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Analysis of variant working vacations on batch arrival queues

Author

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  • P. Vijaya Laxmi

    (Andhra University)

  • P. Rajesh

    (Andhra University)

Abstract

This paper analyzes a batch arrival infinite-buffer single server queueing system with variant working vacations in which customers arrive according to a Poisson process. As soon as the system becomes empty, the server takes working vacation. The service rate during regular busy period, working vacation period and vacation times are assumed to be exponentially distributed. We derive the probability generating function of the steady-state probabilities and obtain the closed form expressions of the system size when the server is in different states. In addition, we obtain some other performance measures and discuss their monotonicity and a cost model is formulated to determine the optimal service rate during working vacation.

Suggested Citation

  • P. Vijaya Laxmi & P. Rajesh, 2016. "Analysis of variant working vacations on batch arrival queues," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 303-316, June.
    • Handle: RePEc:spr:opsear:v:53:y:2016:i:2:d:10.1007_s12597-015-0236-3
    DOI: 10.1007/s12597-015-0236-3
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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, December.
    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.
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    Cited by:

    1. Gabi Hanukov & Michael Hassoun & Oren Musicant, 2021. "On the Benefits of Providing Timely Information in Ticket Queues with Balking and Calling Times," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
    2. Amina Angelika Bouchentouf & Lahcene Yahiaoui & Mokhtar Kadi & Shakir Majid, 2020. "Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 30(4), pages 5-28.
    3. Amita Bhagat & Madhu Jain, 2020. "Retrial queue with multiple repairs, multiple services and non preemptive priority," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 787-814, September.
    4. G. K. Tamrakar & A. Banerjee, 2020. "On steady-state joint distribution of an infinite buffer batch service Poisson queue with single and multiple vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1337-1373, December.

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