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Approximate transient analysis for subclasses of deterministic and stochastic Petri nets.

Ciardo, G.; Li, G.

In: Performance Evaluation, Vol. 35, No. 3-4, pages 109-129. 1999.

Abstract: Transient analysis of non-Markovian stochastic Petri nets is a theoretically interesting and important problem. This paper first presents a method to compute bounds and an approximation on the average state sojourn times for a subclass of deterministic and stochastic Petri nets, (DSPNs) where there is a single persistent deterministic transition that can become enabled only in a special state. Then this class is extended by allowing the transition to become enabled in any state, as long as the time between successive enablings of the deterministic transition is independent of this state, and a new approximate transient analysis approach is developed. In addition to renewal theory, discrete and continuous Markov chain concepts are used. The model of a finite-capacity queue with a server subject to breakdowns is used as an example and the quality of the proposed approximation is assessed.

Keywords: Markov regenerative processes, approximate transient solutions, deterministic Petri nets, renewal processes, stochastic Petri nets.

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