472

IGPM472.pdf November 2017 
TITLE 
Hybrid stochastic kinetic description of twodimensional traffic dynamics

AUTHORS 
Michael Herty, Andrea Tosin, Giuseppe Visconti, Mattia Zanella

ABSTRACT 
In this work we present a twodimensional 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 FokkerPlanckBoltzmann equation in the quasiinvariant interaction limit. By means of suitable numerical methods, precisely structure preserving and direct Monte Carlo schemes, we use this equation to compute theoretical speeddensity diagrams of traffic both along and across the lanes, including estimates of the data dispersion, and validate them against real data.

KEYWORDS 
Boltzmann and FokkerPlanck equations, uncertainty quantification, structure preserving schemes, fundamental diagrams, data dispersion
