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@inproceedings{1206017,
author = {Korenčiak, Ľuboš and Krčál, Jan and Řehák, Vojtěch},
address = {Switzerland},
booktitle = {Computer Performance Engineering},
doi = {http://dx.doi.org/10.1007/978-3-319-10885-8_9},
editor = {András Horváth, Katinka Wolter},
keywords = {phase-type; CTMC; discrete-time transition},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Switzerland},
isbn = {978-3-319-10884-1},
pages = {119-134},
publisher = {Springer International Publishing},
title = {Dealing with Zero Density Using Piecewise Phase-Type Approximation},
year = {2014}
}
TY - JOUR
ID - 1206017
AU - Korenčiak, Ľuboš - Krčál, Jan - Řehák, Vojtěch
PY - 2014
TI - Dealing with Zero Density Using Piecewise Phase-Type Approximation
PB - Springer International Publishing
CY - Switzerland
SN - 9783319108841
KW - phase-type
KW - CTMC
KW - discrete-time transition
N2 - Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC is needed for some standard distributions, in particular most distributions with regions of zero density such as uniform or shifted distributions. Addressing this class of distributions, we suggest an alternative representation by CTMC extended with discrete-time transitions. Using discrete-time transitions we split the density function into multiple intervals. Within each interval, we then approximate the density with standard phase-type fitting. We provide an experimental evidence that our method requires only a moderate number of states to approximate such distributions with regions of zero density. Furthermore, the usage of CTMC with discrete-time transitions is supported by a number of techniques for their analysis. Thus, our results promise an efficient approach to the transient analysis of a class of non-Markovian models.
ER -
KORENČIAK, Ľuboš, Jan KRČÁL a Vojtěch ŘEHÁK. Dealing with Zero Density Using Piecewise Phase-Type Approximation. In András Horváth, Katinka Wolter. \textit{Computer Performance Engineering}. Switzerland: Springer International Publishing, 2014, s.~119-134. ISBN~978-3-319-10884-1. Dostupné z: https://dx.doi.org/10.1007/978-3-319-10885-8\_{}9.
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