Graph-Theoretic Analyses and Model Reduction for an Open Jackson Queueing Network

TL;DR

This paper introduces a graph-theoretic approach to analyze steady-state performance in open Jackson queueing networks and proposes a structure-preserving model reduction algorithm that accurately replicates original network statistics.

Contribution

It develops a novel graph-theoretic framework for analyzing queueing networks and introduces an exact performance-matching model reduction algorithm.

Findings

Performance metrics depend on local network drivers and diminish across graph cutsets.

The proposed model reduction algorithm preserves key performance statistics.

Simulation results validate the effectiveness of the analysis and reduction methods.

Abstract

A graph-theoretic analysis of the steady-state behavior of an open Jackson queueing network is developed. In particular, a number of queueing-network performance metrics are shown to exhibit a spatial dependence on local drivers (e.g. increments to local exogenous arrival rates), wherein the impacts fall off across graph cutsets away from a target queue. This graph-theoretic analysis is also used to motivate a structure-preserving model reduction algorithm, and an algorithm that exactly matches performance statistics of the original model is proposed. The graph-theoretic results and model-reduction method are evaluated via simulations of an example queueing-network model.