. [10.3934/krm.2020010]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1402723
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