Probabilistic Decomposition Method on the ServerIndices of an Mξ/G/1 Vacation Queue

Renbin Liu

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: This paper develops a probabilistic decomposition method for an Mξ/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p. Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during (0, t]. It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single‐server Mξ/G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose.

Date: 2014
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https://doi.org/10.1155/2014/241636

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:241636

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