G/M/3 with server vacations

Abstract

We study a G/M/3 queue with vacations. We consider two models In the first, two servers who find the queue empty take a vacation, other server can not take a vacation even if the system becomes empty. In the second, each server takes a vacation when he completes service and the queue is empty. these vacation models are analyzed by the supplementary variable method. Joint probabilities of the queue length and the number of servers available in the system at arrival time points and random time points are served. It is shown that G/M/3 vacation model is reduced to the ordinary G/M/3 queue without vacation when the rate of vacation time approaches infinity.