Exact analysis for basic multi-rate cyclic executives

Although the academic interest in cyclic executives for multitasking in hard real-time systems decreased significantly during the past decades, industry still uses cyclic executives in embedded real-time systems. Unfortunately, contemporary text books hardly address cyclic executives, if at all. There is therefore a need for analysis techniques for these executives.In this document, we consider two basic cyclic executives, i.e. a multi-rate AFAP (as fast as possible) and a multi-rate time-driven AFAP cyclic executive, scheduling a given sequence of independent hard real-time polling tasks in a single-processor system. We present exact analysis for both cyclic executives. Unlike existing approaches, which typically take periodic tasks as a starting point for cyclic executives and focus on schedulability of tasks, we take the schedulability of the system as a starting point, i.e. whether or not the system meets its deadlines. In particular, we do not assume periods and deadlines for tasks.