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Analysis of Single Server Queue with Modified Vacation Policy

Author

Listed:
  • Priyanka Kalita

    (Institute of Advanced Study in Science and Technology)

  • Gautam Choudhury

    (Institute of Advanced Study in Science and Technology)

  • Dharmaraja Selvamuthu

    (Indian Institute of Technology Delhi)

Abstract

This article deals with single server queue with modified vacation policy. The modified vacation policy captures the operation of a close down period, type 1 vacation period, type 2 vacation period, a start-up period and a dormant period. Here, type 1 vacations takes a short period of random duration and type 2 vacation take a long period of random duration. Explicit expressions have been obtained for steady state queue size distribution at service completion point and steady state system size probabilities. The Laplace-Stieltjes transform of waiting time and its corresponding mean value have been obtained for the system. Finally, some numerical examples have been provided and use the parabolic method to search the optimum value of the control parameter p.

Suggested Citation

  • Priyanka Kalita & Gautam Choudhury & Dharmaraja Selvamuthu, 2020. "Analysis of Single Server Queue with Modified Vacation Policy," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 511-553, June.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09713-9
    DOI: 10.1007/s11009-019-09713-9
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    References listed on IDEAS

    as
    1. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, March.
    2. Minh, Do Le, 1988. "Transient solutions for some exhaustive M/G/1 queues with generalized independent vacations," European Journal of Operational Research, Elsevier, vol. 36(2), pages 197-201, August.
    3. B. Krishna Kumar & S. Anbarasu & S.R. Anantha Lakshmi, 2015. "Performance analysis for queueing systems with close down periods and server under maintenance," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(1), pages 88-110, January.
    4. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    5. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. 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.
    2. M. Vadivukarasi & K. Kalidass, 2022. "Discussion on the transient solution of single server Markovian multiple variant vacation queues with disasters," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1352-1376, December.

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