The hierarchical real-time scheduling framework is a widely accepted model to facilitate the design and analysis of the increasingly complex real-time systems. Interface abstraction and composition are the key issues in the hierarchical scheduling framework analysis. Schedulability is essential to guarantee that the timing requirements of all components are satisfied. In order for the design to be resource efficient, the composition must be bandwidth optimal. Associativity is desirable for open systems in which components may be added or deleted at run time. Previous techniques on compositional scheduling are either not resource efficient in some aspects, or cannot achieve optimality and associativity at the same time. In this paper, several important properties regarding the periodic resource model are identified. Based on those properties, we propose a novel interface abstraction and composition framework which achieves schedulability, optimality, and associativity. Our approach eliminates abstraction overhead in the composition.