Mathematical modeling of multilane vehicular traffic by discrete kinetic theory approach

This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the discrete kinetic theory approach. The nonlinear additive interactions and external actions such as tollgates as well traffic signs are considered and modeled. The well-posedness of the related Cauchy problem for the spatially homogeneous case has been proved by using Banach fixed-point theory. Numerical simulations are carried out to validate the improved model in the cases of spatially homogeneous and inhomogeneous problems.