Computing performability measures in Markov chains by means of matrix functions

作     者：Masetti, G. Robol, L. 

作者机构：Dept Comp Sci Largo B Pontecorvo 3 I-56127 Pisa Italy Dept Math Largo B Pontecorvo 5 I-56127 Pisa Italy Inst Sci & Technol A Faedo Via G Moruzzi 1 I-56124 Pisa Italy 

出 版 物：《JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS》 (计算与应用数学杂志)

年 卷 期：2020年第368卷

页      面：112534-000页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：ISTI-CNR Istituto Nazionale di Alta Matematica "Francesco Severi", INdAM Gruppo Nazionale per il Calcolo Scientifico, GNCS Regione Toscana 

主　　题：Markov chains Performance measures Availability Reliability Matrix functions 

摘      要：We discuss the efficient computation of performance, reliability, and availability measures for Markov chains;these metrics - and the ones obtained by combining them, are often called performability measures. We show that this computational problem can be recasted as the evaluation of a bilinear form induced by appropriate matrix functions, and thus solved by leveraging the fast methods available for this task. We provide a comprehensive analysis of the theory required to translate the problem from the language of Markov chains to the one of matrix functions. The advantages of this new formulation are discussed, and it is shown that this setting allows to easily study the sensitivities of the measures with respect to the model parameters. Numerical experiments confirm the effectiveness of our approach;the tests we have run show that we can outperform the solvers available in state of the art commercial packages on a representative set of large scale examples. (C) 2019 Elsevier B.V. All rights reserved.