On the output process of an M/M/1 queue with randomly varying system parameters

In this paper an analysis of the output process from an M/M/1 queue where the arrival and service rates vary randomly is presented. The results include expressions for the mean, variance and distribution of the interdeparture interval, the joint density function of two successive interdeparture intervals and their correlation. An interesting feature of the results is that the moments of the interdeparture time are expressed in terms of the expected times to first and second departures from an arbitrary point in time.