Comparing Two Approaches to Include Stochasticity in Hybrid Automata

Different stochastic extensions of hybrid automata have been proposed in the past, with unclear expressivity relations between them. To structure and relate these modeling languages, in this paper we formalize two alternative approaches to extend hybrid automata with stochastic choices of discrete events and their time points. The first approach, which we call decomposed scheduling, adds stochasticity via stochastic races, choosing random time points for the possible discrete events and executing a winner with an earliest time. In contrast, composed scheduling first samples the time point of the next event and then the event to be executed at the sampled time point. We relate the two approaches regarding their expressivity and categorize available stochastic extensions of hybrid automata from the literature.