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On the Braess Paradox with Nonlinear Dynamics and Control Theory

Author

Listed:
  • Rinaldo M. Colombo

    (University of Brescia)

  • Helge Holden

    (Norwegian University of Science and Technology)

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.

Suggested Citation

  • Rinaldo M. Colombo & Helge Holden, 2016. "On the Braess Paradox with Nonlinear Dynamics and Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 216-230, January.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-015-0729-5
    DOI: 10.1007/s10957-015-0729-5
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    References listed on IDEAS

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    1. repec:cup:cbooks:9780511771576 is not listed on IDEAS
    2. Anna Nagurney & David Boyce, 2005. "Preface to “On a Paradox of Traffic Planning”," Transportation Science, INFORMS, vol. 39(4), pages 443-445, November.
    3. Dafermos, Stella & Nagurney, Anna, 1984. "On some traffic equilibrium theory paradoxes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 101-110, April.
    4. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    5. Easley,David & Kleinberg,Jon, 2010. "Networks, Crowds, and Markets," Cambridge Books, Cambridge University Press, number 9780521195331, November.
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    Cited by:

    1. Bagloee, Saeed Asadi & (Avi) Ceder, Avishai & Sarvi, Majid & Asadi, Mohsen, 2019. "Is it time to go for no-car zone policies? Braess Paradox Detection," Transportation Research Part A: Policy and Practice, Elsevier, vol. 121(C), pages 251-264.
    2. Adriano Festa & Paola Goatin & Fabio Vicini, 2023. "Navigation System-Based Routing Strategies in Traffic Flows on Networks," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 930-957, September.

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