The M/M/1 queue is Bernoulli
Probability
2008-04-25 v1
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.
Cite
@article{arxiv.0804.3935,
title = {The M/M/1 queue is Bernoulli},
author = {Michael Keane and Neil O'Connell},
journal= {arXiv preprint arXiv:0804.3935},
year = {2008}
}