Geodesic
The $M/M/1$ queue is Bernoulli
Michael Keane 1   ; Neil O'Connell 2
1 Department of Mathematics and Computer Science Wesleyan University Middletown, CT 06459, U.S.A.
2 Department of Mathematics and BCRI University College Cork Cork, Ireland
Colloquium Mathematicum, Tome 110 (2008) no. 1, pp. 205-210 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm110-1-9
Mots-clés : classical output theorem queue due burke states departure process stationary queue equilibrium has law arrivals process poisson process associated measure preserving transformation metrically isomorphic two sided bernoulli shift discuss extensions burkes theorem where remains problem determine under what conditions analogue result holds

Michael Keane  1   ; Neil O'Connell  2

1 Department of Mathematics and Computer Science Wesleyan University Middletown, CT 06459, U.S.A.
2 Department of Mathematics and BCRI University College Cork Cork, Ireland 
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Michael Keane; Neil O'Connell. The $M/M/1$ queue is Bernoulli. Colloquium Mathematicum, Tome 110 (2008) no. 1, pp. 205-210. doi: 10.4064/cm110-1-9

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