Comparaison stochastique de modèles markoviens : une approche algorithmique et ses applications en fiabilité et en évaluation de performance
Auteur / Autrice : | Ana Bušić |
Direction : | Jean-Michel Fourneau |
Type : | Thèse de doctorat |
Discipline(s) : | Informatique |
Date : | Soutenance en 2007 |
Etablissement(s) : | Versailles-St Quentin en Yvelines |
Mots clés
Mots clés contrôlés
Résumé
We consider Markov chain comparison methods and algorithms, and applications to network performance and system reliability analysis. We have extended the classical framework, which uses strong stochastic order on a totally ordered state space and the steady-state analysis, to transient and absorption time analysis to study the point availability or reliability, also considered using level-crossing order. Comparing the chains uses two sufficient conditions: the transition matrix comparison and the stochastic monotonicity. Moving from the classical framework allows to improve the complexity or the quality of bounds. We obtain the algorithms for icx order or for partially ordered state space. In the favorable case we show the monotonicity of the system under natural partial order of states and the numerical analysis is then simple. Otherwise, we provide bounding algorithms using a matrix or event approach.