An Absorbing Markov Chain Approach to GI/M/1 Queues with Generalized Vacations

Abstract

Stationary probabilities of the embedded Markov chains of a class of GI/M/1 queues can be obtained by a simple multiplication y(I-Q)^(-1), where the j th entry of the row vector y is the probability that the system state seen by the first arrival during a busy period is j and (I-Q)^(-1) is the fundamental matrix associated with the standard GI/M/1 queue. In this paper, we present the entries of (I-Q)^(-1) explicitly. Also, we illustrate how to find y by examples such as the N-policy GI/M/1 queue with or without exponential multiple vacations.