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

  • Rinaldo M. ColomboEmail author
  • Helge Holden


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.


Braess paradox Traffic dynamics Hyperbolic conservation laws Nash optimum Control theory 

Mathematics Subject Classification

35L65 90B20 



This work was partially supported by the Research Council of Norway and by the Fund for International Cooperation of the University of Brescia.

Conflict of interest

The authors declare that they have no conflict of interest.


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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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