### 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.

Original language | English |
---|---|

Pages (from-to) | 1781-1790 |

Number of pages | 10 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E79-A |

Issue number | 11 |

Publication status | Published - 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

- Behavior modeling
- Fault tolerance
- Markov renewal process
- Reliability analysis
- Stochastic Petri nets

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture
- Information Systems

### Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E79-A*(11), 1781-1790.

**Non-regenerative stochastic Petri nets : Modeling and analysis.** / Jin, Qun; Yano, Yoneo; Sugasawa, Yoshio.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E79-A, no. 11, pp. 1781-1790.

}

TY - JOUR

T1 - Non-regenerative stochastic Petri nets

T2 - Modeling and analysis

AU - Jin, Qun

AU - Yano, Yoneo

AU - Sugasawa, Yoshio

PY - 1996

Y1 - 1996

N2 - 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.

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.

KW - Behavior modeling

KW - Fault tolerance

KW - Markov renewal process

KW - Reliability analysis

KW - Stochastic Petri nets

UR - http://www.scopus.com/inward/record.url?scp=0030289848&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030289848&partnerID=8YFLogxK

M3 - Article

VL - E79-A

SP - 1781

EP - 1790

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 11

ER -