A BMAP/G/1 retrial queue with a server subject to breakdowns and repairs

A BMAP/G/1 retrial queue with a server subject to breakdowns and repairs

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Article ID: iaor20062938
Country: Netherlands
Volume: 141
Issue: 1
Start Page Number: 233
End Page Number: 270
Publication Date: Jan 2006
Journal: Annals of Operations Research
Authors: , ,
Keywords: markov processes
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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