M/G/1 queue with exponential working vacation and gated service

Abstract

In this paper we consider the analysis of an M/G/1 queue with working vacation. In contrast to the previous literature where the working vacation starts when all customers are served (exhaustive discipline) we consider the case where the vacation period starts when the customers present at the system at beginning of the service period are served (gated discipline). The analysis of the model with gated discipline requires a different approach than the one with exhaustive discipline. We present the probability-generating function of the number of customers in the system and the Laplace-Stieljes transform of the stationary waiting time. © 2011 Springer-Verlag.