Kinetic models for traffic flow resulting in a reduced space of microscopic velocities

Abstract

The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the collision kernel allows one to find the analytical expression of a class of steady-state distributions, which are characterized by being supported on a quantized space of microscopic speeds. The number of these velocities is determined by a physical parameter describing the typical acceleration of a vehicle and the uniqueness of this class of solutions is supported by numerical investigations. This shows that it is possible to have the full richness of a kinetic approach with the simplicity of a space of microscopic velocities characterized by a small number of modes. Moreover, the explicit expression of the asymptotic distribution paves the way to deriving new macroscopic equations using the closure provided by the kinetic model.

Replaced with revised version

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Cited by in corpus (7)

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• Multiscale continuum-velocity kinetic model for vehicular traffic with local and mean field interactions
• Boltzmann-type description with cutoff of Follow-the-Leader traffic models
• A kinetic traffic network model and its macroscopic limit: diverging lanes
• Relaxation models for scalar traffic networks and zero relaxation limit
• Existence and hydrodynamic limit for a Paveri-Fontana type kinetic traffic model