A Stochastic Hybrid Systems framework for analysis of Markov reward models

S. V. Dhople, L. Deville, A. D. Domínguez-García

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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 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.

Original languageEnglish (US)
Pages (from-to)158-170
Number of pages13
JournalReliability Engineering and System Safety
Volume123
DOIs
StatePublished - Mar 2014

Keywords

  • Markov availability models
  • Markov reliability models
  • Performability analysis
  • Reward models
  • Stochastic hybrid systems

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