TY - JOUR
T1 - A Stochastic Hybrid Systems framework for analysis of Markov reward models
AU - Dhople, S. V.
AU - Deville, L.
AU - Domínguez-García, A. D.
PY - 2014/3
Y1 - 2014/3
N2 - 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.
AB - 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.
KW - Markov availability models
KW - Markov reliability models
KW - Performability analysis
KW - Reward models
KW - Stochastic hybrid systems
UR - http://www.scopus.com/inward/record.url?scp=84890452233&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84890452233&partnerID=8YFLogxK
U2 - 10.1016/j.ress.2013.10.011
DO - 10.1016/j.ress.2013.10.011
M3 - Article
AN - SCOPUS:84890452233
SN - 0951-8320
VL - 123
SP - 158
EP - 170
JO - Reliability Engineering and System Safety
JF - Reliability Engineering and System Safety
ER -