Dealing with Zero Density Using Piecewise Phase-Type
Approximation

D 2014

Dealing with Zero Density Using Piecewise Phase-Type Approximation

KORENČIAK, Ľuboš, Jan KRČÁL a Vojtěch ŘEHÁK

Základní údaje

Originální název

Dealing with Zero Density Using Piecewise Phase-Type Approximation

Autoři

KORENČIAK, Ľuboš (703 Slovensko, garant, domácí), Jan KRČÁL (203 Česká republika) a Vojtěch ŘEHÁK (203 Česká republika, domácí)

Vydání

Switzerland, Computer Performance Engineering, od s. 119-134, 16 s. 2014

Nakladatel

Springer International Publishing

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Švýcarsko

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Impakt faktor

Impact factor: 0.402 v roce 2005

Kód RIV

RIV/00216224:14330/14:00074094

Organizační jednotka

Fakulta informatiky

ISBN

978-3-319-10884-1

ISSN

DOI

http://dx.doi.org/10.1007/978-3-319-10885-8_9

Klíčová slova anglicky

phase-type; CTMC; discrete-time transition

Štítky

formela-conference

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 14. 11. 2014 14:27, Mgr. Ľuboš Korenčiak, Ph.D.

Anotace

V originále

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.

Návaznosti

GPP202/12/P612, projekt VaV

Název: Formální verifikace stochastických systémů s reálným časem (Akronym: Formální verifikace stochastických systémů s reáln)

Investor: Grantová agentura ČR, Formální verifikace stochastických systémů s reálným časem

MUNI/A/0855/2013, interní kód MU

Název: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace III. (Akronym: FI MAV III.)

Investor: Masarykova univerzita, Rozsáhlé výpočetní systémy: modely, aplikace a verifikace III., DO R. 2020_Kategorie A - Specifický výzkum - Studentské výzkumné projekty

Citovat

KORENČIAK, Ľuboš, Jan KRČÁL a Vojtěch ŘEHÁK. Dealing with Zero Density Using Piecewise Phase-Type Approximation. In András Horváth, Katinka Wolter. 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.

@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.

Podrobný výpis o publikaci