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Wardrop Equilibrium for Networks with the BPR Latency Function

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Book cover Discrete Optimization and Operations Research (DOOR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9869))

Abstract

This paper considers a network comprised of parallel routes with the Bureau of Public Road (BPR) latency function and suggests an optimal distribution method for incoming traffic flow. The authors analytically derive a system of equations defining the optimal distribution of the incoming flow with minimum social costs, as well as a corresponding system of equations for the Wardrop equilibrium in this network. In particular, the Wardrop equilibrium is applied to the competition model with rational consumers who use the carriers with minimal cost, where cost is equal to the price for service plus the waiting time for the service. Finally, the social costs under the equilibrium and under the optimal distribution are compared. It is shown that the price of anarchy can be infinitely large in the model with strategic pricing.

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Acknowledgements

This research is supported by the Russian Fund for Basic Research (projects 16-51-55006, 16-01-00183), the National Natural Science Foundation of China (project 61661136002) and Tsinghua University Initiative Scientific Research Grant (project 20151080397).

Author information

Authors and Affiliations

  1. Department of Decision Sciences and Managerial Economics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

    Jaimie W. Lien

  2. Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, 11, Pushkinskaya Street, Petrozavodsk, Russia, 185910

    Vladimir V. Mazalov

  3. Saint-Petersburg State University, Universitetskii Prospekt 35, Saint-petrsburg, Russia, 198504

    Anna V. Melnik

  4. Department of Economics, School of Economics and Management, Tsinghua University, Beijing, 100084, China

    Jie Zheng

Authors
  1. Jaimie W. Lien
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  2. Vladimir V. Mazalov
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  3. Anna V. Melnik
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  4. Jie Zheng
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Corresponding author

Correspondence to Vladimir V. Mazalov .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Yury Kochetov

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Vladimir Beresnev

  4. Far Eastern Federal University , Vladivostik, Russia

    Evgeni Nurminski

  5. University of Florida , Gainesville, Florida, USA

    Panos Pardalos

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© 2016 Springer International Publishing Switzerland

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Lien, J.W., Mazalov, V.V., Melnik, A.V., Zheng, J. (2016). Wardrop Equilibrium for Networks with the BPR Latency Function. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_4

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  • DOI: https://doi.org/10.1007/978-3-319-44914-2_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44913-5

  • Online ISBN: 978-3-319-44914-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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