In this work, we address the problem of transient and steadystate analysis of a stochastic Petri net which includes non Markovian distributions with a finite support but without any additional constraint. Rather than computing an approximate distribution of the model (as done in previous methods), we develop an exact analysis of an approximate model. The design of this method leads to a uniform...

This paper describes a symbolic model checking approach for the Continuous Stochastic Reward Logic (CSRL) and stochastic reward nets, stochastic Petri nets augmented with rate rewards. CSRL model checking requires the computation of the joint distribution of time and accumulated reward, which is done by Markovian approximation. An implementation is available in the model checker MARCIE. It appl...

Stochastic Petri nets generalize the notion of queueing systems and are a useful model in performance evaluation of parallel and distributed systems. We give necessary and sufficient conditions for the boundedness of a stochastic process related to these nets. A.M.S. Classification : 60 G 40, 68 M 20, 60 K 25 Research partially supported by project PA86-0028 of the Spanish Comisión Interministe...

We consider equivalence relations for Fluid Stochastic Petri Nets (FSPNs). Based on equivalence relations for Stochastic Petri Nets (SPNs), which are derived from lumpability for Markov Chains, and from lumpability for certain classes of differential equations, we define an equivalence relation for FSPNs. Lumpability for the differential equations is based on a finite discretization approach an...

We present SPNP, a powerful GSPN package developed at Duke University. SPNP allows the modeling of complex system behaviors. Advanced constructs are available, such as markingdependent arc multiplicities, enabling functions, arrays of places or transitions, and subnets; in addition, the full expressive power of the C programming language is available to increase the flexibility of the net descr...

Abstract Reliability modelling for digital instrumentation and control systems in nuclear power plants is one of the new trends. The containment spray system I&C plant selected, generalized stochastic Petri net model used to reliability system. A single-cycle simulation carried out under consideration a variety dynamic events, probability start-up failure obtained. results show that can wel...

We study the introduction of transitions with Phase-type distribution ring time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose a new approach to limit this phenomenon while keeping full stochastic semantics of previous works...

Petri nets have been widely used to model and analyze biochemical reaction networks. This chapter gives an overview of di↵erent types of Petri nets within a unifying Petri net framework that comprises the qualitative, stochastic, continuous and hybrid paradigms at both uncolored and colored levels. The Petri net framework permits to investigate one and the same biological reaction network with ...

We study the introduction of transitions with Phase-type distribution ring time in (bounded) generalized stochastic Petri nets. Such transitions produce large increases of both space and time complexity for the computation of the steady state probabilities of the underlying Markov chain. We propose a new approach to limit this phenomenon while keeping full stochastic semantics of previous works...