Large deviations for polling systems

TL;DR: In this article, the authors present 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.

Abstract: We aim at presenting in short the technical report [5], 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.