Non-Regenerative Stochastic Petri Nets: Modeling and Analysis

Qun JIN; Yoneo YANO; Yoshio SUGASAWA

Non-Regenerative Stochastic Petri Nets: Modeling and Analysis

Qun JIN, Yoneo YANO, Yoshio SUGASAWA

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We develop a new class of stochastic Petri net: non-regenerative stochastic Petri net (NRSPN), which allows the firing time of its transitions with arbitrary distributions, and can automatically generate a bounded reachability graph that is equivalent to a generalization of the Markov renewal process in which some of the states may not constitute regeneration points. Thus, it can model and analyze behavior of a system whose states include some non-regeneration points. We show how to model a system by the NRSPN, and how to obtain numerical solutions for the NRSPN model. The probabilistic behavior of the modeled system can be clarified with the reliability measures such as the steady-state probability, the expected numbers of visits to each state per unit time, availability, unavailability and mean time between system failure. Finally, to demonstrate the modeling ability and analysis power of the NRSPN model, we present an example for a fault-tolerant system using the NRSPN and give numerical results for specific distributions.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.11 pp.1781-1790

Publication Date: 1996/11/25

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Type of Manuscript: Special Section PAPER (Special Section on Description Models for Concurrent Systems and Their Applications)

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Qun JIN, Yoneo YANO, Yoshio SUGASAWA, "Non-Regenerative Stochastic Petri Nets: Modeling and Analysis" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 11, pp. 1781-1790, November 1996, doi: .
Abstract: We develop a new class of stochastic Petri net: non-regenerative stochastic Petri net (NRSPN), which allows the firing time of its transitions with arbitrary distributions, and can automatically generate a bounded reachability graph that is equivalent to a generalization of the Markov renewal process in which some of the states may not constitute regeneration points. Thus, it can model and analyze behavior of a system whose states include some non-regeneration points. We show how to model a system by the NRSPN, and how to obtain numerical solutions for the NRSPN model. The probabilistic behavior of the modeled system can be clarified with the reliability measures such as the steady-state probability, the expected numbers of visits to each state per unit time, availability, unavailability and mean time between system failure. Finally, to demonstrate the modeling ability and analysis power of the NRSPN model, we present an example for a fault-tolerant system using the NRSPN and give numerical results for specific distributions.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e79-a_11_1781/_p

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@ARTICLE{e79-a_11_1781,
author={Qun JIN, Yoneo YANO, Yoshio SUGASAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Non-Regenerative Stochastic Petri Nets: Modeling and Analysis},
year={1996},
volume={E79-A},
number={11},
pages={1781-1790},
abstract={We develop a new class of stochastic Petri net: non-regenerative stochastic Petri net (NRSPN), which allows the firing time of its transitions with arbitrary distributions, and can automatically generate a bounded reachability graph that is equivalent to a generalization of the Markov renewal process in which some of the states may not constitute regeneration points. Thus, it can model and analyze behavior of a system whose states include some non-regeneration points. We show how to model a system by the NRSPN, and how to obtain numerical solutions for the NRSPN model. The probabilistic behavior of the modeled system can be clarified with the reliability measures such as the steady-state probability, the expected numbers of visits to each state per unit time, availability, unavailability and mean time between system failure. Finally, to demonstrate the modeling ability and analysis power of the NRSPN model, we present an example for a fault-tolerant system using the NRSPN and give numerical results for specific distributions.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Non-Regenerative Stochastic Petri Nets: Modeling and Analysis
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1781
EP - 1790
AU - Qun JIN
AU - Yoneo YANO
AU - Yoshio SUGASAWA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1996
AB - We develop a new class of stochastic Petri net: non-regenerative stochastic Petri net (NRSPN), which allows the firing time of its transitions with arbitrary distributions, and can automatically generate a bounded reachability graph that is equivalent to a generalization of the Markov renewal process in which some of the states may not constitute regeneration points. Thus, it can model and analyze behavior of a system whose states include some non-regeneration points. We show how to model a system by the NRSPN, and how to obtain numerical solutions for the NRSPN model. The probabilistic behavior of the modeled system can be clarified with the reliability measures such as the steady-state probability, the expected numbers of visits to each state per unit time, availability, unavailability and mean time between system failure. Finally, to demonstrate the modeling ability and analysis power of the NRSPN model, we present an example for a fault-tolerant system using the NRSPN and give numerical results for specific distributions.
ER -