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A review of Burke's theorem for Brownian motion
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Queueing systems, ISSN 0257-0130, E-ISSN 1572-9443, Vol. 83, no 1-2, 1-12 p.Article, review/survey (Refereed) PublishedText
Abstract [en]

Burke's theorem is a well-known fundamental result in queueing theory, stating that a stationary M/M/1 queue has a departure process that is identical in law to the arrival process and, moreover, for each time t, the following three random objects are independent: the queue length at time t, the arrival process after t and the departure process before t. Burke's theorem also holds for a stationary Brownian queue. In particular, it implies that a certain "complicated" functional derived from two independent Brownian motions is also a Brownian motion. The aim of this overview paper is to present an independent complete explanation of this phenomenon.

Place, publisher, year, edition, pages
2016. Vol. 83, no 1-2, 1-12 p.
Keyword [en]
Brownian motion, Burke's theorem, M/M/1 queue, Stationarity, Skorokhod reflection
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-299381DOI: 10.1007/s11134-016-9478-xISI: 000375790200001OAI: oai:DiVA.org:uu-299381DiVA: diva2:949297
Funder
Swedish Research Council, 2013-4688
Available from: 2016-07-18 Created: 2016-07-18 Last updated: 2016-07-18Bibliographically approved

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