Analyzing system reliability using non-regenerative stochastic Petri nets

We extend the class of Markov models that can be described by a stochastic Petri net and describe analytical techniques for solving the resulting model. We consider a generalization of the Markov renewal process in which some of the states may not constitute regeneration points. We present a non-regenerative stochastic Petri net (NRSPN) that generates such a process, discuss its solution, and present an example of a spare-parts inventory system using the NRSPN model. After reviewing SPNs and Markov renewal processes, we define the NRSPN model in the context of a generalized Markov renewal process. Numerical results for specific distributions are given.

[1]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[2]  Shunji Osaki.  Studies on System Analysis and Synthesis by Markov Renewal Processes , 1970 .

[3]  Gianfranco Balbo,et al.  Alternative methods for incorporating non-exponential distributions into stochastic timed Petri nets , 1989, Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89.

[4]  Peter J. Haas,et al.  Stochastic Petri Net Representation of Discrete Event Simulations , 1989, IEEE Trans. Software Eng..

[5]  Gianfranco Ciardo,et al.  Stochastic Petri Net Analysis of a Replicated File System , 1989, IEEE Trans. Software Eng..

[6]  R. Pyke.  Markov renewal processes: Definitions and preliminary properties , 1961 .

[7]  Marco Ajmone Marsan,et al.  On Petri nets with deterministic and exponentially distributed firing times , 1986, European Workshop on Applications and Theory of Petri Nets.

[8]  William Ewing Riddle,et al.  The modeling and analysis of supervisory systems , 1972 .

[9]  Qun Jin.  Aggregate approach of Markov renewal process and extended stochastic Petri net model and its applications , 1991 .

[10]  Kishor S. Trivedi,et al.  Extended Stochastic Petri Nets: Applications and Analysis , 1984, Performance.

[11]  R. Pyke.  Markov Renewal Processes with Finitely Many States , 1961 .

[12]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .

[13]  中川 覃夫.  Studies on optimum maintenance policies for reliable systems , 1977 .

[14]  Michael K. Molloy,et al.  On the integration of delay and throughput measures in distributed processing models , 1981 .

[15]  Marco Ajmone Marsan,et al.  GSPN models of multiserver multiqueue systems , 1989, Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89.