A probabilistic particle approximation of the “Paveri-Fontana” kinetic model of traffic flow
Résumé
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.