A canonical representation of order 3 phase type distributions

Gábor Horváth, M. Telek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)

Abstract

The characterization and the canonical representation of order n phase type distributions (PH(n)) is an open research problem. This problem is solved for n = 2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical representations have been introduced for the general PH distribution class so far for n > 2. In this paper we summarize the related results for n = 3. Starting from these results we recommend a canonical representation of the PH(3) class and present a transformation procedure to obtain the canonical representation based on any (not only Markovian) vector-matrix representation of the distribution. Using this canonical transformation method we evaluate the moment bounds of the PH(3) distribution set and present the results of our numerical investigations.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages48-62
Number of pages15
Volume4748 LNCS
Publication statusPublished - 2007
Event4th European Performance Engineering Workshop, EPEW 2007 - Berlin, Germany
Duration: Sep 27 2007Sep 28 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4748 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other4th European Performance Engineering Workshop, EPEW 2007
CountryGermany
CityBerlin
Period9/27/079/28/07

Fingerprint

Phase-type Distribution
Canonical Representation
Canonical Transformation
Matrix Representation
Numerical Investigation
Research
Equivalence
Moment
PH.3
Evaluate
Class

Keywords

  • Canonical form
  • Moment bounds
  • Phase type distribution

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Horváth, G., & Telek, M. (2007). A canonical representation of order 3 phase type distributions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4748 LNCS, pp. 48-62). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4748 LNCS).

A canonical representation of order 3 phase type distributions. / Horváth, Gábor; Telek, M.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4748 LNCS 2007. p. 48-62 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4748 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Horváth, G & Telek, M 2007, A canonical representation of order 3 phase type distributions. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4748 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4748 LNCS, pp. 48-62, 4th European Performance Engineering Workshop, EPEW 2007, Berlin, Germany, 9/27/07.
Horváth G, Telek M. A canonical representation of order 3 phase type distributions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4748 LNCS. 2007. p. 48-62. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Horváth, Gábor ; Telek, M. / A canonical representation of order 3 phase type distributions. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4748 LNCS 2007. pp. 48-62 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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