A review of Burke’s theorem for Brownian motion

Takis Konstantopoulos ()
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Takis Konstantopoulos: Uppsala University

Queueing Systems: Theory and Applications, 2016, vol. 83, issue 1, No 1, 12 pages

Abstract: Abstract 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.

Keywords: Brownian motion; Burke’s theorem; M/M/1 queue; Stationarity; Skorokhod reflection; 60K25; 60J65; 60J27 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11134-016-9478-x

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