WCRT Algebra and Scheduling Interfaces for Esterel-Style Synchronous Multithreading

The abstractions used in system design typically limit themselves to encapsulate and guarantee functionality, not timing. Hence, it is very difficult to transfer results on timing behavior across layers, e.g., from the application level through the operating system level to the hardware level. The choice of the model of computation plays a big role in facilitating this transfer. In the realm of reactive systems, the synchronous model of computation has some appeal here, as it inherently limits the number of operations per reaction, and addresses concurrency and preemptive behavior at the language level. Recently, reactive processing architectures have been proposed as execution platform for synchronous languages, notably Esterel. Initially, these architectures were driven by the desire for high performance with low resource usage, including low power consumption. However, by now they have also demonstrated their benefits in terms of predictability. Preliminary work on worst case reaction time (WCRT) analysis has been promising---fairly simple heuristics already achieve an accuracy typically in the 30--40% range. However, these methods so far lack formal grounding, and do not exploit knowledge about signal consistency etc. To provide a formal basis for WCRT analysis, we here propose a type-theoretic, algebraic approach. This approach not only allows to verify the correctness of WCRT analyses methods, but also opens the door for more exact analyses, as it allows to capture functionality and timing precisely and to trade off precision against analysis effort. This approach is still under development; this report presents first results on suitable interface types and the proper characterization of instantaneous nodes, delay nodes and concurrency. As a concrete application, it builds on a multi-threaded Esterel processor, the Kiel Esterel Processor (KEP)