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Traffic Networks as Information Systems

A Viability Approach

  • Jean-Pierre Aubin
  • Anya Désilles
Book

Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Jean-Pierre Aubin, Anya Désilles
    Pages 1-10
  3. Jean-Pierre Aubin, Anya Désilles
    Pages 11-33
  4. Jean-Pierre Aubin, Anya Désilles
    Pages 35-84
  5. Jean-Pierre Aubin, Anya Désilles
    Pages 85-113
  6. Jean-Pierre Aubin, Anya Désilles
    Pages 115-135
  7. Jean-Pierre Aubin, Anya Désilles
    Pages 137-153
  8. Jean-Pierre Aubin, Anya Désilles
    Pages 155-199
  9. Jean-Pierre Aubin, Anya Désilles
    Pages 201-227
  10. Back Matter
    Pages 229-246

About this book

Introduction

This authored monograph covers a viability to approach to  traffic management by advising to vehicles circulated on the network the velocity they should follow for satisfying global traffic conditions;. It presents an investigation of three structural innovations:
 
The objective is to broadcast at each instant and at each position the advised celerity to vehicles, which could be read by auxiliary speedometers or used by cruise control devices.
 
Namely, 
1. Construct regulation feedback providing at each time and position advised velocities (celerities)   for minimizing congestion or other requirements.
2. Taking into account traffic constraints of different type, the first one being to remain on the roads, to stop at junctions, etc.
3. Use information provided by the probe vehicles equipped with GPS to the traffic regulator;
4. Use other global traffic measures of vehicles provided by different types of sensors;
 
These results are based on convex analysis, intertemporal optimization and viability theory as mathematical tools as well as viability algorithms on the computing side, instead of conventional techniques such as partial differential equations and their resolution by finite difference or finite elements algorithms. The target audience primarily covers researchers and mathematically oriented engineers but the book may also be beneficial for graduate students.

Keywords

Attival Maps Celerity Celerity Regulator Cohorts Cournot map Departure Maps Duration functions Geodesic Relations Hamilton-Jacobi Equations Intertemporal Optimization Junction map Reachable map Speed Regulation Traffic Congestion Viability Theory

Authors and affiliations

  • Jean-Pierre Aubin
    • 1
  • Anya Désilles
    • 2
  1. 1.VIMADES (Viabilit´e, March´es, Automatique et D´ecision)ParisFrance
  2. 2.VIMADESParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-54771-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2017
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-642-54770-6
  • Online ISBN 978-3-642-54771-3
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • Buy this book on publisher's site
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