On the sensitivity of stationary solutions of Markov regenerative processes

Abstract

Markov regenerative process (MRGP) is favored for modeling and evaluating system dependability due to its high power and flexibility. However, its analysis presents challenges because of its inherent renewal nature. The embedded Markov chain (EMC) method offers a stationary solution to the MRGP, while the phase expansion approach delivers both stationary and transient solutions. From these solutions, one can derive performance or dependability measures as outputs from the MRGP model. It is crucial to conduct a sensitivity analysis on MRGP to understand the influence of input factor changes on model outputs, aiding efficient system optimization. Yet, a clear analytical method for sensitivity analysis of MRGP models is currently lacking. Filling this gap, this paper introduces an analytical approach to assess parametric sensitivity for steady-state MRGP, utilizing the EMC method for obtaining the stationary solution. Specifically, since system availability closely correlates with the average system available duration, this paper also shifts its focus from mere model parameters to representative values, like the average available time of a system.