An n-Populations Model for Traffic Flow

Introduction Among the many continuous traffic flow models currently available, the Lighthill-Whi- tham [12] and Richards [13] (LWR) model has a prominent role. Its simplicity stems from its being defined through only two assumptions (1) the total number of cars is conserved, and (2) the car speed is a function of the car density. Mathematically ap + ax (pv): 0 (1.1) where t is time, x is the space coordinate, p C [0, R] is the car density, R is the maximal car density, v = v(p) is the average car speed. This very simple model captures several features of real traffic flow and its formal simplicity is a major advantage in its many applications. On the other hand, its simplicity leads also to some limitations. Here, we underline the fact that, according to (1.1), all drivers ad vehicles behave m the same way. This is hardly acceptable in various realistic situations. Aim of this note is to present and study a model for mixed traffic flow, where several classes (populations) of v