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The M/M/1 queue with gated random order of service

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  • Jacques Resing
  • Ronald Rietman

Abstract

We analyse an M/M/1 queueing model with gated random order of service discipline. In this service discipline there is a waiting room, in which arriving customers are collected, and a service queue. Each time the service queue becomes empty, all customers in the waiting room are instantaneously put in random order in the service queue. We find the joint stationary distribution of the number of customers in the waiting room and the service queue. Furthermore, we obtain the bivariate Laplace–Stieltjes transform of the joint distribution of the sojourn times of a customer in the waiting room and the service queue.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:58:y:2004:i:1:p:97-110
    DOI: 10.1046/j.0039-0402.2003.00112.x
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    Cited by:

    1. Brian Fralix, 2022. "Stationary distributions and the random-product representation," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 193-195, April.
    2. 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.
    3. Brian Fralix, 2018. "A new look at a smart polling model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 339-367, December.

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