The right timing : reflections on the modeling and analysis of time

In this paper we discuss several approaches to time in Petri nets. If time is considered for performance analysis, probability distributions for choices should be included into the model and thus we need Petri nets with time and stochastics. In literature, most attention is paid to models where the time is expressed by delaying transitions and for the stochastic case to continuous time models with exponential enabling distributions, known by its software tools as GSPN. Here we focus on discrete models where the time is expressed by delaying tokens and the probability distributions are discrete, because this model class has some advantages. We show how model checking methods can be applied for the non-stochastic case. For the stochastic case we show how Markov techniques can be used. We also consider structural analysis techniques, which do not need the state space.