Iterative analysis of Markov regenerative models

Conventional algorithms for the steady-state analysis of Markov regenerative models suffer from high computational costs which are caused by densely populated matrices. In this paper, a new algorithm is suggested which avoids computing these matrices explicitly. Instead, a two-stage iteration scheme is used. An extended version of uniformization is applied as a subalgorithm to compute the required transient quantities “on-the fly”. The algorithm is formulated in terms of stochastic Petri nets. A detailed example illustrates the proposed concepts.