A novel approach for phase-type fitting with the EM algorithm

Axel Thümmler, Peter Buchholz, Miklós Telek

Research output: Contribution to journalArticle

132 Citations (Scopus)


The representation of general distributions or measured data by phase-type distributions is an important and nontrivial task in analytical modeling. Although a large number of different methods for fitting parameters of phase-type distributions to data traces exist, many approaches lack efficiency and numerical stability. In this paper, a novel approach is presented that fits a restricted class of phase-type distributions, namely, mixtures of Erlang distributions, to trace data. For the parameter fitting, an algorithm of the expectation maximization type is developed. This paper shows that these choices result in a very efficient and numerically stable approach which yields phase-type approximations for a wide range of data traces that are as good or better than approximations computed with other less efficient and less stable fitting methods. To illustrate the effectiveness of the proposed fitting algorithm, we present comparative results for our approach and two other methods using six benchmark traces and two real traffic traces as well as quantitative results from queueing analysis.

Original languageEnglish
Article number1673383
Pages (from-to)245-258
Number of pages14
JournalIEEE Transactions on Dependable and Secure Computing
Issue number3
Publication statusPublished - Jan 1 2006



  • Communication networks
  • Hyper-Erlang distributions
  • Markov processes
  • Performance analysis and design aids
  • Traffic modeling

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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