Scheduling of Offset Free Systems

In this paper, we study the problem of scheduling hard real-time periodic tasks. We consider independent tasks which are characterized by a period, a hard deadline and a computation time, but where the offsets may be chosen by the scheduling algorithm. We first show that we can restrict the problem by considering non-equivalent offset assignments. More precisely, we show that there are finitely many non-equivalent offset assignments and we propose a method to reduce significantly this number and consider only the minimal number of non-equivalent offset assignments. We then propose an optimal offset assignment rule which considers only the non-equivalent offset assignments. However the number of combinations remains exponential; for this reason, we also propose a nearly optimal algorithm with a more reasonable time complexity.