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Waiting times in classical priority queues via elementary lattice path counting

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  • van Vianen, L.A.
  • Gabor, A.F.
  • van Ommeren, J.C.W.

Abstract

In this paper we describe an elementary combinatorial approach for deriving the waiting and response time distributions in a few classical priority queueing models. By making use of lattice paths that are linked in a natural way to the stochastic processes analysed, the proposed method offers new insights and complements the results previously obtained by inverting the associated Laplace Transforms.

Suggested Citation

  • van Vianen, L.A. & Gabor, A.F. & van Ommeren, J.C.W., 2016. "Waiting times in classical priority queues via elementary lattice path counting," Econometric Institute Research Papers EI2016-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:80103
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    References listed on IDEAS

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    1. Jianfu Wang & Opher Baron & Alan Scheller-Wolf, 2015. "M/M/c Queue with Two Priority Classes," Operations Research, INFORMS, vol. 63(3), pages 733-749, June.
    2. Douglas R. Miller, 1981. "Computation of Steady-State Probabilities for M / M /1 Priority Queues," Operations Research, INFORMS, vol. 29(5), pages 945-958, October.
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    Cited by:

    1. Gabor, Adriana F. & van Vianen, Lars A. & Yang, Guangyuan & Axsäter, Sven, 2018. "A base-stock inventory model with service differentiation and response time guarantees," European Journal of Operational Research, Elsevier, vol. 269(3), pages 900-908.
    2. Sofian De Clercq & Joris Walraevens, 2020. "Delay analysis of a two-class priority queue with external arrivals and correlated arrivals from another node," Annals of Operations Research, Springer, vol. 293(1), pages 57-72, October.
    3. Xiaoyuan Liu & Brian Fralix, 2019. "On Lattice Path Counting and the Random Product Representation, with Applications to the Er/M/1 Queue and the M/Er/1 Queue," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1119-1149, December.

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