On tightness and exponential tightness in generalised Jackson networks

TL;DR

This paper provides uniform proofs of tightness and exponential tightness for stationary queue lengths in generalized Jackson networks across various deviation regimes.

Contribution

It introduces a unified approach to establish tightness and exponential tightness in generalized Jackson networks for large, normal, and moderate deviations.

Findings

Proves tightness of stationary queue length sequences.

Establishes exponential tightness in multiple deviation regimes.

Provides a unified proof framework for these properties.

Abstract

We give uniform proofs of tightness and exponential tightness of the sequences of stationary queue lengths in generalised Jackson networks in a number of setups which concern large, normal and moderate deviations.