First order macroscopic traffic flow models for networks in the context of dynamic assignment

The purpose of the paper is to adapt the classical LWR (Lighthill-Whitham-Richards) model, in its continuous version, to networks, in the context of dynamic assignment. This implies several specific adaptations of the basic model: introduction of partial flows, possibly inhomogeneous flows on links, and intersection modeling. The latter proves particularly difficult, and we discuss three different modeling approaches: extended versus pointwise intersection models, and flow maximization. We show that all three types of models are actually closely related, and compatible with the link flow models. The concepts of local traffic supply and demand prove to be essential, both for link and for intersection modeling. A brief comparison with experimental merge data gives some support to the phenomenological models introduced in the paper.