Modelling and Optimisation of Flows on Networks: Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle (Lecture Notes in Mathematics Book 2062)

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. A User's Guide To Optimal Transport / Luigi Ambrosio And Nicola Gigli -- Hyperbolic Conservation Laws : An Illustrated Tutorial / Alberto Bressan -- Derivation Of Non-local Macroscopic Traffic Equations And Consistent Traffic Pressures From Microscopic Car-following Models / Dirk Helbing -- On The Controversy Around Daganzo's Requiem For And Aw-rascle's Resurrection Of The Second-order Traffic Flow Models / Dirk Helbing And Anders Johansson -- Theoretical Vs. Empirical Classification And Prediction Of Congested Traffic States / Dirk Helbing, Martin Treiber, Arne Kesting, And Martin Schönhof -- Self-organized Network Flows / Dirk Helbing, Jan Siegmeier, And Stefan Lämmer -- Operation Regimes And Slower-is-faster-effect In The Control Of Traffic Intersections / Dirk Helbing And Amin Mazloumian -- Modeling And Optimization Of Scalar Flows On Networks / Simone Göttlich And Axel Klar -- Control And Stabilization Of Waves On 1-d Networks / Enrique Zuazua. Luigi Ambrosio .. [et Al.] ; Editors, Benedetto Piccoli, Michel Rascle. The Present Volume Collects Notes From Lectures Delivered For The Cime Course On Modelling And Optimisation Of Flows On Networks, Held In Cetraro In The Summer Of 2009.--p. Vii. Includes Bibliographical References. Front Matter....Pages i-xiv A User’s Guide to Optimal Transport....Pages 1-155 Hyperbolic Conservation Laws: An Illustrated Tutorial....Pages 157-245 Derivation of Non-local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models....Pages 247-269 On the Controversy Around Daganzo’s Requiem for and Aw–Rascle’s Resurrection of Second-Order Traffic Flow Models....Pages 271-302 Theoretical vs. Empirical Classification and Prediction of Congested Traffic States....Pages 303-333 Self-Organized Network Flows....Pages 335-355 Operation Regimes and Slower-is-Faster-Effect in the Control of Traffic Intersections....Pages 357-394 Modeling and Optimization of Scalar Flows on Networks....Pages 395-461 Control and Stabilization of Waves on 1-d Networks....Pages 463-493 Back Matter....Pages 495-497