Traffic Networks as Information Systems

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.

• 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
• complexity

“The book is written in a lively and entertaining style. … The book is well-structured and provides a very readable introduction to the viability approach that will be useful and interesting for mathematicians and mathematical engineers.” (Martin Gugat, zbMATH 1356.90002, 2017)

• VIMADES (Viabilit´e, March´es, Automatique et D´ecision), Paris, France

  Jean-Pierre Aubin

• VIMADES, Paris, France

  Anya Désilles

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