Journal of Optimization Theory and Applications

, Volume 168, Issue 1, pp 216–230 | Cite as

On the Braess Paradox with Nonlinear Dynamics and Control Theory

Article

Abstract

We show the existence of the Braess paradox for a traffic network with nonlinear dynamics described by the Lighthill–Whitham–Richards model for traffic flow. Furthermore, we show how one can employ control theory to avoid the paradox. The paper offers a general framework applicable to time-independent, uncongested flow on networks. These ideas are illustrated through examples.

Keywords

Braess paradox Traffic dynamics Hyperbolic conservation laws Nash optimum Control theory 

Mathematics Subject Classification

35L65 90B20 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.INDAM Unit (c/o DII)University of BresciaBresciaItaly
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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