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Calculation of output characteristics of a priority queue through a busy period analysis

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  • Walraevens, Joris
  • Fiems, Dieter
  • Wittevrongel, Sabine
  • Bruneel, Herwig

Abstract

In this paper, we analyze some output characteristics of a discrete-time two-class priority queue by means of probability generating functions. Therefore, we construct a Markov chain which - after analysis - provides a.o. the probability generating functions of the lengths of the busy periods of both classes. It is furthermore shown how performance measures, related to the output process, are calculated from these functions. The queueing model is kept fairly simple to explain the method of analysis of the busy periods and the output characteristics of priority queues as clearly as possible.

Suggested Citation

  • Walraevens, Joris & Fiems, Dieter & Wittevrongel, Sabine & Bruneel, Herwig, 2009. "Calculation of output characteristics of a priority queue through a busy period analysis," European Journal of Operational Research, Elsevier, vol. 198(3), pages 891-898, November.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:3:p:891-898
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    References listed on IDEAS

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    1. Zeephongsekul, P. & Bedford, A., 2006. "Waiting time analysis of the multiple priority dual queue with a preemptive priority service discipline," European Journal of Operational Research, Elsevier, vol. 172(3), pages 886-908, August.
    2. Walraevens, Joris & Steyaert, Bart & Bruneel, Herwig, 2008. "Analysis of a discrete-time preemptive resume priority buffer," European Journal of Operational Research, Elsevier, vol. 186(1), pages 182-201, April.
    3. Mor Harchol-Balter & Takayuki Osogami & Alan Scheller-Wolf & Adam Wierman, 2005. "Multi-Server Queueing Systems with Multiple Priority Classes," Queueing Systems: Theory and Applications, Springer, vol. 51(3), pages 331-360, December.
    4. David A. Stanford, 1997. "Waiting and Interdeparture Times in Priority Queues with Poisson- and General-Arrival Streams," Operations Research, INFORMS, vol. 45(5), pages 725-735, October.
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    Cited by:

    1. Bruneel, Herwig & Maertens, Tom & Walraevens, Joris, 2014. "Class clustering destroys delay differentiation in priority queues," European Journal of Operational Research, Elsevier, vol. 235(1), pages 149-158.
    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. Herwig Bruneel & Dieter Fiems & Joris Walraevens & Sabine Wittevrongel, 2014. "Rejoinder on: Queueing models for the analysis of communication systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 460-468, July.
    4. Herwig Bruneel & Tom Maertens & Bart Steyaert & Dieter Claeys & Dieter Fiems & Joris Walraevens, 2018. "Analysis of a two-class single-server discrete-time FCFS queue: the effect of interclass correlation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 403-436, October.

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