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Optimizing Flow Thinning Protection in Multicommodity Networks with Variable Link Capacity

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  • Michał Pióro

    (Institute of Telecommunications, Warsaw University of Technology, 00-665 Warsaw, Poland; and Department of Electrical and Information Technology, Lund University, 221 00 Lund, Sweden)

  • Yoann Fouquet

    (Sorbonne universités, Université de technologie de Compiègne, UMR CNRS 7253 Heudiasyc, 60203 Compiègne cedex, France)

  • Dritan Nace

    (Sorbonne universités, Université de technologie de Compiègne, UMR CNRS 7253 Heudiasyc, 60203 Compiègne cedex, France)

  • Michael Poss

    (UMR CNRS 5506 LIRMM, Université de Montpellier, 161 rue Ada, 34392 Montpellier Cedex 5, France)

Abstract

Flow thinning (FT) is a concept of a traffic routing and protection strategy applicable to communication networks with variable capacity of links. In such networks, the links do not attain their nominal (maximum) capacity simultaneously, so in a typical network state only some links are fully available whereas on each of the remaining links only a fraction of its maximum capacity is usable. Every end-to-end traffic demand is assigned a set of logical tunnels whose total capacity is dedicated to carry the demand’s traffic. The nominal (i.e., maximum) capacity of the tunnels, supported by the nominal (maximum) link capacity, is subject to state-dependent thinning to account for variable capacity of the links fluctuating below the maximum. Accordingly, the capacity available on the tunnels is also fluctuating below their nominal levels and hence the instantaneous traffic sent between the demand’s end nodes must accommodate to the current total capacity available on its dedicated tunnels. The related multi-commodity flow optimization problem is (N-script)(P-script) -hard and its noncompact linear programming formulation requires path generation. For that, we formulate an integer programming pricing problem, at the same time showing the cases when the pricing is polynomial. We also consider an important variant of FT, affine thinning, that may lead to practical FT implementations. We present a numerical study illustrating traffic efficiency of FT and computational efficiency of its optimization models. Our considerations are relevant, among others, for wireless mesh networks utilizing multiprotocol label switching tunnels.

Suggested Citation

  • Michał Pióro & Yoann Fouquet & Dritan Nace & Michael Poss, 2016. "Optimizing Flow Thinning Protection in Multicommodity Networks with Variable Link Capacity," Operations Research, INFORMS, vol. 64(2), pages 273-289, April.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:2:p:273-289
    DOI: 10.1287/opre.2016.1486
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Geir Dahl & Mechthild Stoer, 1998. "A Cutting Plane Algorithm for Multicommodity Survivable Network Design Problems," INFORMS Journal on Computing, INFORMS, vol. 10(1), pages 1-11, February.
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    Cited by:

    1. Sara Mattia & Michael Poss, 2018. "A comparison of different routing schemes for the robust network loading problem: polyhedral results and computation," Computational Optimization and Applications, Springer, vol. 69(3), pages 753-800, April.
    2. Sun, Hao & Yang, Jun & Yang, Chao, 2019. "A robust optimization approach to multi-interval location-inventory and recharging planning for electric vehicles," Omega, Elsevier, vol. 86(C), pages 59-75.
    3. Dimitris Bertsimas & Arthur Delarue & Patrick Jaillet & Sébastien Martin, 2019. "Travel Time Estimation in the Age of Big Data," Operations Research, INFORMS, vol. 67(2), pages 498-515, March.
    4. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.

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