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May 2004 Large deviations problems for star networks: The min policy
Franck Delcoigne, Arnaud de La Fortelle
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Ann. Appl. Probab. 14(2): 1006-1028 (May 2004). DOI: 10.1214/105051604000000198

Abstract

We are interested in analyzing the effect of bandwidth sharing for telecommunication networks. More precisely, we want to calculate which routes are bottlenecks by means of large deviations techniques. The method is illustrated in this paper on a star network, where the bandwidth is shared between customers according to the so-called min policy. We prove a sample path large deviation principle for a rescaled process n−1Qnt, where Qt represents the joint number of connections at time t. The main result is to compute the rate function explicitly. The major step consists in deriving large deviation bounds for an empirical generator constructed from the join number of customers and arrivals on each route. The rest of the analysis relies on a suitable change of measure together with a localization procedure. An example shows how this can be used practically.

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Franck Delcoigne. Arnaud de La Fortelle. "Large deviations problems for star networks: The min policy." Ann. Appl. Probab. 14 (2) 1006 - 1028, May 2004. https://doi.org/10.1214/105051604000000198

Information

Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1047.60021
MathSciNet: MR2052911
Digital Object Identifier: 10.1214/105051604000000198

Subjects:
Primary: 60F10
Secondary: 60K30

Keywords: bandwidth sharing , Change of measure , contraction principle , empirical generator , Entropy , large deviations , min protocol , Rate function , star network

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 2 • May 2004
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