Numerical iterative methods for Markovian dependability and performability models: new results and a comparison

In this paper we deal with iterative numerical methods to solve linear systems arising in continuous-time Markov chain (CTMC) models. We develop an algorithm to dynamically tune the relaxation parameter of the successive over-relaxation method. We give a sufficient condition for the Gauss-Seidel met...

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Bibliographic Details
Authors: Suñé, Víctor|||0000-0002-5189-8573, Domingo Fuster, José Luis, Carrasco, Juan A.|||0000-0001-7757-1651
Format: article
Publication Date:2000
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/21068
Online Access:https://hdl.handle.net/2117/21068
Access Level:Open access
Keyword:Markov processes
Markov, Processos de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat
Description
Summary:In this paper we deal with iterative numerical methods to solve linear systems arising in continuous-time Markov chain (CTMC) models. We develop an algorithm to dynamically tune the relaxation parameter of the successive over-relaxation method. We give a sufficient condition for the Gauss-Seidel method to converge when computing the steady-state probability vector of a finite irreducible CTMC, an a suffient condition for the Generalized Minimal Residual projection method not to converge to the trivial solution 0 when computing that vector. Finally, we compare several splitting-based iterative methods an a variant of the Generalized Minimal Residual projection method.