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Unreliable server M/G/1 queue with multi-optional services and multi-optional vacations

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Listed:
  • Madhu Jain
  • G.C. Sharma
  • Richa Sharma

Abstract

This paper deals with an M/G/1 queue with multiple optional services and multiple optional vacations for an unreliable server queue. All arriving customers require a First Essential Service (FES), while only some of them ask for other optional services. The stability and ergodicity condition for the model has been discussed. By introducing supplementary variables and employing the generating function technique, we derive the system size distribution at the random epoch as well as the departure epoch. Waiting time distribution and some other queuing and reliability measures have also been obtained. The sensitivity analysis has been facilitated by taking numerical illustrations to explore the effect of the different parameters on various performance indices.

Suggested Citation

  • Madhu Jain & G.C. Sharma & Richa Sharma, 2013. "Unreliable server M/G/1 queue with multi-optional services and multi-optional vacations," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 5(2), pages 145-169.
    • Handle: RePEc:ids:ijmore:v:5:y:2013:i:2:p:145-169
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    Citations

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    Cited by:

    1. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.
    2. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.

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