The Annals of Applied Probability

Large deviations problems for star networks: The min policy

Franck Delcoigne and Arnaud de La Fortelle

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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.

Article information

Ann. Appl. Probab., Volume 14, Number 2 (2004), 1006-1028.

First available in Project Euclid: 23 April 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]

Large deviations rate function empirical generator change of measure contraction principle entropy star network bandwidth sharing min protocol


Delcoigne, Franck; de La Fortelle, Arnaud. Large deviations problems for star networks: The min policy. Ann. Appl. Probab. 14 (2004), no. 2, 1006--1028. doi:10.1214/105051604000000198.

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