Transient Solution Of Markov Models By Combining Adaptive And Standard Uniformization (1997)
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BibTeX
@MISC{Moorsel97transientsolution,
author = {Aad P. A. Van Moorsel and William H. Sanders and William H. S},
title = {Transient Solution Of Markov Models By Combining Adaptive And Standard Uniformization},
year = {1997}
}
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Abstract
Adaptive uniformization (AU) has recently been proposed as a method to compute transient measures in continuous-time Markov chains and has been shown to be especially attractive for solving large and stiff dependability models. The major advantage This work was carried out when Aad van Moorsel was with the University of Illinois, at UrbanaChampaign. of AU is that it requires at most as many iterations as standard uniformization (SU), and often far fewer, thus resulting in substantial computational savings. However, this computational gain can be offset by the need to compute more complex "jump probabilities" in AU, whose computation is more expensive than computing Poisson probabilities in SU. In particular, it can be shown that AU is computationally superior to SU if and only if the considered time instant is less than some threshold time value. To overcome this drawback, we combine AU and SU such that AU is used over the start of the time interval of interest, while SU is applied ...
