Analytical computation of Markov chain using Padé approximations

The transient analysis of finite-state, continuous-time Markov chains is determined using Padé approximations in the complex plane. Many applications are required to provide interruption-free service for long missions. For these systems, the probability that a system operates without failure during some interval is of interest. The authors will consider the general problem of finding the state probability vector of a discrete-state continuous-time Markov chain. They employ Padé approximation as their analytical tool to determine the state probabilities.