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...
| Authors: | , , |
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| 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 |
| 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. |
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