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The M/M/1 queue is Bernoulli
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Keane, Michael and O'Connell, Neil (2008) The M/M/1 queue is Bernoulli. Colloquium Mathematicum, Vol.110 (No.1). pp. 205-210. doi:10.4064/cm110-1-9 ISSN 0010-1354.
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Official URL: http://dx.doi.org/10.4064/cm110-1-9
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Colloquium Mathematicum | ||||
Publisher: | Polska Akademia Nauk, Instytut Matematyczny | ||||
ISSN: | 0010-1354 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.110 | ||||
Number: | No.1 | ||||
Page Range: | pp. 205-210 | ||||
DOI: | 10.4064/cm110-1-9 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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