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June 2016 Convergence of tandem Brownian queues
Sergio I. López
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J. Appl. Probab. 53(2): 585-592 (June 2016).

Abstract

It is known that in a stationary Brownian queue with both arrival and service processes equal in law to Brownian motion, the departure process is a Brownian motion, identical in law to the arrival process: this is the analogue of Burke's theorem in this context. In this paper we prove convergence in law to this Brownian motion in a tandem network of Brownian queues: if we have an arbitrary continuous process, satisfying some mild conditions, as an initial arrival process and pass it through an infinite tandem network of queues, the resulting process weakly converges to a Brownian motion. We assume independent and exponential initial workloads for all queues.

Citation

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Sergio I. López. "Convergence of tandem Brownian queues." J. Appl. Probab. 53 (2) 585 - 592, June 2016.

Information

Published: June 2016
First available in Project Euclid: 17 June 2016

zbMATH: 1344.60087
MathSciNet: MR3514300

Subjects:
Primary: 60K25
Secondary: 90B15

Keywords: Brownian queue , Burke's theorem , Tandem queues

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 2 • June 2016
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