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Title:A Stochastic Hybrid Systems Framework for Analysis of Markov Reward Models
Author(s):Dhople, S.V.; DeVille, L.; Domínguez-García, A.D.
Subject(s):Markov reliability models
Reward models
Performability analysis
Stochastic hybrid systems
Abstract:In this paper, we propose a framework to analyze Markov reward models, which are commonly used in system performability analysis. The framework builds on a set of analytical tools developed for a class of stochastic processes referred to as “Stochastic Hybrid Systems (SHS).” The state space of an SHS is composed of: i) a discrete state that describes the possible configurations/modes that a system can adopt, which includes the nominal (non-faulty) operational mode, but also those operational modes that arise due to component faults, and ii) a continuous state that describes the reward. Discrete state transitions are stochastic, and governed by transition rates that are (in general) a function of time and the value of the continuous state. The evolution of the continuous state is described by a stochastic differential equation, and reward measures are defined as functions of the continuous state. Additionally, each transition is associated with a reset map that defines the mapping between the pre- and post-transition values of the discrete and continuous states; these mappings enable the definition of impulses and losses in the reward. The proposed SHS-based framework unifies the analysis of a variety of previously studied reward models. We illustrate the application of the framework to performability analysis via analytical and numerical examples.
Issue Date:2013-06
Publisher:Coordinated Science Laboratory, University of Illinois at Urbana-Champaign
Series/Report:Coordinated Science Laboratory Report no. UILU-ENG-13-2205
Genre:Technical Report
Sponsor:National Science Foundation / CMG-0934491
Date Available in IDEALS:2016-07-07

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