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Large deviations for polling systems

Abstract : We aim at presenting in short the technical report, which states a sample path large deviation principle for a resealed process n-1 Qnt, where Qt represents the joint number of clients at time t in a single server 1-limited polling system with Markovian routing. The main goal is to identify the rate function. A so-called empirical generator is introduced, which consists of Q t and of two empirical measures associated with S t the position of the server at time t. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program.
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Submitted on : Monday, April 14, 2014 - 11:37:19 AM
Last modification on : Friday, February 4, 2022 - 3:08:11 AM

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Franck Delcoigne, Arnaud de la Fortelle. Large deviations for polling systems. Danièle Gardy ; Abdelkader Mokkadem. Mathematics and Computer Science: Algorithms, Trees, Combinatorics and Probabilities, Birkhäuser Basel, p. 221-229, 2000, Trends in Mathematics, Print ISBN 978-3-0348-9553-8; Online ISBN 978-3-0348-8405-1. ⟨10.1007/978-3-0348-8405-1_19⟩. ⟨hal-00978458⟩

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