Abstract:
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Randomization 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 expensive
limits its applicability. Recently, a variant of the (standard) randomization method, called split regenerative randomization has been proposed for the efficient analysis of reliability-like models of fault-tolerant systems with deferred repair. In this article, we generalize that method so that it covers more general reward measures: the expected transient reward rate and the expected averaged reward rate. The generalized method has the same good properties as the standard randomization method and, for large models and large values of the time t at which the
measure has to be computed, can be significantly less expensive. The method
requires the selection of a subset of states and a regenerative state satisfying some
conditions. For a class of continuous time Markov models, class C'_2, including
typical failure/repair reliability models with exponential failure and repair time
distributions and deferred repair, natural selections for the subset of states and
the regenerative state exist and results are available assessing approximately the
computational cost of the method in terms of “visible” model characteristics. Using
a large model class C'_2 example, we illustrate the performance of the method and show that it can be significantly faster than previously proposed randomizationbased methods. |