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# Large Deviations Problems for Star Networks: the Min Policy Part I: Finite Time

Abstract : In this paper, we prove a sample path large deviation principle for a rescaled process $n^{-1}Q_{nt}$, where $Q_t$ represents the joint number of connections at time $t$ in a star network where the bandwidth is shared between customers according to the so-called min policy. The rate function is computed explicitly. One of the main steps 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.
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Submitted on : Wednesday, May 24, 2006 - 10:05:00 AM
Last modification on : Friday, February 4, 2022 - 3:07:25 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:09:48 PM

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• HAL Id : inria-00072481, version 1

### Citation

Franck Delcoigne, Arnaud de la Fortelle. Large Deviations Problems for Star Networks: the Min Policy Part I: Finite Time. [Research Report] RR-4143, INRIA. 2001. ⟨inria-00072481⟩

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