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Discrete-time queues with discretionary priorities

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  • Kim, Kilhwan
  • Chae, Kyung C.

Abstract

In this paper, we consider a discrete-time two-class discretionary priority queueing model with generally distributed service times and per slot i.i.d. structured inputs in which preemptions are allowed only when the elapsed service time of a lower-class customer being served does not exceed a certain threshold. As the preemption mode of the discretionary priority discipline, we consider the Preemptive Resume, Preemptive Repeat Different, and Preemptive Repeat Identical modes. We derive the Probability Generating Functions (PGFs) and first moments of queue lengths of each class in this model for all the three preemption modes in a unified manner. The obtained results include all the previous works on discrete-time priority queueing models with general service times and structured inputs as their special cases. A numerical example shows that, using the discretionary priority discipline, we can more subtly adjust the system performances than is possible using either the pure non-preemptive or the preemptive priority disciplines.

Suggested Citation

  • Kim, Kilhwan & Chae, Kyung C., 2010. "Discrete-time queues with discretionary priorities," European Journal of Operational Research, Elsevier, vol. 200(2), pages 473-485, January.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:2:p:473-485
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    References listed on IDEAS

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    1. Joris Walraevens & Bart Steyaert & Herwig Bruneel, 2006. "A preemptive repeat priority queue with resampling: Performance analysis," Annals of Operations Research, Springer, vol. 146(1), pages 189-202, September.
    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.
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    Cited by:

    1. Walraevens, Joris & Maertens, Tom & Bruneel, Herwig, 2013. "A semi-preemptive priority scheduling discipline: Performance analysis," European Journal of Operational Research, Elsevier, vol. 224(2), pages 324-332.
    2. Vanlerberghe, Jasper & Walraevens, Joris & Maertens, Tom & Bruneel, Herwig, 2018. "Calculation of the performance region of an easy-to-optimize alternative for Generalized Processor Sharing," European Journal of Operational Research, Elsevier, vol. 270(2), pages 625-635.
    3. Przemysław Korytkowski & Tomasz Wiśniewski, 2011. "Performance analysis of commercial offset printing under dynamic priority rules," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(1), pages 53-64.
    4. Jasper Vanlerberghe & Tom Maertens & Joris Walraevens & Stijn Vuyst & Herwig Bruneel, 2016. "On the optimization of two-class work-conserving parameterized scheduling policies," 4OR, Springer, vol. 14(3), pages 281-308, September.
    5. Ning Zhao & Zhaotong Lian & Kan Wu, 2015. "Analysis of a MAP/PH/1 Queue with Discretionary Priority Based on Service Stages," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-22, December.

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