%0 Journal Article
%T The M/M/1 queue is Bernoulli
%A Michael Keane
%A Neil O'Connell
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0804.3935v1