Hybrid Petri nets have been extended to include general transitions that fire after a randomly distributed amount of time. With a single general one-shot transition the state space and evolution over time can be represented either as a Parametric Location Tree or as a Stochastic Time Diagram. Recent work has shown that both representations can be combined and then allow multiple stochastic firings. This work presents an algorithm for building the Parametric Location Tree with multiple general transition firings and shows how its transient probability distribution can be computed using multi-dimensional integration. We discuss the (dis-)advantages of an interval arithmetic and a geometric approach to compute the areas of integration. Furthermore, we provide details on how to perform a Monte Carlo integration either directly on these intervals or convex polytopes, or after transformation to standard simplices. A case study on a battery-backup system shows the feasibility of the approach and discusses the performance of the different integration approaches.

中文翻译：

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具有多次随机触发的混合 Petri 网的状态空间构造

混合 Petri 网已扩展为包括在随机分布的时间后触发的一般转换。通过单个通用一次性转换，状态空间和随时间的演变可以表示为参数位置树或随机时间图。最近的工作表明，这两种表示可以结合起来，然后允许多次随机触发。这项工作提出了一种用于构建具有多个一般转换触发的参数位置树的算法，并展示了如何使用多维积分计算其瞬态概率分布。我们讨论了区间算术和几何方法来计算积分区域的（不利）优势。此外，我们提供了有关如何直接在这些区间或凸多面体上或在转换为标准单纯形之后执行蒙特卡罗积分的详细信息。电池备份系统的案例研究表明了该方法的可行性，并讨论了不同集成方法的性能。