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A review of Burke’s theorem for Brownian motion

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  • Takis Konstantopoulos

    (Uppsala University)

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.

Suggested Citation

  • Takis Konstantopoulos, 2016. "A review of Burke’s theorem for Brownian motion," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 1-12, June.
    • Handle: RePEc:spr:queues:v:83:y:2016:i:1:d:10.1007_s11134-016-9478-x
    DOI: 10.1007/s11134-016-9478-x
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    References listed on IDEAS

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    1. Paul J. Burke, 1956. "The Output of a Queuing System," Operations Research, INFORMS, vol. 4(6), pages 699-704, December.
    2. O'Connell, Neil & Yor, Marc, 2001. "Brownian analogues of Burke's theorem," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 285-304, December.
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