Intersection Modeling, Application to Macroscopic Network Traffic Flow Models and Traffic Management

The object of the paper is to analyze intersection modeling in the context of macroscopic traffic flow models. The paper begins with a brief review of classical boundary conditions of the Dubois-LeFloch and the Bardos-Nedelec-LeRoux type, and their relation to the concepts of local traffic supply and demand. It will be shown that the local traffic supply and demand concept extends and simplifies these classical approaches. The resulting constraints on phenomenological intersection models will be discussed. Several examples of intersection models are deduced. Some of these recapture earlier models; others are specifically designed for congested traffic conditions and take into account the bounds on car acceleration. The last part of the paper is devoted to network modeling and to applications to network traffic management.