Sojourn time distributions for the M/M/1 queue in a Markovian environment |
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Institution: | 1. Predictive Technology Laboratory, Department of Systems & Information Engineering, University of Virginia, Charlottesville, VA 22904, USA;2. U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA |
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Abstract: | In this paper, we study 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 λj and μj 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 are of data communication. |
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