Our primary goal is to develop a compositional real-time scheduling framework where global (system-level) timing properties are established by composing together independently (specified and) analyzed local (component-level) timing properties. In this paper, we define two problems and one design issue in developing such a framework and present our approaches to the problems and the design issue. The two problems are (1) the scheduling interface derivation problem that is to (exactly) abstract the collective real-time requirements of a component as a single real-time requirement, or a scheduling interface and (2) the scheduling interface composition problem that is to (exactly) compose the scheduling interfaces of components into the system-level scheduling interface. The design issue is how to define a scheduling interface model. Our approach is to use the standard periodic model as the scheduling interface model and to address the two problems with the periodic model. We introduce exact conditions under which our proposed periodic scheduling interface model can abstract the collective real-time requirements that a set of periodic tasks demands under EDF (earliest deadline first) and RM (rate monotonic) scheduling. We present simulation results to evaluate the overheads that the periodic scheduling interfaces incur in terms of utilization increase.