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Transient analysis of Markov models of fault-tolerant systems with deferred repair using split regenerative randomization. (English) Zbl 1134.60049

The standard randomization (uniformization) method, and the regenerative randomization method, are common methods for the transient analysis of continuous time Markov models. The main advantages of these methods are numerical stability, well-controlled computation error, and ability to specify the computation error in advance. However, these methods can be computationally expensive. In this paper the authors develop a new numerical method, called split regenerative randomization, which has the same good properties as the common methods, namely, numerical stability, well-controlled computation error, and ability to specify the computation error in advance. However, for large enough models and large enough times, the new method is significantly faster than the common methods.

MSC:

60J22 Computational methods in Markov chains
60K10 Applications of renewal theory (reliability, demand theory, etc.)
90B25 Reliability, availability, maintenance, inspection in operations research
68M15 Reliability, testing and fault tolerance of networks and computer systems
62N05 Reliability and life testing

Software:

SPNP; Möbius
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