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Busy Periods for Queues Alternating Between Two Modes

Author

Listed:
  • Igor Kleiner

    (Haifa University)

  • Esther Frostig

    (Haifa University)

  • David Perry

    (Holon Institute of Technology)

Abstract

We study the busy period of a single server queueing system operating in two alternating modes - working and vacation. In the two modes the systems run as an $$M^{X}/G/1$$ M X / G / 1 queue with disasters, but with different parameters. The vacation mode starts once the number of customers drops to zero. It is terminated randomly (when it is not empty) with a transition to the working mode. At such a transition moment all the customers are transferred to the working mode; the service of the customer being served is lost and it starts from scratch in the working mode. Every busy period starts with a batch arrival into an empty system and terminates at the first time that the number of customers drops to zero. The working and the vacation periods are analyzed too. Finally, we apply the results to obtain the probability generating functions of the number of customers in the working, as well as in the vacation periods.

Suggested Citation

  • Igor Kleiner & Esther Frostig & David Perry, 2023. "Busy Periods for Queues Alternating Between Two Modes," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-16, June.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10037-y
    DOI: 10.1007/s11009-023-10037-y
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    References listed on IDEAS

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    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, September.
    2. 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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