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arXiv · 0804.3935

The M/M/1 queue is Bernoulli

Michael Keane·Neil O'Connell
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Abstract

The classical output theorem for the M/M/1 queue, due to Burke (1956), states that the departure process from a stationary M/M/1 queue, in equilibrium, has the same law as the arrivals process, that is, it is a Poisson process. In this paper we show that the associated measure-preserving transformation is metrically isomorphic to a two-sided Bernoulli shift. We also discuss some extensions of Burke's theorem where it remains an open problem to determine if, or under what conditions, the analogue of this result holds.

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Michael Keane, Neil O'Connell. 2008-04-24. The M/M/1 queue is Bernoulli. https://arxiv.org/abs/0804.3935

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