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

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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.

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Authors and Affiliations

  1. Department of Industrial Engineering, Tsinghua University, Beijing, 100084, P.R. China

    Quan-Lin Li

  2. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada

    Quan-Lin Li & Yiqiang Q. Zhao

  3. School of Electrical and Computer Engineering, Purdue University, West Lafayette, 47907, IN, U.S.A

    Yu Ying

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  1. Quan-Lin Li
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  2. Yu Ying
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Li, QL., Ying, Y. & Zhao, Y.Q. A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs. Ann Oper Res 141, 233–270 (2006). https://doi.org/10.1007/s10479-006-5301-0

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