Component-based software development provides a modular approach to develop complex software systems. In the context of real-time systems, it is desirable to abstract the timing properties of software components using an interface for each component. The timing properties of the whole system, composed of multiple components, is studied using the component interfaces. In this paper we focus on periodic interface models. In the case of components developed for single processor platforms, for examining the system schedulability, the interfaces can be regarded as periodic tasks. Thus, making it possible to use the conventional schedulability analyses for the system level schedulability test. In the case of components developed for multiprocessors, since interfaces may have utilization larger than 100% of a single processor, it is not possible to directly use the component interfaces for the system schedulability test. Therefore, the interfaces have to be decomposed before performing the system level schedulability test. In this paper, we target the special case of partitioned EDF for scheduling the components integrated on a multiprocessor. Therefore, the system level schedulability test is equivalent to finding a feasible allocation of component interfaces on the multiprocessor. We propose two algorithms for allocating the multiprocessor periodic interfaces. In addition, we propose an orthogonal approach for developing component-based real-time systems on multiprocessors in which components with utilization more than 100% of a single processor are divided into smaller subcomponents before abstracting their interfaces. We show, through extensive evaluations, that our alternative approach significantly reduces the interface overhead.