Modelling and Optimisation of Flows on Networks : Cetraro Italy 2009 Editors: Benedetto Piccoli Michel Rascle A User’s Guide to Optimal Transport Hyperbolic Conservation Laws: an Illustrated Tutorial Derivation of Non Local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car Following Models On the Controversy around Daganzo’s Requiem for and Aw Rascle’s Resurrection of Second Order Traffic Flow Models Theoretical vs. Empirical Classification and Prediction of Congested Traffic States Self Organized Network Flows Operation Regimes and Slower is Faster Effect in the Control of Traffic Intersections Modeling and Optimization of Scalar Flows on Networks The Wave Equation: Control and Numerics. In recent years flows in networks have attracted the interest of many researchers from different areas e.g. applied mathematicians engineers physicists economists. The main reason for this ubiquity is the wide and diverse range of applications such as vehicular traffic supply chains blood flow irrigation channels data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems together with investigations into specific applications. The main focus is on partial differential equations in networks but ordinary differential equations and optimal transport are also included. Moreover the modeling is completed by analysis numerics control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject.