A Stochastic Hybrid Systems Framework for Analysis of Markov Reward Models

Dhople, S.V.; DeVille, L.; Domínguez-García, A.D.

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https://hdl.handle.net/2142/90438 Copy

Description

Title

A Stochastic Hybrid Systems Framework for Analysis of Markov Reward Models

Author(s)

• Dhople, S.V.
• DeVille, L.
• Domínguez-García, A.D.

Issue Date

2013-06

Keyword(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.

Publisher

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign

Series/Report Name or Number

Coordinated Science Laboratory Report no. UILU-ENG-13-2205

Type of Resource

text

Language

en

Permalink

http://hdl.handle.net/2142/90438

Sponsor(s)/Grant Number(s)

National Science Foundation / CMG-0934491

Owning Collections