Asymptotic Behavior of a Critical Fluid Model for a Processor Sharing Queue via Relative Entropy

Amber L Puha,Ruth J Williams

doi:10.1287/15-ssy198

Abstract

In this paper, we develop a new approach to studying the asymptotic behavior of fluid model solutions for critically loaded processor sharing queues. For this, we introduce a notion of relative entropy associated with measure-valued fluid model solutions. In contrast to the approach used in [12], which does not readily generalize to networks of processor sharing queues, we expect the approach developed in this paper to be more robust. Indeed, we anticipate that similar notions involving relative entropy may be helpful for understanding the asymptotic behavior of critical fluid model solutions for stochastic networks operating under various resource sharing protocols naturally described by measure-valued processes.

Highlights

We develop a new approach to studying the asymptotic behavior of fluid model solutions for critically loaded processor sharing queues
In the context of multiclass queueing networks operating under head-of-the-line (HL) service disciplines, Bramson [1] and Williams [15] have developed a modular approach for establishing heavy traffic diffusion approximations to such networks
The HL assumption covers a wide variety of service disciplines, including firstin-first-out (FIFO) and static priorities, it requires that service for a given job class is concentrated on the job at the head-of-the-line

Summary

Stochastic Systems

Publication details, including instructions for authors and subscription information: http://pubsonline.informs.org. Asymptotic Behavior of a Critical Fluid Model for a Processor Sharing Queue via Relative Entropy. Williamshttp://math.ucsd.edu/williams (2016) Asymptotic Behavior of a Critical Fluid Model for a Processor Sharing Queue via Relative Entropy. Full terms and conditions of use: https://pubsonline.informs.org/Publications/Librarians-Portal/PubsOnLine-Terms-andConditions. Descriptions of, or references to, products or publications, or inclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, or support of claims made of that product, publication, or service. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org

RELATIVE ENTROPY

Introduction

Given u

Also fix κ