A Multi-class Vehicular Flow Model for Aggressive Drivers

Abstract

TheMarques Jr., Wilsonkinetic theory approachesVelasco, Rosa Maríato vehicularMéndez, Almatraffic modelling have given very good results in the understanding of the dynamical phenomena involved [3, 8]. In this work, we deal with the kinetic approach modelling of a traffic situation where there are many classes of aggressive drivers [5]. Their aggressiveness is characterised through their relaxation times. The reduced Paveri-Fontana equation is taken as a starting point to set the model. It contains the usual drift terms and the interactions between drivers of the same class, as well as the corresponding one between different classes. The reference traffic state used in the kinetic treatment is determined by a dimensionless parameter. The balance equations for the density and average speed for each class are obtained through the usual methods in the kinetic theory. In this model, we consider that each class of drivers preserve the corresponding aggressiveness, in such a way that there will be no adaptation effects [6]. It means that the number of drivers in a class is conserved. As preliminary results, we have obtained a closure relation to derive the Euler-like equations for two drivers classes. Some characteristics of the model are explored with the usual methods.