Minimal schedulability interval for real-time systems of periodic tasks with offsets

We consider real-time systems in highly safety context where tasks have to meet strict deadlines. Tasks are periodic, may have offsets, share critical resources and be precedence constrained. Off-line scheduling should be of great help for such systems, but methods proposed in the literature cannot deal with them. Our aim is to extend and improve the well-known cyclicity result of Leung and Merill to every scheduling algorithm and to systems of interacting tasks with offsets. One of the main benefit of our result is to enable the use of off-line scheduling methods for those real-time critical systems.