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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

Author

Listed:
  • G. Ayyappan

    (Department of Mathematics, Pondicherry Engineering College, Puducherry 605014, India)

  • S. Karpagam

    (Department of Mathematics, Pondicherry Engineering College, Puducherry 605014, India)

Abstract

In this paper, we discuss a non-Markovian batch arrival general bulk service single-server queueing system with server breakdown and repair, a stand-by server, multiple vacation and re-service. The main server’s regular service time, re-service time, vacation time and stand-by server’s service time are followed by general distributions and breakdown and repair times of the main server with exponential distributions. There is a stand-by server which is employed during the period in which the regular server remains under repair. The probability generating function of the queue size at an arbitrary time and some performance measures of the system are derived. Extensive numerical results are also illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:6:p:101-:d:152625
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    References listed on IDEAS

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    3. Farzana A. Maraghi & Kailash C. Madan & Ken Darby-Dowman, 2010. "Bernoulli schedule vacation queue with batch arrivals and random system breakdowns having general repair time distribution," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 7(2), pages 240-256.
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    9. K. Lakshmi & Kasturi Ramanath, 2014. "An M/G/1 two phase multi-optional retrial queue with Bernoulli feedback, non-persistent customers and breakdown and repair," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 19(1), pages 78-95.
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