A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs |
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| Authors: | Quan-Lin Li Yu Ying Yiqiang Q Zhao |
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| Institution: | (1) Department of Industrial Engineering, Tsinghua University, Beijing, 100084, P.R. China;(2) School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada;(3) School of Electrical and Computer Engineering, Purdue University, West Lafayette, 47907, IN, U.S.A |
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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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| Keywords: | Retrial queues Batch Markov arrival processes (BMAP) Markov chains of M/G/1 type Markov renewal processes of M/G/1 type Supplementary variable method Matrix-analytic method Censoring technique RG-factorization Reliability |
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