Hybrid stochastic kinetic description of two-dimensional traffic dynamics

Abstract

In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than interactions along the same lane and considering that their mathematical description can be done up to some uncertainty in the model parameters, we derive a hybrid stochastic Fokker-Planck-Boltzmann equation in the quasi-invariant interaction limit. By means of suitable numerical methods, precisely structure preserving and direct Monte Carlo schemes, we use this equation to compute theoretical speed-density diagrams of traffic both along and across the lanes, including estimates of the data dispersion, and validate them against real data.

References in corpus (1)

• Control strategies for road risk mitigation in kinetic traffic modelling

Cited by in corpus (6)

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• Hydrodynamic traffic flow models including random accidents: A kinetic derivation
• Stability Analysis of Quadrature-based Moment Methods for Kinetic Equations