On the mathematical theory of vehicular traffic flow II: Discrete velocity kinetic models

This paper deals with the modelling of vehicular traffic flow by methods of the discrete mathematical kinetic theory. The discretization is developed in the velocity space by a grid adapted to the local density. The discretization overcomes, at least in part, some technical difficulties related to the selection of the correct representation scale, while the adaptative grid allows an improved description of various phenomena related to vehicular traffic flow. Specific models are proposed and a qualitative and computational analysis is developed to show the properties of the model and their ability to describe real flow conditions. A critical analysis, proposed in the last part of the paper, outlines suitable research perspectives.