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On Exponential Ergodicity of Multiclass Queueing Networks

Author(s)
Gamarnik, David; Meyn, Sean P.
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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Abstract
One of the key performance measures in queueing systems is the exponential decay rate of the steady-state tail probabilities of the queue lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have finite moments, then the queue lengths also have finite moments, so that the tail probability P(· > s) decays faster than s−n [s superscript -n] for any n. It is natural to conjecture that the decay rate is in fact exponential. In this paper an example is constructed to demonstrate that this conjecture is false. For a specific stationary policy applied to a network with exponentially distributed interarrival and service times it is shown that the corresponding fluid limit model is stable, but the tail probability for the buffer length decays slower than s−log s [s superscript -log s].
Date issued
2010-04
URI
http://hdl.handle.net/1721.1/65922
Department
Sloan School of Management
Journal
Queueing Systems
Publisher
Springer
Citation
Gamarnik, David, and Sean Meyn. “On Exponential Ergodicity of Multiclass Queueing Networks.” Queueing Systems 65.2 (2010) : 109-133. Copyright © 2010, Springer Science+Business Media, LLC
Version: Author's final manuscript
ISSN
0257-0130
0340-4384

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