Response time in a pair of processor sharing queues with Join-the-Shortest-Queue scheduling
File(s)
Accepted version
Author(s)
Bor, Julianna
Harrison, Peter G
Type
Conference Paper
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 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 with 500,000 regeneration cycles.
Date Issued
2024-12-13
Date Acceptance
2024-10-01
Citation
2024 32nd International Conference on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS), 2024, pp.1-8
ISSN
1526-7539
Publisher
IEEE
Start Page
1
End Page
8
Journal / Book Title
2024 32nd International Conference on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS)
Copyright Statement
© 2024 IEEE. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Source
2024 32nd International Conference on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS)
Publication Status
Published
Start Date
2024-10-21
Finish Date
2024-10-23