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.
Ghasemieh, H., Remke, A. K. I., Haverkort, B. R. H. M., & Gribaudo, M. (2012, Sep). Region-Based Analysis of Hybrid Petri Nets with a Single General One-Shot Transition. London: Springer Verlag. https://doi.org/10.1007/978-3-642-33365-1_11