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Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications

Classical and Non–Classical Advanced Mathematics for Real Life Applications

  • Book
  • © 2013

Overview

Authors:
  1. Massimiliano Daniele Rosini

    1. , ICM, University of Warsaw, Warsaw, Poland

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  • Presents macroscopic models for vehicular and pedestrian dynamics
  • The described models are simple enough to permit a complete understanding, but rich enough to describe important phenomena typical of urban traffic
  • Introduces to more specialized investigations, such as traffic on networks, supply chains, telecommunications, blood flow, phase transitions, fluid dynamics

Part of the book series: Understanding Complex Systems (UCS)

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Table of contents (17 chapters)

  1. Front Matter

    Pages 1-10
    Download chapter PDF

  2. Introduction

    • Massimiliano Daniele Rosini
    Pages 1-7

  3. Part I-Mathematical Theory

    1. Front Matter

      Pages 9-9
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    2. Mathematical Preliminaries

      • Massimiliano Daniele Rosini
      Pages 11-21

    3. One-Dimensional Scalar Conservation Laws

      • Massimiliano Daniele Rosini
      Pages 23-42

    4. The Riemann Problem

      • Massimiliano Daniele Rosini
      Pages 43-50

    5. The Cauchy Problem

      • Massimiliano Daniele Rosini
      Pages 51-62

    6. The Initial-Boundary Value Problem and the Constraint

      • Massimiliano Daniele Rosini
      Pages 63-91

    7. One-Dimensional Systems of Conservation Laws

      • Massimiliano Daniele Rosini
      Pages 93-110

    8. One-Dimensional Systems of Balance Laws (Weakly Coupled)

      • Massimiliano Daniele Rosini
      Pages 111-120

  4. Part II-Models for Vehicular Traffic

    1. Front Matter

      Pages 121-121
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    2. Vehicular Traffic

      • Massimiliano Daniele Rosini
      Pages 123-138

    3. Equilibrium Traffic Models

      • Massimiliano Daniele Rosini
      Pages 139-148

    4. Generalizations of Equilibrium Traffic Models

      • Massimiliano Daniele Rosini
      Pages 149-160

    5. Cost Functionals

      • Massimiliano Daniele Rosini
      Pages 161-166

    6. Numerical Applications

      • Massimiliano Daniele Rosini
      Pages 167-173

    7. Non-equilibrium Traffic Models

      • Massimiliano Daniele Rosini
      Pages 175-190

  5. Part III-Models for Pedestrian Traffic

    1. Front Matter

      Pages 191-191
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    2. General Concepts

      • Massimiliano Daniele Rosini
      Pages 193-201

    3. The CR Model

      • Massimiliano Daniele Rosini
      Pages 203-226
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Keywords

About this book

This monograph presents a systematic treatment of the theory for hyperbolic conservation laws and their applications to vehicular traffics and crowd dynamics. In the first part of the book, the author presents very basic considerations and gradually introduces the mathematical tools necessary to describe and understand the mathematical models developed in the following parts focusing on vehicular and pedestrian traffic. The book is a self-contained valuable resource for advanced courses in mathematical modeling, physics and civil engineering. A number of examples and figures facilitate a better understanding of the underlying concepts and motivations for the students. Important new techniques are presented, in particular the wave front tracking algorithm, the operator splitting approach, the non-classical theory of conservation laws and the constrained problems. This book is the first to present a comprehensive account of these fundamental new mathematical advances.

Authors and Affiliations

  • , ICM, University of Warsaw, Warsaw, Poland

    Massimiliano Daniele Rosini

Bibliographic Information

  • Book Title: Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications

  • Book Subtitle: Classical and Non–Classical Advanced Mathematics for Real Life Applications

  • Authors: Massimiliano Daniele Rosini

  • Series Title: Understanding Complex Systems

  • DOI: https://doi.org/10.1007/978-3-319-00155-5

  • Publisher: Springer Cham

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer International Publishing Switzerland 2013

  • Hardcover ISBN: 978-3-319-00154-8Published: 31 May 2013

  • Softcover ISBN: 978-3-319-03348-8Published: 23 June 2015

  • eBook ISBN: 978-3-319-00155-5Published: 15 March 2013

  • Series ISSN: 1860-0832

  • Series E-ISSN: 1860-0840

  • Edition Number: 1

  • Number of Pages: XII, 242

  • Topics: Complexity, Applications of Nonlinear Dynamics and Chaos Theory

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