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Stochastic Petri Nets: Modeling Power and Limit Theorems

Published online by Cambridge University Press:  27 July 2009

Peter J. Haas  and
Gerald S. Shedler
Peter J. Haas
Affiliation:
IBM Research Division Almaden Research Center San Jose, California 95120-6099
Gerald S. Shedler
Affiliation:
IBM Research Division Almaden Research Center San Jose, California 95120-6099
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Abstract

Generalized semi-Markov processes and stochastic Petri nets provide building blocks for specification of discrete event system simulations on a finite or countable state space. The two formal systems differ, however, in the event scheduling (clock-setting) mechanism, the state transition mechanism, and the form of the state space. We have shown previously that stochastic Petri nets have at least the modeling power of generalized semi-Markov processes. In this paper we show that stochastic Petri nets and generalized semi-Markov processes, in fact, have the same modeling power. Combining this result with known results for generalized semi-Markov processes, we also obtain conditions for time-average convergence and convergence in distribution along with a central limit theorem for the marking process of a stochastic Petri net.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 4 , October 1991 , pp. 477 - 498
Copyright
Copyright © Cambridge University Press 1991

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