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Queueing Problems with Two Parallel Servers

In: Fair Queueing

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  • Youngsub Chun

    (Seoul National University)

Abstract

We generalize the queueing problem by assuming that the facility has two parallel servers so that two agents can be served at the same time. Once again, we are interested in finding the order in which to serve agents and the monetary transfers they should receive. Similarly to the queueing problem with one server, we introduce the “minimal transfer rule” and the “maximal transfer rule” for the queueing problem with two parallel servers and show that they correspond to the Shapley (Contributions to the theory of games II. Princeton University Press, Princeton, 1953) value of queueing games with two parallel servers, for two alternative definitions of the worth of a coalition. If the worth of a coalition is defined by assuming the coalitional members are served before the non-coalitional members, then the minimal transfer rule is obtained. If it is defined by assuming the coalitional members are served after the non-coalitional members, then the maximal transfer rule is obtained.

Suggested Citation

  • Youngsub Chun, 2016. "Queueing Problems with Two Parallel Servers," Studies in Choice and Welfare, in: Fair Queueing, chapter 0, pages 141-157, Springer.
    • Handle: RePEc:spr:stcchp:978-3-319-33771-5_10
    DOI: 10.1007/978-3-319-33771-5_10
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    References listed on IDEAS

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    1. Kar, Anirban & Mitra, Manipushpak & Mutuswami, Suresh, 2009. "On the coincidence of the prenucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 16-25, January.
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    Cited by:

    1. Stark, Oded & Budzinski, Wiktor & Kosiorowski, Grzegorz, 2019. "Switching queues, cultural conventions, and social welfare," European Journal of Operational Research, Elsevier, vol. 278(3), pages 837-844.
    2. Kazuhiko Hashimoto & Hiroki Saitoh, 2008. "Strategy-Proof and Anonymous Rule in Queueing Problems: A Relationship between Equity and Efficiency," Discussion Papers in Economics and Business 08-17, Osaka University, Graduate School of Economics.
    3. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2019. "Recent developments in the queueing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 1-23, April.
    4. Ata Atay & Christian Trudeau, 2022. "Queueing games with an endogenous number of machines," Working Papers 2202, University of Windsor, Department of Economics.
    5. Kazuhiko Hashimoto & Hiroki Saitoh, 2012. "Strategy-proof and anonymous rule in queueing problems: a relationship between equity and efficiency," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 473-480, March.

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