A FLUID-DYNAMIC MODEL FOR TRAFFIC FLOW ON A ROAD NETWORK 1. Traffic Flows

Here we refer to the book of Haberman [2] and to the papers [1, 3] for the description of the mathematical model of trac ows on road networks. The study of trac problems proposes to answer to several questions: where to install trac lights or stop signs; how long the cycle of trac lights should be; where to construct entrances, exits, and overpasses. The principal aim is to discover trac phenomena in order to eventually take decisions which may alleviate congestion, maximize ow of trac, eliminate accidents, and so on. Here we focus our attention on the trac ow along a unidirectional highway. We will analyze trac situations resulting from the complex interaction of many vehicles, instead of studying the behavior of individual cars. Here we will only formulate deterministic mathematical models, but it is also possible to develop statistical theories. The treatment of these problems is based on the fundamental trac variables: velocity, density and ow. The nonlinear partial dierential equation (1.1