Stein's Method for the Single Server Queue in Heavy Traffic

TL;DR

This paper demonstrates how Stein's method can be applied to analyze the single server queue in heavy traffic, offering two approaches: equilibrium couplings and generator comparison.

Contribution

It introduces two novel methods for applying Stein's method to the single server queue in heavy traffic, expanding analytical tools in queueing theory.

Findings

Effective approximation of queue behavior in heavy traffic

Comparison of two Stein's method approaches

Potential for improved queue analysis techniques

Abstract

Following recent developments in the application of Stein's method in queueing theory, this paper is intended to be a short treatment showing how Stein's method can be developed and applied to the single server queue in heavy traffic. Here we provide two approaches to this approximation: one based on equilibrium couplings and another involving comparison of generators.