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A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs

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  • Quan-Lin Li
  • Yu Ying
  • Yiqiang Zhao

Abstract

In this paper, we consider a BMAP/G/1 retrial queue with a server subject to breakdowns and repairs, where the life time of the server is exponential and the repair time is general. We use the supplementary variable method, which combines with the matrix-analytic method and the censoring technique, to study the system. We apply the RG-factorization of a level-dependent continuous-time Markov chain of M/G/1 type to provide the stationary performance measures of the system, for example, the stationary availability, failure frequency and queue length. Furthermore, we use the RG-factorization of a level-dependent Markov renewal process of M/G/1 type to express the Laplace transform of the distribution of a first passage time such as the reliability function and the busy period. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Quan-Lin Li & Yu Ying & Yiqiang Zhao, 2006. "A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs," Annals of Operations Research, Springer, vol. 141(1), pages 233-270, January.
    • Handle: RePEc:spr:annopr:v:141:y:2006:i:1:p:233-270:10.1007/s10479-006-5301-0
    DOI: 10.1007/s10479-006-5301-0
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    References listed on IDEAS

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    1. Gyemin Lee & Jongwoo Jeon, 1999. "Analysis of an N / G / 1 finite queue with the supplementary variable method," International Journal of Stochastic Analysis, Hindawi, vol. 12, pages 1-6, January.
    2. Jeffrey Diamond & Attahiru Alfa, 1999. "Matrix analytic methods for a multi-server retrial queue with buffer," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 249-266, December.
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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. Kousik Das & Sujit Kumar Samanta, 2023. "Computational analysis of $$GI^{[X]}/D$$ G I [ X ] / D - $$MSP^{(a,b)}/1$$ M S P ( a , b ) / 1 queueing system via RG-factorization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 1-39, August.
    3. Sujit Kumar Samanta & Kousik Das, 2023. "Detailed Analytical and Computational Studies of D-BMAP/D-BMSP/1 Queueing System," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-37, March.
    4. 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.
    5. 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.
    6. Kim, Chesoong & Klimenok, Valentina I. & Orlovsky, Dmitry S., 2008. "The BMAP/PH/N retrial queue with Markovian flow of breakdowns," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1057-1072, September.
    7. Baoliang Liu & Lirong Cui & Yanqing Wen, 2014. "Interval reliability for aggregated Markov repairable system with repair time omission," Annals of Operations Research, Springer, vol. 212(1), pages 169-183, January.
    8. Wee Meng Yeo & Xue-Ming Yuan & Joyce Mei Wan Low, 2017. "On $$M^{X}/G(M/H)/1$$ M X / G ( M / H ) / 1 retrial system with vacation: service helpline performance measurement," Annals of Operations Research, Springer, vol. 248(1), pages 553-578, January.
    9. Kuo, Ching-Chang & Ke, Jau-Chuan, 2016. "Comparative analysis of standby systems with unreliable server and switching failure," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 74-82.
    10. Falin, G.I., 2010. "A single-server batch arrival queue with returning customers," European Journal of Operational Research, Elsevier, vol. 201(3), pages 786-790, March.
    11. Zhou, Wenhui & Zheng, Zhibin & Xie, Wei, 2017. "A control-chart-based queueing approach for service facility maintenance with energy-delay tradeoff," European Journal of Operational Research, Elsevier, vol. 261(2), pages 613-625.

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