Petri-Nets and Hybrid-State Markov Processes in a Power-Hierarchy of Dependability Models

Internet Host Reliability Modeling with Time Petri Nets

“…Their approach involves converting fault trees into a GSPN model for the purpose of obtaining both qualitative and quantitative analysis results for the modeled system. Everdij and Blom develop piecewise deterministic Markov processes (PDP) models using dynamically colored Petri nets (DCPN) [8]. Petri nets are also applied in safety analysis of a system as shown by Leveson and Stolzy, where Petri nets are used to design and analyze the safety and fault tolerance of a system [9].…”

Free Flight Collision Risk Estimation by Sequential MC Simulation

“…In order to make the Petri net formalism useful in modelling air traffic operations, we need an extension of the Petri net formalism including a one-to-one transformation to and from GSHS. Everdij and Blom [26]- [28] have developed such extension in the form of (Stochastically and) Dynamically Coloured Petri Net, or for short (S)DCPN.…”

“…In [36], [42] a colour does not change as long as the token to which it is attached remains at its place. Everdij and Blom [26], [27] defined a Dynamically Coloured Petri Net (DCPN) by incorporating the following extensions: (1) a colour assumes values from a Euclidean state space, its value evolves as solution of a differential equation and influences the time period between enabling and firing; (2) the new tokens and attached colours are produced as random functions of the removed tokens and colours. An SDCPN extends an DCPN in the sense that colours evolve as solutions of a stochastic differential equation [28].…”

Value passing for communicating piecewise deterministic Markov processes

“…This system is a part of the larger system 'free flight', which was originally modelled as a Dynamically Colored Petri Net [3]. The system describes a pilot in an aircraft (the so called 'pilot flying') who has to execute different tasks.…”