Ambrosio / Bressan / Helbing Modelling and Optimisation of Flows on Networks

Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle
Erscheinungsjahr 2012
ISBN: 978-3-642-32160-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2062, 497 Seiten, eBook

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Ambrosio, Luigi

Bressan, Alberto

Helbing, Dirk

Klar, Axel

Zuazua, Enrique

Inhaltsverzeichnis

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