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Discussion on the transient solution of single server Markovian multiple variant vacation queues with disasters

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  • M. Vadivukarasi

    (Karpagam Academy of Higher Education)

  • K. Kalidass

    (Karpagam Academy of Higher Education)

Abstract

This paper studies a single server Markovian queue with the possibility of catastrophes at the service station. In this model, the server takes a maximum number of J vacations till it finds at least one customer in the queue at a vacation completion instant. The time dependent probabilities of the system size are obtained. Four special cases are derived from the model presented in this study. Finally, some numerical computations are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:59:y:2022:i:4:d:10.1007_s12597-022-00574-4
    DOI: 10.1007/s12597-022-00574-4
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    References listed on IDEAS

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    1. Ammar, Sherif I., 2015. "Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 97-105.
    2. 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, April.
    3. K. Kalidass & J. Gnanaraj & S. Gopinath & Ramanath Kasturi, 2014. "Transient analysis of an M/M/1 queue with a repairable server and multiple vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 6(2), pages 193-216.
    4. B. Krishna Kumar & A. Vijayakumar & S. Sophia, 2009. "Transient analysis of a Markovian queue with chain sequence rates and total catastrophes," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(4), pages 375-391.
    5. Shweta Upadhyaya, 2016. "Queueing systems with vacation: an overview," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 9(2), pages 167-213.
    6. M. Hlynka & L.M. Hurajt & M. Cylwa, 2009. "Transient results for M/M/1/c queues via path counting," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 1(1/2), pages 20-36.
    7. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 31, pages 123-146.
    8. 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.
    9. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 123-146.
    10. 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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