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Waiting times in classical priority queues via elementary lattice path counting

Author

Listed:
  • Lars A. Vianen

    (Erasmus School of Economics)

  • Adriana F. Gabor

    (United Arab Emirates University)

  • Jan-Kees Ommeren

    (University of Twente)

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 analyzed, the proposed method offers new insights and complements the results previously obtained by inverting the associated Laplace transforms.

Suggested Citation

  • Lars A. Vianen & Adriana F. Gabor & Jan-Kees Ommeren, 2016. "Waiting times in classical priority queues via elementary lattice path counting," Queueing Systems: Theory and Applications, Springer, vol. 84(3), pages 295-307, December.
    • Handle: RePEc:spr:queues:v:84:y:2016:i:3:d:10.1007_s11134-016-9498-6
    DOI: 10.1007/s11134-016-9498-6
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    References listed on IDEAS

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    1. 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.
    2. Richard H. Davis, 1966. "Waiting-Time Distribution of a Multi-Server, Priority Queuing System," Operations Research, INFORMS, vol. 14(1), pages 133-136, February.
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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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