We address the problem of providing compositional hard real-time guarantees in a hierarchy of schedulers. We first propose a resource model to characterize a periodic resource allocation and present exact schedulability conditions for our proposed resource model under the EDF and RM algorithms. Using the exact schedulability conditions, we then provide methods to abstract the timing requirements that a set of periodic tasks demands under the EDF and RM algorithms as a single periodic task. With these abstraction methods, for a hierarchy of schedulers, we introduce a composition method that derives the timing requirements of a parent scheduler from the timing requirements of its child schedulers in a compositional manner such that the timing requirement of the parent scheduler is satisfied, if and only if, the timing requirements of its child schedulers are satisfied
