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.

DOI: https://doi.org/10.5802/smai-jcm.15

Classification: 65N35, 15A15

Keywords: Stochastic particle methods, Paveri-Fontana model, Traffic flow

@article{SMAI-JCM_2016__2__229_0, author = {Jyda Mint Moustapha and Benjamin Jourdain and Dimitri Daucher}, title = {A probabilistic particle approximation of the {{\textquotedblleft}Paveri-Fontana{\textquotedblright}} kinetic model of traffic flow}, journal = {The SMAI journal of computational mathematics}, pages = {229--253}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {2}, year = {2016}, doi = {10.5802/smai-jcm.15}, mrnumber = {3633551}, zbl = {1416.65038}, language = {en}, url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.15/} }

Jyda Mint Moustapha; Benjamin Jourdain; Dimitri Daucher. A probabilistic particle approximation of the “Paveri-Fontana” kinetic model of traffic flow. The SMAI journal of computational mathematics, Volume 2 (2016) , pp. 229-253. doi : 10.5802/smai-jcm.15. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.15/

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