PolyGraph: a data flow model with frequency arithmetic

Data flow formalisms are commonly used to model systems in order to solve problems of buffer sizing and task scheduling. A prerequisite for static analysis of a modeled system is the existence of a periodic schedule in which the sizes of communication channels can be bounded for an unbounded execution (consistency), and that communication dependencies do not introduce a deadlock in such an execution (liveness). In the context of Cyber-Physical Systems, components are often interfaced with the physical world and have frequency constraints. The existing data flow formalisms lack expressiveness to fully cover the expected behavior of these components. We propose an extension to static data flow paradigms, called PolyGraph, that includes frequency constraints and adjustable communication rates. We show that with these extensions, the conditions for a model to be consistent and live are no longer sufficient, and we extend the corresponding theorems with necessary and sufficient conditions to preserve these properties. We illustrate how PolyGraph can be used in practice on a realistic Advanced Driver Assistance System, and present a framework to check PolyGraph properties in the tool DIVERSITY, along with experiments on realistic and random models.