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Analysis of a Single-Sever Queue with Disasters and Repairs Under Bernoulli Vacation Schedule

Author

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  • Ye Jingjing

    (School of Science, Nanjing University of Science and Technology, Nanjing210094, China)

  • Liu Liwei

    (School of Science, Nanjing University of Science and Technology, Nanjing210094, China)

  • Jiang Tao

    (School of Science, Nanjing University of Science and Technology, Nanjing210094, China)

Abstract

This paper studies a single-sever queue with disasters and repairs, in which after each service completion the server may take a vacation with probability q(0 ≤q≤ 1), or begin to serve the next customer, if any, with probability p(= 1 − q). The disaster only affects the system when the server is in operation, and once it occurs, all customers present are eliminated from the system. We obtain the stationary probability generating functions (PGFs) of the number of customers in the system by solving the balance equations of the system. Some performance measures such as the mean system length, the probability that the server is in different states, the rate at which disasters occur and the rate of initiations of busy period are determined. We also derive the sojourn time distribution and the mean sojourn time. In addition, some numerical examples are presented to show the effect of the parameters on the mean system length.

Suggested Citation

  • Ye Jingjing & Liu Liwei & Jiang Tao, 2016. "Analysis of a Single-Sever Queue with Disasters and Repairs Under Bernoulli Vacation Schedule," Journal of Systems Science and Information, De Gruyter, vol. 4(6), pages 547-559, December.
    • Handle: RePEc:bpj:jossai:v:4:y:2016:i:6:p:547-559:n:5
    DOI: 10.21078/JSSI-2016-547-13
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    References listed on IDEAS

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    1. Spiros Dimou & Antonis Economou, 2013. "The Single Server Queue with Catastrophes and Geometric Reneging," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 595-621, September.
    2. Economou, Antonis & Fakinos, Demetrios, 2003. "A continuous-time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes," European Journal of Operational Research, Elsevier, vol. 149(3), pages 625-640, September.
    3. Boudali, Olga & Economou, Antonis, 2012. "Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes," European Journal of Operational Research, Elsevier, vol. 218(3), pages 708-715.
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