research-article

Efficient vector-descriptor product exploiting time-memory trade-offs

Authors:

Ricardo M. Czekster,

Paulo Fernandes,

Thais WebberAuthors Info & Claims

ACM SIGMETRICS Performance Evaluation Review, Volume 39, Issue 3

Pages 2 - 9

https://doi.org/10.1145/2160803.2160805

Published: 21 December 2011 Publication History

Abstract

The description of large state spaces through stochastic structured modeling formalisms like stochastic Petri nets, stochastic automata networks and performance evaluation process algebra usually represent the infinitesimal generator of the underlying Markov chain as a Kronecker descriptor instead of a single large sparse matrix. The best known algorithms used to compute iterative solutions of such structured models are: the pure sparse solution approach, an algorithm that can be very time efficient, and almost always memory prohibitive; the Shuffle algorithm which performs the product of a descriptor by a probability vector with a very impressive memory efficiency; and a newer option that offers a trade-off between time and memory savings, the Split algorithm. This paper presents a comparison of these algorithms solving some examples of structured Kronecker represented models in order to numerically illustrate the gains achieved considering each model's characteristics.

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Cited By

Czekster RFernandes PLopes LSales ASantos AWebber T(2016)Stochastic Performance Analysis of Global Software Development TeamsACM Transactions on Software Engineering and Methodology10.1145/295509325:3(1-32)Online publication date: 22-Aug-2016
https://dl.acm.org/doi/10.1145/2955093
Fernandes PLopes LYeralan S(2013)Symbolic Solution of Kronecker-Based Structured Markovian ModelsProceedings of the 2013 IEEE 21st International Symposium on Modelling, Analysis & Simulation of Computer and Telecommunication Systems10.1109/MASCOTS.2013.62(409-413)Online publication date: 14-Aug-2013
https://dl.acm.org/doi/10.1109/MASCOTS.2013.62
Fernandes PO’Kelly MPapadopoulos CSales A(2013)Analysis of exponential reliable production lines using Kronecker descriptorsInternational Journal of Production Research10.1080/00207543.2012.75455051:14(4240-4257)Online publication date: Jul-2013
https://doi.org/10.1080/00207543.2012.754550
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Published In

cover image ACM SIGMETRICS Performance Evaluation Review

ACM SIGMETRICS Performance Evaluation Review Volume 39, Issue 3

December 2011

163 pages

ISSN:0163-5999

DOI:10.1145/2160803

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Copyright © 2011 Authors.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 December 2011

Published in SIGMETRICS Volume 39, Issue 3

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Cited By

Czekster RFernandes PLopes LSales ASantos AWebber T(2016)Stochastic Performance Analysis of Global Software Development TeamsACM Transactions on Software Engineering and Methodology10.1145/295509325:3(1-32)Online publication date: 22-Aug-2016
https://dl.acm.org/doi/10.1145/2955093
Fernandes PLopes LYeralan S(2013)Symbolic Solution of Kronecker-Based Structured Markovian ModelsProceedings of the 2013 IEEE 21st International Symposium on Modelling, Analysis & Simulation of Computer and Telecommunication Systems10.1109/MASCOTS.2013.62(409-413)Online publication date: 14-Aug-2013
https://dl.acm.org/doi/10.1109/MASCOTS.2013.62
Fernandes PO’Kelly MPapadopoulos CSales A(2013)Analysis of exponential reliable production lines using Kronecker descriptorsInternational Journal of Production Research10.1080/00207543.2012.75455051:14(4240-4257)Online publication date: Jul-2013
https://doi.org/10.1080/00207543.2012.754550
Assunção JEspindola LFernandes PPivel MSales A(2013)A Structured Stochastic Model for Prediction of Geological Stratal Stacking PatternsElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2013.07.003296(27-42)Online publication date: 1-Aug-2013
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Fernandes PO’Kelly MPapadopoulos CSales A(2013)Exact Analysis of Discrete Part Production Lines: The Markovian Queueing Network and the Stochastic Automata Networks FormalismsHandbook of Stochastic Models and Analysis of Manufacturing System Operations10.1007/978-1-4614-6777-9_3(73-113)Online publication date: 1-Apr-2013
https://doi.org/10.1007/978-1-4614-6777-9_3
Lima ANetto MWebber TCzekster RDe Rose CFernandes P(2012)Performance evaluation of OpenMP-based algorithms for handling Kronecker descriptorsJournal of Parallel and Distributed Computing10.1016/j.jpdc.2012.02.00172:5(678-692)Online publication date: 1-May-2012
https://dl.acm.org/doi/10.1016/j.jpdc.2012.02.001
Luís Dotti FFernandes PNunes C(2011)Structured Markovian models for discrete spatial mobile node distributionJournal of the Brazilian Computer Society10.1007/s13173-010-0026-y17:1(31-52)Online publication date: 12-Jan-2011
https://doi.org/10.1007/s13173-010-0026-y

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