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Mean sojourn times in multiclass feedback queues with gated disciplines

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  • Tetsuji Hirayama

Abstract

In this paper, we investigate multiclass feedback queues with gated disciplines. The server selects the stations by a nonpreemptive priority scheduling algorithm and serves customers in the selected station by either a gated FCFS discipline or a gated priority discipline. We take a rather systematic approach to their mean sojourn times. We define conditional expected sojourn times for all customers and derive their expressions from an analysis of busy periods. Since they are shown to be linear in some components of the system states, their steady state mean values can be derived from simple limiting procedures. These mean values can be obtained from a set of linear equations. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 719–741, 2003.

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  • Tetsuji Hirayama, 2003. "Mean sojourn times in multiclass feedback queues with gated disciplines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 719-741, October.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:7:p:719-741
    DOI: 10.1002/nav.10086
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    References listed on IDEAS

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    1. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    2. Benjamin Melamed & Ward Whitt, 1990. "On Arrivals That See Time Averages," Operations Research, INFORMS, vol. 38(1), pages 156-172, February.
    3. Peter W. Glynn & Ward Whitt, 1989. "Extensions of the Queueing Relations L = λ W and H = λ G," Operations Research, INFORMS, vol. 37(4), pages 634-644, August.
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    Cited by:

    1. Tetsuji Hirayama, 2012. "Analysis of multiclass Markovian polling systems with feedback and composite scheduling algorithms," Annals of Operations Research, Springer, vol. 198(1), pages 83-123, September.
    2. Jerim Kim & Bara Kim & Hsing Luh, 2019. "Analysis of a Markovian feedback queue with multi-class customers and its application to the weighted round-robin queue," Annals of Operations Research, Springer, vol. 277(2), pages 137-159, June.

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