Sensitivity analysis for a Markov regenerative software rejuvenation model

Abstract

This article considers the parametric sensitivity of a software rejuvenation model for transaction systems whose system behavior is described by a quasi-birth-and-death (QBD) process with Markovian arrivals, and the software rejuvenation model is represented by a Markov regenerative process (MRGP). The stationary analysis of the MRGP model is based on the embedding Markov chain (EMC) approach. Then the sensitivities of the stationary solution and the performance criteria of interest, i.e., the loss probability of transactions, with respect to all model parameters, are formulated. Finally, a numerical experiment was conducted to illustrate the critical parameters for a transaction system with software rejuvenation. The numerical results showed that the proposed approach effectively revealed critical model parameters and provided significant insights into performance optimization and parameter estimation.