Fast evaluation of the moments of the interval availability of large Markov models
Reinaldo Vallejos C · Performance Evaluation Methodolgies and Tools · 2007
This paper proposes a new numerically stable method for evaluating the first K moments (K ≥ 1) of the interval availability for repairable systems. Its time complexity is O(|S|KdNmax), where |S| is the cardinality of the Markov model state space; d is the average degree of connectivity of the Markov chain states; and Nmax represents the number os transition of the Markov chain in [0, t]). This time complexity is O(L|S|) times faster than the best existing method, without extra memory requirements, where L is the number of different time intervals for which the moments are evaluated.