Response time in a pair of processor sharing queues with Join-the-Shortest-Queue scheduling
File(s)
Published version
Author(s)
Bor, Julianna
Harrison, Peter G
Type
Journal Article
Abstract
Join-the-Shortest-Queue (JSQ) is the scheduling policy of choice for many network providers, cloud servers, and traffic management systems, where individual queues are served under the processor sharing (PS) queueing discipline. A numerical solution for the response time distribution in two parallel PS queues with JSQ scheduling is derived for the first time. Using the generating function method, two partial differential equations (PDEs) are obtained corresponding to conditional response times, where the conditioning is on a particular traced task joining the first or the second queue. These PDEs are functional equations that contain partial generating functions and their partial derivatives, and therefore cannot be solved by commonly used techniques. We are able to solve these PDEs numerically with good accuracy and perform the deconditioning with respect to the queue-length probabilities by evaluating a certain complex integral. Numerical results for the density and the first four moments compare well against regenerative simulation.
Date Issued
2025-11-01
Date Acceptance
2025-09-01
Citation
Performance evaluation (Print), 2025, 170
ISSN
0166-5316
Publisher
Elsevier
Journal / Book Title
Performance evaluation (Print)
Volume
170
Copyright Statement
© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Subjects
Computer Science
Computer Science, Hardware & Architecture
Computer Science, Theory & Methods
Generating functions
Queueing theory
Response times
Science & Technology
Technology
Publication Status
Published
Article Number
102509
Date Publish Online
2025-09-02