The M/M/1 queue is Bernoulli
| dc.creator | Keane, Michael | |
| dc.creator | O'Connell, Neil | |
| dc.date | 2008-04-24 | |
| dc.date.accessioned | 2026-07-07T09:35:00Z | |
| dc.date.available | 2026-07-07T09:35:00Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0804.3935 | |
| dc.identifier | http://arxiv.org/abs/0804.3935 | |
| dc.identifier | Colloq. Math. 110 (2008), 205-210 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159693 | |
| dc.subject | Probability | |
| dc.subject | 60K25; 37A50 | |
| dc.title | The M/M/1 queue is Bernoulli | |
| dc.type | text |