Performance analysis for the Geom/G/1 queue with single working vacation

Abstract

In this paper, we analyzed a Geom/G/1 queue with single working vacation. Firstly, we obtained the M/G/1-type structure matrix of the two-dimensional embedded Markov chain. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived. Furthermore, we got the stochastic decomposition formulae for the PGF of the stationary queue size and the stationary waiting time. Finally, several numerical examples are presented to verify these results.