New results for the analysis of deterministic and stochastic Petri nets

This paper presents new methods for the transient and stationary analysis of stochastic Petri nets with exponentially distributed and deterministic firing delays. The method of supplementary variables is used for the derivation of general state equations which describe the temporal behavior of the underlying stochastic process. Numerical algorithms are presented for the solution of the state equations and illustrated by numerical examples. The results of this paper allow an enhanced performance and reliability analysis based on stochastic Petri net models.<<ETX>>

[1]  Reinhard German.  Transient analysis of deterministic and stochastic Petri nets by the method of supplementary variables , 1995 .

[2]  Andrea Bobbio,et al.  Markov regenerative SPN with non-overlapping activity cycles , 1995, Proceedings of 1995 IEEE International Computer Performance and Dependability Symposium.

[3]  Winfried K. Grassmann,et al.  Transient solutions in Markovian Queueing Systems , 1977, Comput. Oper. Res..

[4]  Winfried K. Grassmann.  Transient solutions in markovian queueing systems , 1977, Comput. Oper. Res..

[5]  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.

[6]  Günter Hommel,et al.  TimeNET: A Toolkit for Evaluating Non-Markovian Stochastic Petri Nets , 1995, Perform. Evaluation.

[7]  Hoon Choi,et al.  Transient Analysis of Deterministic and Stochastic Petri Nets , 1993, Application and Theory of Petri Nets.

[8]  Gianfranco Ciardo,et al.  A Characterization of the Stochastic Process Underlying a Stochastic Petri Net , 1994, IEEE Trans. Software Eng..

[9]  Reinhard German,et al.  Analysis of Stochastic Petri Nets by the Method of Supplementary Variables , 1994, Perform. Evaluation.

[10]  Kishor S. Trivedi,et al.  Time-Dependent Behavior of Redundant Systems with Deterministic Repair , 1995 .

[11]  Kishor S. Trivedi,et al.  Transient analysis of the leaky bucket rate control scheme under Poisson and ON-OFF sources , 1994, Proceedings of INFOCOM '94 Conference on Computer Communications.

[12]  Tadao Murata,et al.  Analysis of Self-Stabilizing Clock Synchronization by Means of Stochastic Petri Nets , 1990, IEEE Trans. Computers.

[13]  D. Cox.  The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[14]  Miklós Telek,et al.  Markov Regenerative Stochastic Petri Nets with Age Type General Transitions , 1995, Application and Theory of Petri Nets.