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Jyda Mint Moustapha; Benjamin Jourdain; Dimitri Daucher
A probabilistic particle approximation of the “Paveri-Fontana” kinetic model of traffic flow
SMAI-Journal of computational mathematics, 2 (2016), p. 229-253, doi: 10.5802/smai-jcm.15
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Class. Math.: 65N35, 15A15
Keywords: Stochastic particle methods, Paveri-Fontana model, Traffic flow

Abstract

This paper is devoted to the Paveri-Fontana model and its computation. The master equation of this model has no analytic solution in nonequilibrium case. We develop a stochastic approach to approximate this evolution equation. First, we give a probabilistic interpretation of the equation as a nonlinear Fokker-Planck equation. Replacing the nonlinearity by interaction, we deduce how to approximate its solution thanks to an algorithm based on a fictitious jump simulation of the interacting particle system. This algorithm is improved to obtain a linear complexity regarding the number of particles. Finally, the numerical method is illustrated on one traffic flow scenario and compared with a finite differences deterministic method.

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