Large deviations for polling systems

Franck Delcoigne (1) , Arnaud de La Fortelle (2)

1 UPN SEGMI - Université Paris Nanterre - UFR Sciences économiques, gestion, mathématiques, informatique
2 MEVAL - Methods, algorithms and software in automatic control

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.

Mots clés: Large deviations; Polling system; Fluid limits; Empirical generator; Change of measure; Contraction principle; Entropy; Convex program

Domaines: Réseaux et télécommunications [cs.NI]

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⟩