In this paper we revisit the admission of applicationsupon a processor share modeled by the explicit-deadlineperiodic (EDP) resource-supply model. In particular, we considerapplications that represent a fixed-priority sporadic task system.Existing works heavily build on the analysis of a hierarchy ofpreemptive task schedulers. We instead consider the feasibilityof such tasks and applications for a hierarchy of deferredpreemptiveschedulers, so that we can efficiently deal with thescenario where tasks and applications execute their work in nonpreemptivechunks. Our model therefore gives better control overpreemptions of tasks of different applications.We present exact analysis for deferred-preemptive schedulingof tasks on EDP resources. In addition, we propose algorithmsfor dimensioning an application’s budget tightly.