Abstract
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.
Highlights
The framework of Hybrid Petri-nets with General one-shot transitions (HPnG) has been introduced for the analysis of, e.g., fluid critical infrastructures [13]
We tackle the above limitation of existing HPnG analysis algorithms to one stochastic transition firing and generalise the state space representation and the analysis algorithm, cf. [12], to an arbitrary but finite number of stochastic variables
Due to the limitations of existing computational geometry libraries, at the moment the implementation is limited to only two stochastic firings
Summary
The framework of Hybrid Petri-nets with General one-shot transitions (HPnG) has been introduced for the analysis of, e.g., fluid critical infrastructures [13]. Efficient algorithms have been introduced for investigating, among others, reachability properties in the presence of a single stochastic transition firing [12, 11] Such HPnGs are very well able to capture the rather deterministic evolution of a physical process with many continuous variables, as for example present in the application area of water management. We tackle the above limitation of existing HPnG analysis algorithms to one stochastic transition firing and generalise the state space representation and the analysis algorithm, cf [12], to an arbitrary but finite number of stochastic variables.
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