From the Modelling of Driver's Behaviour to Hydrodynamic Models and Problems of Traffic Flow

The optimization and control of traffic flow along a road or networks of roads, either highways or urban streets, is an interesting and challenging field of interactions between mathematics and engineering sciences. Dealing with such a problem may take advantage of suitable models which describe the evolution in time and space of the flow conditions: car density and velocity. Due to several economical and social motivations, the literature on this topic is vast and characterized by contributions covering modelling aspects, statement of problems, qualitative analysis and simulations related to applications. On the other hand, modelling has not yet reached a satisfactory level so that further analysis and improvements may be necessary in order to reach the standards needed by the qualitative analysis related to applications. The aim of this paper consists in providing a critical analysis suitable to open new research perspectives in the field.