Probabilistic decomposition method on the serverindices of an M ζ/G/1 vacation queue

This paper develops a probabilistic decomposition method for an m /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 m /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. © 2014 renbin liu.