Traffic Flow on Networks
This book is devoted to a detailed exposition of the nowadays classical approach to modelling traffic flow by first order hyperbolic conservation laws. Networks can be thought of as oriented graphs, where the flow on adjacent edges is related by suitable conditions on the common vertices (= junctions). In this setting, one can model a more complicated traffic setup, including multilanes and junctions with lights or circles. After reviewing the basic theory of conservation laws, the book discusses the background of several models (chapter 3), in particular the Lighthill-Whitham model and the Aw-Rascle model. Some higher order models are mentioned as well. The core of the book (chapters 5-7) is devoted to a study of the dynamics of these models on networks. An interesting case study comparing the regulation using traffic lights with the traffic on circles is presented (chapter 8). The related problem of flow on telecommunications networks is addressed in chapter 9, while numerical results are discussed in the concluding chapter 10. The presentation is clear and readable, accompanied with a lot of graphs and diagrams as well as exercises concluding each chapter. The book is accessible with a mild background in partial differential equations.