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Transient analysis of an M/M/1 queue with a repairable server and multiple vacations

Author

Listed:
  • K. Kalidass
  • J. Gnanaraj
  • S. Gopinath
  • Ramanath Kasturi

Abstract

In this paper, we discuss the time dependent behaviour of an M/M/1 queueing system with multiple vacations. We assume that the system is subject to sudden breakdowns and that during this period the system is flushed out. After the repair, the server waits for the arrival of the next customer. We have obtained analytical expressions for the transient state probabilities of the system size. We also obtain expressions for the transient expected value and variance of the system length. The corresponding steady state results are derived. We have performed a busy period analysis of this system in the steady state. We have obtained analytical expressions for the expected duration of a busy period and the expected duration of the vacation period. We present numerical examples to illustrate the sensitivity of the performance measures of the system to the changes in the parameters of the system.

Suggested Citation

  • 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.
    • Handle: RePEc:ids:ijmore:v:6:y:2014:i:2:p:193-216
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    Citations

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    Cited by:

    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. M. I. G. Suranga Sampath & K. Kalidass & Jicheng Liu, 2020. "Transient Analysis of an M/M/1 Queueing System Subjected to Multiple Differentiated Vacations, Impatient Customers and a Waiting Server with Application to IEEE 802.16E Power Saving Mechanism," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 297-320, March.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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