Transient analysis of Markov models of fault-tolerant systems with deferred repair using split regenerative randomization

Abstract

The (standard) randomization method is an attractive alternative for the transient analysis of continuous time Markov models. The main advantages of the method are numerical stability, well-controlled computation error, and ability to specify the computation error in advance. However, the fact that the method can be computationally very expensive limits its applicability. In this paper, we develop a new method called split regenerative randomization, which, having the same good properties as standard randomization, can be significantly more efficient. The method covers reliability-like models with a particular but quite general structure and requires the selection of a subset of states and a regenerative state satisfying some conditions. For a class of continuous time Markov models, model class C_2, including typical failure/repair reliability-like models with exponential failure and repair time distributions and deferred repair, natural selections are available for both the subset of states and the regenerative state and, for those natural selections, theoretical results are available assessing the efficiency of the method in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be competitive. We illustrate the application of the method using a large class C_2 model and show that for models in that class the method can indeed be significantly more efficient than previously available randomization-based methods