Stabilizing Queuing Networks with Model Data-Independent Control

TL;DR

This paper develops model data-independent control policies for multi-class queuing networks that do not require knowledge of arrival or service rates, ensuring stability and optimal throughput using traffic state observations.

Contribution

It introduces a new class of MDI control policies for queuing networks, providing stability criteria and explicit policies that achieve maximal throughput without model data.

Findings

Existence of centralized stabilizing MDI policies for multi-class networks

Existence of decentralized stabilizing MDI policies for single-class networks

Constructed explicit policies that attain maximal throughput

Abstract

Classical queuing network control strategies typically rely on accurate knowledge of model data, i.e., arrival and service rates. However, such data are not always available and may be time-variant. To address this challenge, we consider a class of model data-independent (MDI) control policies that only rely on traffic state observation and network topology. Specifically, we focus on the MDI control policies that can stabilize multi-class Markovian queuing networks under centralized and decentralized policies. Control actions include routing, sequencing, and holding. By expanding the routes and constructing piecewise-linear test functions, we derive an easy-to-use criterion to check the stability of a multi-class network under a given MDI policy. For stabilizable multi-class networks, we show that a centralized, stabilizing MDI policy exists. For stabilizable single-class networks, we further show that a decentralized, stabilizing MDI policy exists. In addition, for both settings, we construct explicit policies that attain maximal throughput and present numerical examples to illustrate the results.