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A discrete-time queueing system with server breakdowns and changes in the repair times

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  • I. Atencia

Abstract

We consider a discrete-time queueing system in which the arriving customers can decide to follow a LCFS discipline or to join the queue. Breakdowns can occur with geometrical lifetime and repair times governed by an arbitrary distribution. The repair times can exert changes governed by a geometrical law. We carry out a thorough study of the model deriving analytical results for the stationary distributions. We obtain generating functions of the number of customers in the queue and in the system. We also obtain the generating function of the repair times taking into account possible changes in the remaining repair times. The generating functions of the busy period, sojourn time in the server, sojourn time in the queue as well as some performance measures are also provided. Copyright Springer Science+Business Media New York 2015

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  • 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.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:37-49:10.1007/s10479-015-1940-3
    DOI: 10.1007/s10479-015-1940-3
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    References listed on IDEAS

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    1. Harrison White & Lee S. Christie, 1958. "Queuing with Preemptive Priorities or with Breakdown," Operations Research, INFORMS, vol. 6(1), pages 79-95, February.
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    6. I. Atencia & A. Pechinkin, 2013. "A discrete-time queueing system with optional LCFS discipline," Annals of Operations Research, Springer, vol. 202(1), pages 3-17, January.
    7. Ndreca, Sokol & Scoppola, Benedetto, 2008. "Discrete time GI/Geom/1 queueing system with priority," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1403-1408, September.
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    Cited by:

    1. Sheng Zhu & Jinting Wang & Bin Liu, 2020. "Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs," Operational Research, Springer, vol. 20(4), pages 2163-2187, December.
    2. Atencia, I., 2017. "A Geo/G/1 retrial queueing system with priority services," European Journal of Operational Research, Elsevier, vol. 256(1), pages 178-186.
    3. 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.
    4. Lan Shaojun & Tang Yinghui, 2017. "Performance Analysis of a Discrete-Time Queue with Working Breakdowns and Searching for the Optimum Service Rate in Working Breakdown Period," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 176-192, April.
    5. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2019. "Service system design for managing interruption risks: A backup-service risk-mitigation strategy," European Journal of Operational Research, Elsevier, vol. 274(2), pages 417-431.

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