Asymptotic Product-form Steady-state for Multiclass Queueing Networks: A Reentrant Line Case Study

TL;DR

This paper demonstrates the asymptotic product-form steady-state behavior of a multiclass reentrant queueing network under specific policies, providing theoretical proofs and bounds for a complex two-station, five-class system.

Contribution

It offers a concrete example illustrating the main theoretical results on asymptotic steady-state limits in multiclass queueing networks with general distributions.

Findings

Proves asymptotic steady-state limit for the reentrant line.

Establishes uniform moment bounds under general distributions.

Provides a simplified illustration of main theoretical results.

Abstract

This paper serves as a companion to "Asymptotic Product-form Steady-state for Multiclass Queueing Networks with SBP Service Policies in Multi-scale Heavy Traffic." In this short paper, we illustrate the main results of the main paper through a two-station, five-class reentrant line under a specific static buffer priority policy, while avoiding heavy notations. For this example, we prove the asymptotic steady-state limit and uniform moment bound under general inter-arrival and service time distributions.