A family of multiclass LCFS networks with a novel
product-form solution
product-form solution
File(s)
Published version
Author(s)
Casale, Giuliano
Type
Journal Article
Abstract
We study two-station closed queueing network models where jobs cyclically visit a non-preemptive last-come first-serve (LCFS-NP) station and a last-come first serve preemptive-resume (LCFS-PR) station. Jobs belong to multiple classes and receive at both stations exponential service times with arbitrary means. Even though multiclass LCFS-NP stations are not quasi-reversible, we show that the considered models still admit a product-form solution. A feature of the new product form expression is to include factors that relate the mean service times at the LCFS-NP queue with the positions occupied by the jobs at both stations. To account for job positions, we propose a strategy to compute the normalizing constant of the state probabilities using permanents which, for a fixed number of classes, solves the model exactly in polynomial time as the total number of jobs grows. A mean-value analysis algorithm is also derived, using a recursion on networks where the job holding the last position at the LCFS-PR queue is removed from the model.
Date Issued
2026-06-01
Date Acceptance
2026-04-21
Citation
Queueing Systems, 2026, 110 (2)
ISSN
0257-0130
Publisher
Springer
Journal / Book Title
Queueing Systems
Volume
110
Issue
2
Copyright Statement
© The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
10.1007/s11134-026-09992-3
Subjects
Queueing network
Multiclass
Product form
Last-come first-serve
Permanent Mathematics Subject Classification Mathematics Subject Classification 60K25
Publication Status
Published
Article Number
ARTN 32
Date Publish Online
2026-05-24