A generalization of the decomposition property in the M/G/1 queue with server vacations

This paper considers the M/G/1 queueing systems with server vacations. For a very general class of such systems, Fuhrmann and Cooper have shown that the stationary queue length at a random point in time is distributed as the sum of two independent random variables, one of which is the stationary queue length at a random point in time in the corresponding standard M/G/1 queue. This property is called the stochastic decomposition in the M/G/1 queue with server vacations. In this paper, the authors show that this decomposition property is also valid for the joint probability distribution of the queue length and the forward recurrence service time.