Phase-type approximation of stochastic petri nets for analysis of manufacturing systems

Shang Tae Yee, Jose Antonio Ventura

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Non-Markovian stochastic Petri nets (SPN's) have received special attention due to their functionality in reflecting nonexponential dynamic behavior encountered in modeling and analysis of real systems. In the paper, a novel analysis approach, based on phase-type approximation, is proposed to provide transient and steady-state probabilities and determine performance measures of these non-Markovian SPN's. The approach can accommodate a wide variety of nonexponential distributions and provide a stronger mechanism than other methods proposed to date for analyzing system performance. The proposed procedure primarily consists of three steps. First, all generally distributed transitions are fitted with phase-type transitions. Next, the non-Markovian SPN with the approximated phase-type transitions is converted into a Markov chain. Last, transient-state probabilities are obtained by employing the uniformization method and steady-state probabilities are determined by utilizing the preconditioned biconjugate gradient method. Pertinent performance measures can be computed by using these probabilities. The proposed methodology is validated through a real example with respect to its accuracy and speed.

Original languageEnglish (US)
Pages (from-to)318-322
Number of pages5
JournalIEEE Transactions on Robotics and Automation
Volume16
Issue number3
DOIs
StatePublished - Jun 1 2000

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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