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A Discrete-Time Geo/ G/1 retrial queue with the server subject to starting failures

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  • I. Atencia
  • P. Moreno

Abstract

This paper studies a discrete-time Geo/G/1 retrial queue where the server is subject to starting failures. We analyse the Markov chain underlying the regarded queueing system and present some performance measures of the system in steady-state. Then, we give two stochastic decomposition laws and find a measure of the proximity between the system size distributions of our model and the corresponding model without retrials. We also develop a procedure for calculating the distributions of the orbit and system size as well as the marginal distributions of the orbit size when the server is idle, busy or down. Besides, we prove that the M/G/1 retrial queue with starting failures can be approximated by its discrete-time counterpart. Finally, some numerical examples show the influence of the parameters on several performance characteristics. Copyright Springer Science + Business Media, Inc. 2006

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  • I. Atencia & P. Moreno, 2006. "A Discrete-Time Geo/ G/1 retrial queue with the server subject to starting failures," Annals of Operations Research, Springer, vol. 141(1), pages 85-107, January.
    • Handle: RePEc:spr:annopr:v:141:y:2006:i:1:p:85-107:10.1007/s10479-006-5295-7
    DOI: 10.1007/s10479-006-5295-7
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    References listed on IDEAS

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    1. J. Artalejo & J. Falin, 1994. "Stochastic decomposition for retrial queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(2), pages 329-342, December.
    2. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    3. Dieter Fiems & Bart Steyaert & Herwig Bruneel, 2002. "Randomly Interrupted GI-G-1 Queues: Service Strategies and Stability Issues," Annals of Operations Research, Springer, vol. 112(1), pages 171-183, April.
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    Cited by:

    1. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    2. 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.
    3. Nobel, Rein & Moreno, Pilar, 2008. "A discrete-time retrial queueing model with one server," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1088-1103, September.
    4. Artalejo, Jesus R. & Economou, Antonis & Gómez-Corral, Antonio, 2008. "Algorithmic analysis of the Geo/Geo/c retrial queue," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1042-1056, September.
    5. Rein Nobel, 2016. "Retrial queueing models in discrete time: a short survey of some late arrival models," Annals of Operations Research, Springer, vol. 247(1), pages 37-63, December.
    6. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    7. 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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