NDLI: Phase-type approximation of stochastic Petri nets for analysis of manufacturing systems

Content Provider	IEEE Xplore Digital Library
Author	Shang-Tae Yee Ventura, J.A.
Copyright Year	1989
Abstract	NonMarkovian stochastic Petri nets (SPN) have received special attention due to their functionality in reflecting nonexponential dynamic behavior encountered in modeling and analysis of real systems. In this 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 nonMarkovian SPN. 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 nonMarkovian 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.
Starting Page	318
Ending Page	322
Page Count	5
File Size	181095
File Format	PDF
ISSN	1042296X
Volume Number	16
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2000-06-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stochastic systems Petri nets Manufacturing systems Performance analysis Transient analysis Steady-state Stochastic processes Throughput Phase measurement System performance
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering

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