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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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    1. M. Haridass & R. Arumuganathan, 2012. "A batch service queueing system with multiple vacations, setup time and server's choice of admitting reservice," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 14(2), pages 156-186.
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    3. M. Balasubramanian & R. Arumuganathan & A. Senthil Vadivu, 2010. "Steady state analysis of a non-Markovian bulk queueing system with overloading and multiple vacations," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 9(1), pages 82-103.
    4. 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.
    5. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    6. 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.
    7. 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.
    8. M. Haridass & R. Arumuganathan, 2011. "Analysis of a batch arrival general bulk service queueing system with variant threshold policy for secondary jobs," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 3(1), pages 56-77.
    9. Kamlesh Kumar & Madhu Jain, 2014. "Bi-level control of degraded machining system with two unreliable servers, multiple standbys, startup and vacation," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 21(2), pages 123-142.
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