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The shorter queue polling model

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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.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Ivo J. B. F. Adan

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Onno J. Boxma & Stella Kapodistria

  3. Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC, 27599, USA

    Vidyadhar G. Kulkarni

Authors
  1. Ivo J. B. F. Adan
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  2. Onno J. Boxma
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  3. Stella Kapodistria
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  4. Vidyadhar G. Kulkarni
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Correspondence to Stella Kapodistria.

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Adan, I.J.B.F., Boxma, O.J., Kapodistria, S. et al. The shorter queue polling model. Ann Oper Res 241, 167–200 (2016). https://doi.org/10.1007/s10479-013-1495-0

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