An Homogenized Hyperbolic Model of Multiclass Traffic Flow: a Few Examples

Abstract

We introduce a new homogenized hyperbolic (multiclass) traffic flow model which allows to take into account the behaviors of different type of vehicles (cars, trucks, buses, etc.). We discretize the system with a Godunov Lagrangian scheme with oscillating initial data which describe the non homogeneity of the traffic, and we study the propagation of oscillations as time goes. We show the convergence of the scheme and the existence and uniqueness of the entropy solution to the homogenized system, which allows to completely identify the Young measure for all (x, t). Moreover, we show that this limit system is the hydrodynamic limit of the corresponding multi-class discrete system. Simulations are also presented.