On Exponential Ergodicity of Multiclass Queueing Networks
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0612544v1.pdf
Description
http://arxiv.org/abs/math/0612544
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296.44 KB
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Author(s)
Gamarnik, David
Meyn, Sean P.
Date Issued
April 2010
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
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].
MIT Department
Sloan School of Management
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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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DOI of Published Version
https://doi.org/10.1007/s11134-010-9173-2
