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BRAVO for Many-Server QED Systems with Finite Buffers

Part of: Markov processes Special processes

Published online by Cambridge University Press:  04 January 2016

D. J. Daley ,
Johan S. H. Van Leeuwaarden  and
Yoni Nazarathy
D. J. Daley*
Affiliation:
The University of Melbourne
Johan S. H. Van Leeuwaarden*
Affiliation:
Eindhoven University of Technology
Yoni Nazarathy*
Affiliation:
The University of Queensland
*
∗ Postal address: Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia. Email address: [email protected]
∗∗ Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: [email protected]
∗∗∗ Postal address: School of Mathematics and Physics, The University of Queensland, St Lucia, Brisbane, 4072, Australia. Email address: [email protected]
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Abstract

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This paper demonstrates the occurrence of the feature called BRAVO (balancing reduces asymptotic variance of output) for the departure process of a finite-buffer Markovian many-server system in the QED (quality and efficiency-driven) heavy-traffic regime. The results are based on evaluating the limit of an equation for the asymptotic variance of death counts in finite birth-death processes.

Keywords

Queueing system critical pointstochastic process limitPoisson distribution asymptoticsstationary Poisson queue asymptoticsHalfin-Whitt regimequeueing output variance asymptoticsbirth-death asymptotic variance

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 47 , Issue 1 , March 2015 , pp. 231 - 250
Copyright
© Applied Probability Trust 

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