2020/10/21 by Jannik Hüls, Hüls, Jannik, Carina Pilch +9 · 2 citations
Computer Science · Decision Sciences · #Advanced Database Systems and Queries #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Petri Nets in System Modeling #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2010.11056
openalex publication_date 2020/10/21 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Hybrid Petri nets have been extended to include general transitions that fire\nafter a randomly distributed amount of time. With a single general one-shot\ntransition the state space and evolution over time can be represented either as\na Parametric Location Tree or as a Stochastic Time Diagram. Recent work has\nshown that both representations can be combined and then allow multiple\nstochastic firings. This work presents an algorithm for building the Parametric\nLocation Tree with multiple general transition firings and shows how its\ntransient probability distribution can be computed using multi-dimensional\nintegration. We discuss the (dis-)advantages of an interval arithmetic and a\ngeometric approach to compute the areas of integration. Furthermore, we provide\ndetails on how to perform a Monte Carlo integration either directly on these\nintervals or convex polytopes, or after transformation to standard simplices. A\ncase study on a battery-backup system shows the feasibility of the approach and\ndiscusses the performance of the different integration approaches.\n