Optimizing reachability probabilities for a restricted class of Stochastic Hybrid Automata via Flowpipe-Construction

Stochastic hybrid automata (SHA) are a powerful tool to evaluate the dependability and safety of critical infrastructures. However, the resolution of nondeterminism, which is present in many purely hybrid models, is often only implicitly considered in SHA. This paper instead proposes algorithms for computing maximum and minimum reachability probabilities for singular automata with urgent transitions and random clocks which follow arbitrary continuous probability distributions. We borrow a well-known approach from hybrid systems reachability analysis, namely flowpipe construction, which is then extended to optimize nondeterminism in the presence of random variables. Firstly, valuations of random clocks which ensure reachability of specific goal states are extracted from the computed flowpipes and secondly, reachability probabilities are computed by integrating over these valuations. We compute maximum and minimum probabilities for history-dependent prophetic and non-prophetic schedulers using set-based methods. The implementation featuring the library HyPro and the complexity of the approach are discussed in detail. Two case studies featuring nondeterministic choices show the feasibility of the approach.