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A Queue with Starter and a Queue with Vacations: Delay Analysis by Decomposition

Author

Listed:
  • Hanoch Levy

    (AT&T Bell Laboratories, Holmdel, New Jersey)

  • Leonard Kleinrock

    (University of California, Los Angeles, California)

Abstract

This paper analyzes both a queueing system that incurs a start-up delay whenever an idle period ends and one in which the server takes vacation periods. We show that the delay distribution in the queue with starter is composed of the direct sum of two independent variables: (1) the delay in the equivalent queue without starter, and (2) the additional delay suffered due to the starter's presence. Using this decomposition property, we easily derive the distribution of the delay suffered in the system with starter. This analysis is done for systems (both discrete and continuous time) whose interarrival times possess the memoryless property. Using this approach, we then analyze the M / G /1 system with vacation periods. First, we show that the M / G /1 with vacations can be considered as a special case of the M / G /1 with starter, so that the delay in the M / G /1 with vacations can be easily found by using the formula for the delay of the M / G /1 with starter. Second, using geometric arguments, we explain why the additional delay in the vacation system is distributed as the residual life of the vacation period.

Suggested Citation

  • Hanoch Levy & Leonard Kleinrock, 1986. "A Queue with Starter and a Queue with Vacations: Delay Analysis by Decomposition," Operations Research, INFORMS, vol. 34(3), pages 426-436, June.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:3:p:426-436
    DOI: 10.1287/opre.34.3.426
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    Citations

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    Cited by:

    1. B. Kumar & D. Arivudainambi & A. Krishnamoorthy, 2006. "Some results on a generalized M/G/1 feedback queue with negative customers," Annals of Operations Research, Springer, vol. 143(1), pages 277-296, March.
    2. Deena Merit C.K. & Haridass M. & Dharmaraja Selvamuthu & Priyanka Kalita, 2023. "Energy Efficiency in a Base Station of 5G Cellular Networks using M/G/1 Queue with Multiple Sleeps and N-Policy," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-28, June.
    3. Offer Kella & Uri Yechiali, 1988. "Priorities in M/G/1 queue with server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 23-34, February.

    More about this item

    Keywords

    688 busy period analysis;

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