Hybrid Petri nets with multiple stochastic transition firings

This paper introduces an algorithm for the efficient computation of transient measures of interest in Hybrid Petri nets in which the stochastic transitions are allowed to fire an arbitrary but finite number of times. Each firing increases the dimensionality of the underlying discrete/continuous state space. The algorithm evolves around a partitioning of the multi-dimensional state-space into regions, making use of advanced algorithms (and libraries) for computational geometry. To bound the number of stochastic transition firings the notion of control tokens is newly introduced. While the new partitioning algorithm is general, the implementation is currently limited to only two stochastic firings. The feasibility and usefulness of the new algorithm is illustrated in a case study of a water refinery plant with cascading failures

Fluid Survival Tool: A Model Checker for Hybrid Petri Nets

Recently, algorithms for model checking Stochastic Time Logic (STL) on Hybrid Petri nets with a single general one-shot transition (HPNG) have been introduced. This paper presents a tool for model checking HPNG models against STL formulas. A graphical user interface (GUI) not only helps to demonstrate and validate existing algorithms, it also eases use. From the output of the model checker, 2D and 3D plots can be generated. The extendable object-oriented tool has been developed using the Model-View-Controller and Facade patterns, Doxygen for documentation and Qt for GUI development written in C++

Region-Based Analysis of Hybrid Petri Nets with a Single General One-Shot Transition

Recently, hybrid Petri nets with a single general one-shot transition (HPnGs) have been introduced together with an algorithm to analyze their underlying state space using a conditioning/deconditioning approach. In this paper we propose a considerably more efficient algorithm for analysing HPnGs. The proposed algorithm maps the underlying state-space onto a plane for all possible firing times of the general transition s and for all possible systems times t. The key idea of the proposed method is that instead of dealing with infinitely many points in the t-s-plane, we can partition the state space into several regions, such that all points inside one region are associated with the same system state. To compute the probability to be in a specific system state at time τ, it suffices to find all regions intersecting the line t = τ and decondition the firing time over the intersections. This partitioning results in a considerable speed-up and provides more accurate results. A scalable case study illustrates the efficiency gain with respect to the previous algorithm

Hybrid Petri nets with general one-shot transitions

A hybrid Petri net formalism that allows deterministic, and fluid transitions is extended by generally distributed transitions that moves discrete tokens. Models in this formalism can be analyzed with Parametric Reachability Analysis, by computing all reachable locations, and by separating the deterministic and the stochastic evolution of the system. Several performance metrics, such as the distribution of fluid over time, can be derived by deconditioning according to arbitrary continuous probability distributions. This efficient concept allows for the analysis of an arbitrary number of fluid places, as opposed to classical stochastic hybrid Petri net approaches. Moreover, validation of our results against a FSPN tool shows that parametric reachability analysis provides more accurate results. A case study motivates and shows the potential of our approach

Hybrid Petri Nets with General One-Shot Transitions for Dependability Evaluation of Fluid Critical Infrastructures

A hybrid Petri net formalism that is specifically tailored towards so-called fluid critical infrastructures is introduced, allowing for timed, generally distributed and fluid transitions. Such models are analyzed with Parametric Reachability Analysis, by separating the deterministic and the stochastic evolution of the system. Several performance metrics, such as the distribution of fluid over time, can be derived by deconditioning according to arbitrary continuous probability distributions. This efficient concept allows for the analysis of an arbitrary number of fluid places, as opposed to classical stochastic hybrid Petri net approaches. Moreover, validation of our results against the FSPN tool shows that parametric reachability analysis provides more accurate results. A case study motivates and shows the feasibility of our approach