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Optimal Transport Flow Distribution and Construction of Wardrop Optimal Networks

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Numerical Computations: Theory and Algorithms (NUMTA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14477))

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Abstract

This paper is motivated by the problem of optimal flow allocation in transportation networks. We consider equilibrium and optimal flow distribution on networks of parallel links. In a parallel network, a user (or Wardrop) equilibrium is the optimal distribution of flow across alternative parallel links that minimize the effective costs of the links, while the system optimum is the optimal distribution of flow for which the average effective cost is minimal. We study Wardrop optimal networks, i.e., the networks that admit Wardrop optimal flows which satisfy both the Wardrop equilibrium and the system optimum. We first present the characterization of Wardrop optimal flows, and then propose a matrix approach for constructing Wardrop optimal networks by means of convex, strictly increasing, and continuously differentiable functions. Some special classes of Wardrop optimal networks are also introduced.

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Authors and Affiliations

  1. College of Engineering and Technology, American University of the Middle East, 54200, Egaila, Kuwait

    Armen Bagdasaryan, Antonios Kalampakas & Mansoor Saburov

  2. Institute of Mathematics, National Academy of Sciences of Armenia, 24/5 Baghramyan ave., 0019, Yerevan, Republic of Armenia

    Armen Bagdasaryan

Authors
  1. Armen Bagdasaryan
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  2. Antonios Kalampakas
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  3. Mansoor Saburov
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Correspondence to Armen Bagdasaryan .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

  3. University of Calabria, Rende, Italy

    Annabella Astorino

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Bagdasaryan, A., Kalampakas, A., Saburov, M. (2025). Optimal Transport Flow Distribution and Construction of Wardrop Optimal Networks. In: Sergeyev, Y.D., Kvasov, D.E., Astorino, A. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2023. Lecture Notes in Computer Science, vol 14477. Springer, Cham. https://doi.org/10.1007/978-3-031-81244-6_13

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  • DOI: https://doi.org/10.1007/978-3-031-81244-6_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-81243-9

  • Online ISBN: 978-3-031-81244-6

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