472 RWTH Publication No: 707794        2017        IGPM472.pdf
TITLE Hybrid stochastic kinetic description of two-dimensional traffic dynamics
AUTHORS Michael Herty, Andrea Tosin, Giuseppe Visconti, Mattia Zanella
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.
KEYWORDS Boltzmann and Fokker-Planck equations, uncertainty quantification, structure preserving schemes, fundamental diagrams, data dispersion
DOI 10.1137/17M1155909
78(5), pp 2737-2762, 2018