Stochastic Petri nets with Low variation matrix exponentially distributed firing time

P. Buchholz, A. Horváth, M. Telek

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6 Citations (Scopus)

Abstract

Matrix exponential (ME) distributions with low squared coefficient of variation (scv) are such that the density function becomes zero at some points in (0,∞). For such distributions there is no equivalent finite dimensional PH representation, which inhibits the application of existing methodologies for the numerical analysis of stochastic Petri nets (SPNs) with this kind of ME distributed firing time. To overcome the limitations of existing methodologies we apply the flow interpretation of ME distributions and study the transient and the stationary behaviour of stochastic Petri nets with ME distributed firing times via ordinary differential and linear equations, respectively. The main result of this study is a theory stating that all kinds of ME distributions can be used like phase type (PH) distributions in stochastic Petri nets and the numerical computation of transient or stationary measures is possible with methods similar to those used for Markov models.

Original languageEnglish
Pages (from-to)441-454
Number of pages14
JournalInternational Journal of Performability Engineering
Volume7
Issue number5
Publication statusPublished - Sep 1 2011

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Keywords

  • Matrix exponential distribution
  • Phase type distribution
  • Stochastic petri net

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality

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