Large deviations for stochastic fluid networks with Weibullian tails

TL;DR

This paper develops large deviations estimates for stochastic fluid networks with heavy-tailed Weibullian inputs, providing explicit results for tandem queues and advancing the theoretical understanding of such systems.

Contribution

It introduces a new large deviations framework for fluid networks with Weibullian tails, including a novel continuity result for the Skorokhod reflection map.

Findings

Large deviations estimates for buffer content in Weibullian tail networks

Explicit results for tandem queue models

New continuity results for the Skorokhod reflection map

Abstract

We consider a stochastic fluid network where the external input processes are compound Poisson with heavy-tailed Weibullian jumps. Our results comprise of large deviations estimates for the buffer content process in the vector-valued Skorokhod space which is endowed with the product $J_1$ topology. To illustrate our framework, we provide explicit results for a tandem queue. At the heart of our proof is a recent sample-path large deviations result, and a novel continuity result for the Skorokhod reflection map in the product $J_1$ topology.