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Modelling and Optimisation of Flows on Networks

Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle

  • Book
  • © 2013

Overview

Authors:
  1. Luigi Ambrosio

    1. Department of Mathematics, Scuola Normale Superiore, Pisa, Italy

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  2. Alberto Bressan

    1. State College, Dept. Mathematics, Penn State University, University Park, USA

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  3. Dirk Helbing

    1. Chair of Sociology, in particular of Mod, CLU E 1, ETH Zurich, Swiss Federal Institute of T, Zurich, Switzerland

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  4. Axel Klar

    1. , Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

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  5. Enrique Zuazua

    1. , Depto. Matematicas, BCAM – Basque Center for Applied Mathema, Bilbao, Spain

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  • Rich notes on most recent advances on traffic flow on networks, including control and optimization.
  • Tutorials on conservation laws,,wave equations and optimal transport theory Diverse applications such as vehicular traffic, supply chains and others
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2062)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiv
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  2. A User’s Guide to Optimal Transport

    • Luigi Ambrosio, Nicola Gigli
    Pages 1-155

  3. Hyperbolic Conservation Laws: An Illustrated Tutorial

    • Alberto Bressan
    Pages 157-245

  4. Derivation of Non-local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models

    • Dirk Helbing
    Pages 247-269

  5. On the Controversy Around Daganzo’s Requiem for and Aw–Rascle’s Resurrection of Second-Order Traffic Flow Models

    • Dirk Helbing, Anders Johansson
    Pages 271-302

  6. Theoretical vs. Empirical Classification and Prediction of Congested Traffic States

    • Dirk Helbing, Martin Treiber, Arne Kesting, Martin Schönhof
    Pages 303-333

  7. Self-Organized Network Flows

    • Dirk Helbing, Jan Siegmeier, Stefan Lämmer
    Pages 335-355

  8. Operation Regimes and Slower-is-Faster-Effect in the Control of Traffic Intersections

    • Dirk Helbing, Amin Mazloumian
    Pages 357-394

  9. Modeling and Optimization of Scalar Flows on Networks

    • Simone Göttlich, Axel Klar
    Pages 395-461

  10. Control and Stabilization of Waves on 1-d Networks

    • Enrique Zuazua
    Pages 463-493

  11. Back Matter

    Pages 495-497
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Scuola Normale Superiore, Pisa, Italy

    Luigi Ambrosio

  • State College, Dept. Mathematics, Penn State University, University Park, USA

    Alberto Bressan

  • Chair of Sociology, in particular of Mod, CLU E 1, ETH Zurich, Swiss Federal Institute of T, Zurich, Switzerland

    Dirk Helbing

  • , Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Axel Klar

  • , Depto. Matematicas, BCAM – Basque Center for Applied Mathema, Bilbao, Spain

    Enrique Zuazua

Bibliographic Information

  • Book Title: Modelling and Optimisation of Flows on Networks

  • Book Subtitle: Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle

  • Authors: Luigi Ambrosio, Alberto Bressan, Dirk Helbing, Axel Klar, Enrique Zuazua

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-32160-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2013

  • Softcover ISBN: 978-3-642-32159-7Published: 14 December 2012

  • eBook ISBN: 978-3-642-32160-3Published: 14 December 2012

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 497

  • Number of Illustrations: 109 b/w illustrations, 32 illustrations in colour

  • Topics: Partial Differential Equations, Mathematical Modeling and Industrial Mathematics, Analysis

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