Kinetic FRG Young Researchers Workshop
March 2-5, 2009

CSIC Building (#406), Seminar Room 4122.

Stochastic Traffic Flow Models and Hierarchical Closures

Dr. Alexandros Sopasakis

University of North Carolina at Charlotte

Abstract:  We propose a stochastic microscopic model in order to describe vehicular trafic on highways. The model incorporates Arrhenius dynamics and local, look-ahead, interac­tion potentials in order to effectively describe vehicle interactions and behavior under all concentration regimes in different geometries.

We subsequently derive the correcponding mean field approximations based on this stochastic model in order to produce linear and nonlinear trafic flow PDEs. Our approach relies heavily on first deriving approximate differential mesoscopic equations. These approximations become exact either in the long range, Kac interaction case. Although these approximations can in some cases be crude, they can still give a first indication, via linearized stability analysis, of the interesting regimes for the stochastic model.

Numerical kinetic Monte Carlo simulations are implemented to assist in producing solutions and understanding their behavior.