Fitting traffic traces with discrete canonical phase type distributions and Markov arrival processes

András Meszáros, János Papp, Miklós Telek

Research output: Contribution to journalArticle

9 Citations (Scopus)


Recent developments of matrix analytic methods make phase type distributions (PHs) and Markov Arrival Processes (MAPs) promising stochastic model candidates for capturing traffic trace behaviour and for efficient usage in queueing analysis. After introducing basics of these sets of stochastic models, the paper discusses the following subjects in detail: (i) PHs and MAPs have different representations. For efficient use of these models, sparse (defined by a minimal number of parameters) and unique representations of discrete time PHs and MAPs are needed, which are commonly referred to as canonical representations. The paper presents new results on the canonical representation of discrete PHs and MAPs. (ii) The canonical representation allows a direct mapping between experimental moments and the stochastic models, referred to as moment matching. Explicit procedures are provided for this mapping. (iii) Moment matching is not always the best way to model the behavior of traffic traces. Model fitting based on appropriately chosen distance measures might result in better performing stochastic models. We also demonstrate the efficiency of fitting procedures with experimental results.

Original languageEnglish
Pages (from-to)453-470
Number of pages18
JournalInternational Journal of Applied Mathematics and Computer Science
Issue number3
Publication statusPublished - Sep 1 2014


  • canonical representation
  • discrete Markov arrival process
  • discrete phase type distribution
  • fitting traffic traces

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Engineering (miscellaneous)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Fitting traffic traces with discrete canonical phase type distributions and Markov arrival processes'. Together they form a unique fingerprint.

  • Cite this