A Moment Generating Function Based Approach for Evaluating Extended Stochastic Petri Nets

Document Type

Article

Publication Date

1-1-1993

Abstract

This note presents a moment generating function (MGF) based approach for performance analysis of extended stochastic Petri nets (ESPN). The method integrates Petri nets (PN), MGF and stochastic network concepts, and Mason’s rule into a new tool for evaluating various discrete event dynamic systems. In this method, the ESPNs are first modeled given the specification of a system, then the state machine PN is derived, the transfer functions based on MGF of the related transitions are found, the network is reduced to a single transition with its transfer function for each performance measure, and finally system performance is calculated. Firing delays of transitions in ESPN can be either deterministic or stochastic with an extended distribution. Three fundamental structures that can be reduced into a single transition are discussed. The machine-repairman model with a buffer is given as an example to illustrate the proposed method for evaluating such performance parameters as mean passage time, mean recurrence time, mean sojourn time, and steady-state probability. The major advantages of this method over existing PN performance evaluation techniques are the ease in finding transient performance parameters such as mean passage time and the ability to compute symbolic solutions for performance. The computational complexity is the same as existing methods since the same state explosion problem is encountered. As a practical matter, this method is more cumbersome if computing only steady state probabilities since symbolic computation is required as opposed to numerical solution of linear equations. © 1993, IEEE. All rights reserved.

Identifier

0027544542 (Scopus)

Publication Title

IEEE Transactions on Automatic Control

External Full Text Location

https://doi.org/10.1109/9.250484

e-ISSN

15582523

ISSN

00189286

First Page

321

Last Page

327

Issue

2

Volume

38

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