Performance analysis of GI/Geom/1 queue with single working vacation and setup times

In this paper, we consider a GI/Geom/1 queue with single working vacation and setup times. With the transition probability matrix of the two-dimensional Markov chain embedded in the time that the customers arrive at the system, its transition probability can be expressed in Block-Jocabi form. By the matrix-geometric solution method, probability distribution of the stationary queue length is firstly derived. Furthermore, we obtain the highly complicated PGF of the stationary waiting time from which we got its stochastic decomposition, and can deduce the waiting time of an arbitrary customer arrived at the system. Meanwhile, we gain the mean queue length and the mean waiting time. Some numerical examples are persented. 1548-7741/Copyright © 2011 Binary Information Press December 2011.