A study on the accuracy of a numerical iteration for Markov processes by using reliability models
Hyeonah Park, Seongryong Na · Korean Journal of Applied Statistics · 2024
For Markov processes whose stationary probabilities are difficult to obtain in the analytical form, approximate solutions can be considered using numerical methods such as a matrix operation method or an iterative calculation method.In this paper we perform the study to verify the accuracy of a numerical iteration formula which calculate the stationary probabilities of Markov chains or processes.Especially, the convergence and accuracy of the numerical method are investigated by using Markov models for system availability.We compare the values of the system availability based on the numerical calculation and those based on the complicated but analytical solutions.We also calculate the iteration numbers necessary for the convergence of the numerical solutions.The accuracy and usefulness of the numerical iterative calculation method can be ascertained through this study.