Date: 02 Jun 2005

Transient analysis of deterministic and stochastic Petri nets

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Deterministic and stochastic Petri nets (DSPNs) are recognized as a useful modeling technique because of their capability to represent constant delays which appear in many practical systems. If at most one deterministic transition is allowed to be enabled in each marking, the state probabilities of a DSPN can be obtained analytically rather than by simulation. We show that the continuous time stochastic process underlying the DSPN with this condition is a Markov regenerative process and develop a method for computing the transient (time dependent) behavior. We also provide a steady state solution method using Markov regenerative process theory and show that it is consistent with the method of Ajmone Marsan and Chiola.

This research was supported in part by the IBM Graduate Fellowship and by the Overseas Study Program of ETRI.
This research was supported in part by the National Science Foundation under Grant CCR-9108114, and by the Naval Surface Warfare Center under contract N60921-92-C-0161.