A New General-Purpose Method for the Computation of the Interval Availability Distribution

What is it about?

The paper develops a proven experimentally numerically stable for the computation of the interval availability distribution (the distribution of the proportion of time that a continuous-time Markov chain -CTMC- is in a subset of states) which when the output rates from that subset and the complementary subset of the state space of the CTMC are significantly different and one is interested in the queue of the distribution is significantly less costly computationally than the previously available state-of-the-art general-purpose method

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Why is it important?

The method has been proved numerically stable by quite thorough experiments. It can be much faster than the previously available state-of-the-art general purpose method. Theorem 1 proves the validity of the uniformization construct for uniformizable CTMCs with denumerable state space for the completely general case in which a particular, potentially different uniformization rate can be used in each particular state. There is an erratum, though, in the statement of the theorem: the subscript of the sum has to start at k=0.