  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.
