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Analysis of N-policy queues with disastrous breakdown

Author

Listed:
  • R. Sudhesh

    (Bharathidasan Institute of Technology (BIT) Campus, Anna University)

  • R. Sebasthi Priya

    (Bharathidasan Institute of Technology (BIT) Campus, Anna University)

  • R. B. Lenin

    (University of Central Arkansas)

Abstract

In the area of optimal design and control of queues, the N-policy has received great attention. A single server queueing system with system disaster is considered where the server waits till N customers accumulate in the queue and upon the arrival of Nth customer the server begins to serve the customers until the system becomes idle or the occurrence of disaster whichever happens earlier. The system size probabilities in transient state are obtained in closed form using generating functions and steady-state system size probabilities are derived in closed form using generating functions and continued fractions. Further, the mean and variance for the number of customers in the system are derived for both transient and steady states and these results are deduced for the specific models. Time-dependent busy period distribution is also obtained. Numerical illustrations are also shown to visualize the system effect.

Suggested Citation

  • R. Sudhesh & R. Sebasthi Priya & R. B. Lenin, 2016. "Analysis of N-policy queues with disastrous breakdown," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 612-634, October.
    • Handle: RePEc:spr:topjnl:v:24:y:2016:i:3:d:10.1007_s11750-016-0411-6
    DOI: 10.1007/s11750-016-0411-6
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    References listed on IDEAS

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    1. Amita Bhagat & Madhu Jain, 2013. "Unreliable M x /G/1 retrial queue with multi-optional services and impatient customers," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 17(2), pages 248-273.
    2. A.V.S. Suhasini & K. Srinivasa Rao & P. Rajasekhara Reddy, 2014. "Queueing model with non-homogeneous bulk arrivals having state-dependent service rates," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 21(1), pages 84-99.
    3. Charan Jeet Singh & Madhu Jain & Binay Kumar, 2014. "Analysis of M X / G / 1 queueing model with balking and vacation," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 19(2), pages 154-173.
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    Cited by:

    1. R. Sudhesh & P. Savitha & S. Dharmaraja, 2017. "Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 179-205, April.
    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. Jiang Tao, 2018. "Analysis of a Discrete-Time Geo/G/1 Queue in a Multi-Phase Service Environment with Disasters," Journal of Systems Science and Information, De Gruyter, vol. 6(4), pages 349-365, August.

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