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Analysis of M [X] /G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown

Author

Listed:
  • P. Rajadurai
  • M. Varalakshmi
  • M.C. Saravanarajan
  • V.M. Chandrasekaran

Abstract

This paper investigates the steady state behaviour of an M[X]/G/1 retrial queue with two phases of service under Bernoulli vacation schedule and breakdown. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters the service immediately while the rest join the orbit. After completion of each two phases of service, the server either goes for a vacation with probability p or may wait for serving the next customer with probability (1-p). While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. We construct the mathematical model and derive the probability generating functions of number of customers in the system when it is idle, busy, on vacation and under repair. Some system performances are obtained.

Suggested Citation

  • P. Rajadurai & M. Varalakshmi & M.C. Saravanarajan & V.M. Chandrasekaran, 2015. "Analysis of M [X] /G/1 retrial queue with two phase service under Bernoulli vacation schedule and random breakdown," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(1), pages 19-41.
    • Handle: RePEc:ids:ijmore:v:7:y:2015:i:1:p:19-41
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    Citations

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    Cited by:

    1. G. Ayyappan & S. Karpagam, 2018. "An M [ X ] / G ( a , b )/1 Queueing System with Breakdown and Repair, Stand-By Server, Multiple Vacation and Control Policy on Request for Re-Service," Mathematics, MDPI, vol. 6(6), pages 1-18, June.
    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.
    3. P. Rajadurai & V. M. Chandrasekaran & M. C. Saravanarajan, 2016. "Analysis of an M[X]/G/1 unreliable retrial G-queue with orbital search and feedback under Bernoulli vacation schedule," OPSEARCH, Springer;Operational Research Society of India, vol. 53(1), pages 197-223, March.

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