Facilitating load-dependent queueing analysis through factorization (extended abstract)
File(s)
Accepted version
Author(s)
Casale, Giuliano
Harrison, Peter G
Hong Ong, Wai
Type
Journal Article
Abstract
We construct novel exact and approximate solutions for meanvalue analysis and probabilistic evaluation of closed queueing network models with limited load-dependent (LLD) nodes.
In this setting, load-dependent functions are assumed to become constant after a finite queue-length threshold. For
single-class models, we provide an explicit formula for the
normalizing constant that applies to models with arbitrary
LLD functions, whilst retaining constant complexity with
respect to the total population size. From this result, we
then derive corresponding closed-form solutions for the multiclass case and show that these yield a novel mean value
analysis approach for LLD models. Significantly, this allows us to determine exactly the correction factor between
a load-independent solution and a limited load-dependent
one, enabling the reuse of state-of-the-art methods for loadindependent models in the analysis of load-dependent networks
In this setting, load-dependent functions are assumed to become constant after a finite queue-length threshold. For
single-class models, we provide an explicit formula for the
normalizing constant that applies to models with arbitrary
LLD functions, whilst retaining constant complexity with
respect to the total population size. From this result, we
then derive corresponding closed-form solutions for the multiclass case and show that these yield a novel mean value
analysis approach for LLD models. Significantly, this allows us to determine exactly the correction factor between
a load-independent solution and a limited load-dependent
one, enabling the reuse of state-of-the-art methods for loadindependent models in the analysis of load-dependent networks
Date Issued
2022-03-22
Date Acceptance
2019-07-19
Citation
ACM SIGMETRICS Performance Evaluation Review, 2022, 49 (3), pp.51-52
ISSN
0163-5999
Publisher
Association for Computing Machinery
Start Page
51
End Page
52
Journal / Book Title
ACM SIGMETRICS Performance Evaluation Review
Volume
49
Issue
3
Copyright Statement
Copyright is held by author/owner(s). This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ACM SIGMETRICS Performance Evaluation Review, https://doi.org/10.1145/3529113.3529129
Identifier
https://dl.acm.org/doi/10.1145/3529113.3529129
Publication Status
Published
Date Publish Online
2022-03-25