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Queueing problems with two parallel servers

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  • Youngsub Chun
  • Eun Jeong Heo

Abstract

Agents are waiting for their jobs to be processed at a service facility. All agents need the same processing time but have different waiting costs per unit of time. The facility has two parallel servers and can serve two agents at a time. We are interested in finding the order in which to serve agents and the (positive or negative) monetary transfers they should receive. We introduce two rules, the “minimal transfer rule” and the “maximal transfer rule”. We show that they correspond to the Shapley (1953) values of associated queueing games, for two alternative definitions of the worth of a coalition. The two‐server queueing games correspond to the games similarly defined by Maniquet (2003) and Chun (2006a) for one server. If the worth of a coalition is defined by assuming that the coalitional members are served before the non‐coalitional members, then the minimal transfer rule is obtained. If it is defined by assuming that the coalitional members are served after the non‐coalitional members, then the maximal transfer rule is obtained.

Suggested Citation

  • Youngsub Chun & Eun Jeong Heo, 2008. "Queueing problems with two parallel servers," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(2), pages 299-315, June.
    • Handle: RePEc:bla:ijethy:v:4:y:2008:i:2:p:299-315
    DOI: 10.1111/j.1742-7363.2008.00077.x
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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. 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.
    2. 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.
    3. Ata Atay & Christian Trudeau, 2022. "Queueing games with an endogenous number of machines," Working Papers 2202, University of Windsor, Department of Economics.
    4. 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.
    5. 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.

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