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It is desirable to develop large complex systems using components based on systematic abstraction and composition. Our goal is to develop a compositional real-time scheduling framework to support abstraction and composition techniques for real-time aspects of components. In this paper, we present a formal description of compositional real-time scheduling problems, which are the component abstraction and composition problems. We identify issues that need be addressed by solutions and provide our framework for the solutions, which is based on the periodic interface. Specifically, we introduce the periodic resource model to characterize resource allocations provided to a single component. We present exact schedulability conditions for the standard Liu and Layland periodic task model and the proposed periodic resource model under EDF and RM scheduling, and we show that the component abstraction and composition problems can be addressed with periodic interfaces through the exact schedulability conditions. We also provide the utilization bounds of a periodic task set over the periodic resource model and the abstraction bounds of periodic interfaces for a periodic task set under EDF and RM scheduling. We finally present the analytical bounds of overheads that our solution incurs in terms of resource utilization increase and evaluate the overheads through simulations.