We present an extension to Continuous Time Bayesian Networks (CTBN) called Generalized CTBN (GCTBN). The formalism allows one to model continuous time delayed variables (with exponentially distributed transition rates), as well as non delayed or “immediate” variables, which act as standard chance nodes in a Bayesian Network. The usefulness of this kind of model is discussed through an example c...

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...

The compositional representation of a Markov chain using Kronecker algebra, according to a compositional model representation as a superposed generalized stochastic Petri net or a stochastic automata network, has been studied for a while. In this paper we describe a Kronecker expression and associated data structures, that allows to handle nets with synchronization over activities of different ...

High availability constraints ensure a high level of operational performance that must be maintained during a contractual measurement period. Such constraints must be satisfied, particularly, for critical systems related to global security and human safety. High availability often results from material redundancies and lead to large stochastic discrete event models with numerous states. Markov ...

Stochastic performance models are widely used to analyse the performance of systems that process customers and resources. However, the construction of such models is traditionally manual and therefore expensive, intrusive and prone to human error. In this paper we introduce PEPERCORN, a Petri Net Performance Model (PNPM) construction tool, which, given a dataset of raw location tracking traces ...

This paper addresses the computation of upper bounds for the steady-state throughput of stochastic Petri net systems with immediate and generally distributed timed transitions. It is achieved through the use of a kind of decomposition of the whole net system. Results are obtained deeply bridging stochastic Petri net theory to untimed Petri net and queueing network theories. Previous results are...