A Stochastic Hybrid Systems framework for analysis of Markov reward models

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...

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Bibliographic Details
Published in:Reliability engineering & system safety 2014-03, Vol.123, p.158-170
Main Authors: Dhople, S.V., DeVille, L., Domínguez-García, A.D.
Format: Article
Language:English
Subjects:
Applied sciences
Differential equations
Exact sciences and technology
Hybrid systems
Mapping
Markov availability models
Markov models
Markov reliability models
Mathematical analysis
Mathematical models
Mathematics
Operational research and scientific management
Operational research. Management science
Performability analysis
Probability and statistics
Probability theory and stochastic processes
Reliability theory. Replacement problems
Reward models
Sciences and techniques of general use
Self-propagating synthesis
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Stochastic hybrid systems
Stochasticity
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Summary: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 comprised 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.
ISSN:0951-8320
1879-0836
DOI:10.1016/j.ress.2013.10.011