Dealing with Zero Density Using Piecewise Phase-Type
Approximation

D 2014

Dealing with Zero Density Using Piecewise Phase-Type Approximation

KORENČIAK, Ľuboš; Jan KRČÁL and Vojtěch ŘEHÁK

Basic information

Original name

Dealing with Zero Density Using Piecewise Phase-Type Approximation

Authors

KORENČIAK, Ľuboš (703 Slovakia, guarantor, belonging to the institution); Jan KRČÁL (203 Czech Republic) and Vojtěch ŘEHÁK (203 Czech Republic, belonging to the institution)

Edition

Switzerland, Computer Performance Engineering, p. 119-134, 16 pp. 2014

Publisher

Springer International Publishing

Other information

Language

English

Type of outcome

Proceedings paper

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Switzerland

Confidentiality degree

is not subject to a state or trade secret

Publication form

printed version "print"

Impact factor

Impact factor: 0.402 in 2005

RIV identification code

RIV/00216224:14330/14:00074094

Organization unit

Faculty of Informatics

ISBN

978-3-319-10884-1

ISSN

DOI

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

EID Scopus

2-s2.0-84906972002

Keywords in English

phase-type; CTMC; discrete-time transition

Abstract

In the original language

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.

Links

GPP202/12/P612, research and development project

Name: Formální verifikace stochastických systémů s reálným časem (Acronym: Formální verifikace stochastických systémů s reáln)

Investor: Czech Science Foundation

MUNI/A/0855/2013, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace III. (Acronym: FI MAV III.)

Investor: Masaryk University, Category A

Cite

KORENČIAK, Ľuboš; Jan KRČÁL and Vojtěch ŘEHÁK. Dealing with Zero Density Using Piecewise Phase-Type Approximation. In András Horváth, Katinka Wolter. Computer Performance Engineering. Switzerland: Springer International Publishing, 2014, p. 119-134. ISBN 978-3-319-10884-1. Available from: 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  - CONF
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 and 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, p.~119-134. ISBN~978-3-319-10884-1. Available from: https://dx.doi.org/10.1007/978-3-319-10885-8\_{}9.

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