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

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.