Abstract
This paper develops a probabilistic decomposition method for anMξ/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probabilityp. 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-serverMξ/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.
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