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Asymptotic Fluid Optimality and Efficiency of the Tracking Policy for Bandwidth-Sharing Networks

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  14 July 2016

Konstantin Avrachenkov ,
Alexey Piunovskiy  and
Yi Zhang
Konstantin Avrachenkov*
Affiliation:
INRIA
Alexey Piunovskiy*
Affiliation:
INRIA
Yi Zhang*
Affiliation:
University of Liverpool
*
∗Postal address: INRIA, MAESTRO Team, 2004 Route des Lucioles - BP 93 FR-06902 Sophia Antipolis Cedex, France. Email address: k.avrachenkov@sophia.inria.fr
∗∗Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.
∗∗Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.
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Abstract

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Optimal control of stochastic bandwidth-sharing networks is typically difficult. In order to facilitate the analysis, deterministic analogues of stochastic bandwidth-sharing networks, the so-called fluid models, are often taken for analysis, as their optimal control can be found more easily. The tracking policy translates the fluid optimal control policy back to a control policy for the stochastic model, so that the fluid optimality can be achieved asymptotically when the stochastic model is scaled properly. In this work we study the efficiency of the tracking policy, that is, how fast the fluid optimality can be achieved in the stochastic model with respect to the scaling parameter. In particular, our result shows that, under certain conditions, the tracking policy can be as efficient as feedback policies.

Keywords

Bandwidth-sharing networkfluid modeloptimal controltracking policyrate of convergence

MSC classification

Secondary: 60K25: Queueing theory 68M20: Performance evaluation; queueing; scheduling
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 90 - 113
Copyright
Copyright © Applied Probability Trust 2011 

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