Kronecker结构Markov链的分解分析

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Electronic Transactions on Numerical Analysis Pub Date : 2008-01-01 DOI:10.5072/ZENODO.47488

Yujuan Bao, I. N. Bozkurt, T. Dayar, Xiaobai Sun, Kishor S. Trivedi

{"title":"Kronecker结构Markov链的分解分析","authors":"Yujuan Bao, I. N. Bozkurt, T. Dayar, Xiaobai Sun, Kishor S. Trivedi","doi":"10.5072/ZENODO.47488","DOIUrl":null,"url":null,"abstract":"This contribution proposes a decompositional iterative method with low memory requirements for the steady-state analysis of Kronecker structured Markov chains. The Markovian system is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions. Even though the interactions among subsystems, which are captured by synchronized transitions, need not be weak, numerical experiments indicate that the solver benefits considerably from weak interactions among subsystems, and is to be recommended specifically in this case.","PeriodicalId":50536,"journal":{"name":"Electronic Transactions on Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Decompositional Analysis of Kronecker Structured Markov Chains\",\"authors\":\"Yujuan Bao, I. N. Bozkurt, T. Dayar, Xiaobai Sun, Kishor S. Trivedi\",\"doi\":\"10.5072/ZENODO.47488\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This contribution proposes a decompositional iterative method with low memory requirements for the steady-state analysis of Kronecker structured Markov chains. The Markovian system is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions. Even though the interactions among subsystems, which are captured by synchronized transitions, need not be weak, numerical experiments indicate that the solver benefits considerably from weak interactions among subsystems, and is to be recommended specifically in this case.\",\"PeriodicalId\":50536,\"journal\":{\"name\":\"Electronic Transactions on Numerical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2008-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Transactions on Numerical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5072/ZENODO.47488\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Transactions on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5072/ZENODO.47488","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 10

摘要

本文提出了一种低内存要求的分解迭代方法，用于Kronecker结构马尔可夫链的稳态分析。马尔可夫系统是由子系统组成的，对局部过渡使用Kronecker和算子，对同步过渡使用Kronecker积算子。尽管被同步转换捕获的子系统之间的相互作用不一定是弱的，但数值实验表明，求解器从子系统之间的弱相互作用中获益很大，并且在这种情况下特别推荐。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Decompositional Analysis of Kronecker Structured Markov Chains

This contribution proposes a decompositional iterative method with low memory requirements for the steady-state analysis of Kronecker structured Markov chains. The Markovian system is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions. Even though the interactions among subsystems, which are captured by synchronized transitions, need not be weak, numerical experiments indicate that the solver benefits considerably from weak interactions among subsystems, and is to be recommended specifically in this case.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Electronic Transactions on Numerical Analysis 数学-应用数学

CiteScore

2.10

自引率

7.70%

发文量

审稿时长

6 months

期刊介绍： Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM).