Automata-theoretic modeling of fixed-priority non-preemptive scheduling for formal timing verification

Abstract

The design process of safety-critical systems requires formal analysis methods to ensure their correct functionality without over-sized safety margins and extensive testing. For architectures with state-based events or scheduling, such as load-dependent frequency scaling, model checking has emerged as a promising tool. It formally verifies timing behavior of realtime systems with minimal over-approximation of the worst case delays. In this context, Event Count Automata (ECAs) have become a valuable modeling approach because they are specifically designed to handle typical arrival patterns and integrate well with analytic techniques.In this work, we propose an extension of the ECA framework's semantics and use it in a Fixed-Priority Non-preemptive Scheduling (FPNS) model that correctly abstracts the intra-slot behavior in the slotted-time model of the ECA. This is challenging because straightforward implementations cannot capture the full behavior of event-triggered scheduling with such a time model that the ECA shares with most model checking based methods. In a case study, we obtain bounds via model checking a basic model and then our proposed model. We compare these bounds with a SystemC simulation. This shows that the bounds from the basic model are too optimistic -and exceeded in practicebecause it does not capture the full behavior, while the bounds from the proposed extended model are both safe and reasonably tight.