uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
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
URN: urn:nbn:se:uu:diva-299381DOI: 10.1007/s11134-016-9478-xISI: 000375790200001OAI: oai:DiVA.org:uu-299381DiVA: diva2:949297
Swedish Research Council, 2013-4688
Available from: 2016-07-18 Created: 2016-07-18 Last updated: 2016-07-18Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Konstantopoulos, Takis
By organisation
Analysis and Probability Theory
In the same journal
Queueing systems
Other Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 54 hits
ReferencesLink to record
Permanent link

Direct link