The M/M/1 queue with single working vacation and set-up times

Abstract

Using quasi birth and death process and matrix-geometric solution method, an M/M/1 queue with single working vacation and set-up times is discussed in this paper. The distributions for the stationary queue length and waiting time of a customer in the system are derived. Furthermore, stochastic decomposition structures of stationary indices are obtained, and the distributions of the additional queue length and additional delay are gained. Finally, several special cases and numerical examples demonstrate the results.