Canonical representation of discrete order 2 MAP and RAP

András Mészáros, Miklós Telek

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

4 Citations (Scopus)

Abstract

Matrix-geometric distributions (MG) and discrete (time) rational arrival processes (DRAP) are natural extensions of discrete phase-type distributions (DPH) and discrete Markov arrival processes (DMAP) respectively. However, the exact relation of the Markovian classes and their non-Markovian counterparts and the boundaries of these classes are not known yet. It has been shown that for the order two case the MG and DPH classes are equivalent. In this paper we prove that the equivalence holds for the order two DMAPs and DRAPs as well. We prove this equivalence by introducing a Markovian canonical form for order two DRAPs and by showing, that this canonical form can indeed be used to describe the whole order two DRAP class.

Original languageEnglish
Title of host publicationComputer Performance Engineering - 10th European Workshop, EPEW 2013, Proceedings
Pages89-103
Number of pages15
DOIs
Publication statusPublished - Oct 7 2013
Event10th European Workshop on Performance Engineering, EPEW 2013 - Venice, Italy
Duration: Sep 16 2013Sep 17 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8168 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th European Workshop on Performance Engineering, EPEW 2013
CountryItaly
CityVenice
Period9/16/139/17/13

Keywords

  • canonical representation
  • discrete Markov arrival process
  • discrete rational arrival process

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Mészáros, A., & Telek, M. (2013). Canonical representation of discrete order 2 MAP and RAP. In Computer Performance Engineering - 10th European Workshop, EPEW 2013, Proceedings (pp. 89-103). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8168 LNCS). https://doi.org/10.1007/978-3-642-40725-3-8