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Markov Chains and Stochastic Petri Nets for Availability and Reliability Modeling
Published in Mangey Ram, Reliability Engineering, 2019
Paulo Romero Martins Maciel, Jamilson Ramalho Dantas, Rubens de Souza Matos Júnior
Stochastic Petri Nets—Let SPN = (P, T, I, O, H, M0,Atts) be an SPN, where P, T, I, O, and M0 are defined as for Place-Transition nets, that is, P is the set of places, T is the set of transitions, I in input matrix, O is the output matrix, and M0 is the initial marking. The set of transition, T, is, however, divided into immediate transitions (Tim ), timed exponentially distributed transitions (Texp ), deterministic timed transitions (Tdet ), and timed generically distributed transitions (Tg ): T=Tim∪Texp∪Tdet∪Tg.
Petri Nets
Published in Richard L. Shell, Ernest L. Hall, Handbook of Industrial Automation, 2000
Generalized stochastic Petri nets (GSPNs) [14] incorporate both stochastic timed transitions and immediate transitions. The immediate transitions fire in zero time. Additional modeling capabilities are introduced to GSPNs without destroying the equivalence with Markov chains. They are inhibitor arcs, priority functions, and random switches. An inhibitor arc in the net prevents a transition from firing when certain conditions are true. A priority function specifies a rule for the marking in which both timed and immediate transitions are enabled. The random switch, as a discrete probability distribution, resolves conflicts between two or more immediate transitions.
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Published in Phillip A. Laplante, Dictionary of Computer Science, Engineering, and Technology, 2017
stochastic Petri net a Petri net in which the elapsed time from the moment that all of its input places are filled until a transition fires is determined by a random variable. Typically, these random variables are exponentially distributed, in which case the model is equivalent to a Markov process.
Stochastic maintenance models for ceramic claddings
Published in Structure and Infrastructure Engineering, 2020
Cláudia Ferreira, Luís Canhoto Neves, Ana Silva, Jorge de Brito
The main objective of this work is the development and implementation of a life-cycle model for ceramic claddings, considering preventive and reactive maintenance actions. The proposed model will be implemented using a stochastic Petri net framework. The case study selected was composed of 195 ceramic claddings, located in Lisbon, Portugal, as detailed data on the deterioration of these elements were available. The sample was established based on the diagnosis of the degradation condition of these claddings in-service performance, through in situ visual inspections. The model developed is, nevertheless, very general and can be applied to a range of building components, including natural stone claddings, wall renderings, painted walls, among others.
Overview and Recommendations for Cyber Risk Assessment in Nuclear Power Plants
Published in Nuclear Technology, 2023
Taleb-Berrouane et al.11 propose a hybrid Bayesian stochastic Petri nets (BSPN) modeling tool, which combines the adaptability of the BN with the time dependence and system analysis capabilities of stochastic Petri nets (SPN). Petri nets comprise nodes, which hold tokens, and transitions, which allow flow of tokens when enabled. The stochastic nature arises when a function is used to delay how quickly tokens are fired once a transition is enabled. This work utilizes SPN with predicates, which allows for conditional variable elements to be tied to transition activation.
Parallel algorithm development and testing using Petri-object simulation
Published in International Journal of Parallel, Emergent and Distributed Systems, 2021
Inna V. Stetsenko, Alexander A. Pavlov, Oleksandra Dyfuchyna
Unlike classical Petri net, stochastic Petri net not only allows modelling the logic of a program but also reproduces the program execution in time. This advantage is especially important when creating a model of a multithreaded algorithm because it provides high accuracy of modelling the interaction of threads. The stochastic behaviour of threads, when they compete for computing resources, is close to the behaviour of a stochastic Petri net.