SOJOURN TIME DISTRIBUTIONS FOR THE M/M/1 QUEUE IN A MARKOVIAN ENVIRONMENT

The author a single server queue in which both the arrival rate and service rate depend on the state of an external Markov Process (called the environment) with a finite state space. Given that the environment is in state j, the mean arrival and service rates are lambda //j and mu //j respectively. For such a queue, the queue length distribution is known to be matrix geometric. In this paper, we characterize the Laplace-Stieltjes transform of the sojourn time distribution under four disciplines - last come first served preemptive resume, last come first served, processor sharing and round robin. We also discuss a potential application of this queue in the area of data communication.