The Stochastic Decomposition Results of Batch Arrival Poisson Queue with A Grand Vacation Process

Recently many authors have obtained various steady state results of batch arrival queues with single and multiple vacations through analytical methods. In this paper we discuss and derive analytically some stochastic decompostion results for a class of batch arrival Poisson queues with a grand vacation process (see Lee et al. 1994a), at various points of time e.g. random point of time, departure point of time, stationary point of time in distribution(s)). Also, we obtain some new results as generalizations of known results for the vacation model, which lead to a remarkable simplification when solving more complex$M^{X}/M/1$type of queues.