This paper develops a probabilistic decomposition method for an /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 . 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 /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.
"Probabilistic Decomposition Method on the ServerIndices of an /G/1 Vacation Queue." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/241636