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An M/G/1 unreliable server queue with two phases of service and Bernoulli vacation schedule under randomised vacation policy

Author

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  • Gautam Choudhury
  • Mitali Deka

Abstract

This paper deals with an M/G/1 Bernoulli vacation queue with two phases of service in which an unreliable server operates a randomised vacation policy with at most M consecutive vacations. If the system is empty by the end of the Mth vacation, the server becomes idle in the system until at least one customer arrives at the queue. Assume that the server may meet an unpredictable breakdown according to a Poisson process and the repair time has a general distribution. For such a system, we derive the joint distribution of state of the server and queue size, the pgf of the stationary queue size distribution at a departure epoch, LST of busy period distribution and waiting time distribution along with some important performance measures of the model. Finally, we develop a cost model to determine optimal randomised policy along with some numerical illustration.

Suggested Citation

  • Gautam Choudhury & Mitali Deka, 2015. "An M/G/1 unreliable server queue with two phases of service and Bernoulli vacation schedule under randomised vacation policy," International Journal of Applied Management Science, Inderscience Enterprises Ltd, vol. 7(4), pages 309-337.
    • Handle: RePEc:ids:injams:v:7:y:2015:i:4:p:309-337
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    Citations

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    Cited by:

    1. Ahuja, Anjali & Jain, Anamika & Jain, Madhu, 2022. "Transient analysis and ANFIS computing of unreliable single server queueing model with multiple stage service and functioning vacation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 464-490.
    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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