The Stochastic Quality Calculus

We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated with the outputs and at the same time the inputs impose constraints on the waiting times. Consequently, the expected inputs may not be available when needed and therefore the calculus allows to express the absence of data. The communication delays are expressed by general distributions and the resulting semantics is given in terms of Generalised Semi-Markov Decision Processes. By restricting the distributions to be continuous and by allowing truly concurrent communication we eliminate the non-determinism and arrive at Generalised Semi-Markov Processes (GSMPs); further restriction to exponential distributions gives rise to numerically analysable GSMPs, in particular using techniques from stochastic model checking.