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The shorter queue polling model

Author

Listed:
  • Ivo J. B. F. Adan

    (Eindhoven University of Technology)

  • Onno J. Boxma

    (Eindhoven University of Technology)

  • Stella Kapodistria

    (Eindhoven University of Technology)

  • Vidyadhar G. Kulkarni

    (University of North Carolina)

Abstract

We consider a two-queue polling model in which customers upon arrival join the shorter of two queues. Customers arrive according to a Poisson process and the service times in both queues are independent and identically distributed random variables having the exponential distribution. The two-dimensional process of the numbers of customers at the queue where the server is and at the other queue is a two-dimensional Markov process. We derive its equilibrium distribution using two methodologies: the compensation approach and a reduction to a boundary value problem.

Suggested Citation

  • Ivo J. B. F. Adan & Onno J. Boxma & Stella Kapodistria & Vidyadhar G. Kulkarni, 2016. "The shorter queue polling model," Annals of Operations Research, Springer, vol. 241(1), pages 167-200, June.
    • Handle: RePEc:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-013-1495-0
    DOI: 10.1007/s10479-013-1495-0
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    References listed on IDEAS

    as
    1. Blanc, J.P.C., 2009. "Bad luck when joining the shortest queue," European Journal of Operational Research, Elsevier, vol. 195(1), pages 167-173, May.
    2. Jacques Resing & Ronald Rietman, 2004. "The M/M/1 queue with gated random order of service," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(1), pages 97-110, February.
    3. Ward Whitt, 1986. "Deciding Which Queue to Join: Some Counterexamples," Operations Research, INFORMS, vol. 34(1), pages 55-62, February.
    4. D. J. Houck, 1987. "Comparison of Policies for Routing Customers to Parallel Queueing Systems," Operations Research, INFORMS, vol. 35(2), pages 306-310, April.
    5. Uri Yechiali, 1972. "Customers' Optimal Joining Rules for the GI/M/s Queue," Management Science, INFORMS, vol. 18(7), pages 434-443, March.
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    Cited by:

    1. Ioannis Dimitriou, 2021. "On partially homogeneous nearest-neighbour random walks in the quarter plane and their application in the analysis of two-dimensional queues with limited state-dependency," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 95-143, June.
    2. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    3. Sem Borst & Onno Boxma, 2018. "Polling: past, present, and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 335-369, October.

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