Abstraction Techniques for Compositional State-Based Scheduling Analysis

Nowadays, most embedded safety critical systems have to work in a timely manner in order to deliver desired services. In such timed systems not only ordering of events but timing properties are relevant for correctness and performance. In order to be safe and reliable, it is important to have rigorous analysis techniques of timing-dependent (state) behavior. Classical scheduling approaches consider only the system behavior stateless. Especially for safety critical systems this is not sufficient as the state space gives important information of the system which has to be considered by analysis approaches. Our approach for scheduling analysis combines analytical and model checking methods. We consider not only critical instances but the full state space for analysis, where all inter-leavings and task dependencies are preserved. For this, the state space of the entire system architecture is constructed with the aid of input event streams for tasks, and the known behavior of the scheduler of each resource. Based on the state space response times can be determined, and safety properties can be verified by means of reachability checks. As this approach alone is not scalable we present abstraction techniques based on determining output event streams for each resource. For this we exploit well known analytical methods for scheduling analysis. These methods typically abstracts from all inter-leavings leading to very pessimistic results. In this work we present an abstraction technique that is relevant if multiple activations of one task can occur. This technique lies in the middle of both approaches mentioned above.