Analysis of multi-server queue with synchronous vacations and gated discipline

In this paper we present the analysis of an M/M/c multiple synchronous vacation model. In contrast to the previous works on synchronous vacation model we consider the model with gated service discipline and with independent and identically distributed vacation periods. The analysis of this model requires different methodology compared to those ones used for synchronous vacation model so far. The main results are the mean and the probability-generating function of the stationary number of customers at an arbitrary epoch. Numerical examples are also provided to illustrate the solution of the model. This vacation queue is suitable to model a single operator controlled system consisting of more machines. Hence the provided analysis can be applied to study and optimize such systems.