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On the Tail of the Waiting Time in a Markov-Modulated M/G/1 Queue

Department of Mathematical Statistics, University of Lund, Box 118, S-221 00, Lund, Sweden
8 Warfield Street, Montclair, New Jersey 07043
asmus{at}maths.lth.se
colm{at}ecn.purdue.edu

We show that the "exponential decay parameter" of the waiting time in a Markov-modulated M/G/1 queue is no larger than that of the corresponding M/G/1 queue with "averaged" parameters, and we give a necessary and sufficient condition for equality. We also explore the effect of speeding up the modulation process. A key tool is a Markov-modulated fluid model.

Subject classifications: Queues, approximations and limit theorems: effect of modulation on probability of a long wait.
History: Received October 1998; revision received October 2000; accepted November 2000.