The M/M/1 queue is Bernoulli

Michael Keane, and Neil O'Connell. "The M/M/1 queue is Bernoulli." Colloquium Mathematicae 110.1 (2008): 205-210. <http://eudml.org/doc/283537>.

@article{MichaelKeane2008,
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. 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.},
author = {Michael Keane, Neil O'Connell},
journal = {Colloquium Mathematicae},
keywords = { queue; Bernoulli shift},
language = {eng},
number = {1},
pages = {205-210},
title = {The M/M/1 queue is Bernoulli},
url = {http://eudml.org/doc/283537},
volume = {110},
year = {2008},
}

TY - JOUR
AU - Michael Keane
AU - Neil O'Connell
TI - The M/M/1 queue is Bernoulli
JO - Colloquium Mathematicae
PY - 2008
VL - 110
IS - 1
SP - 205
EP - 210
AB - 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. 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.
LA - eng
KW - queue; Bernoulli shift
UR - http://eudml.org/doc/283537
ER -