Embedded systems are complex as a whole but consist of smaller independent modules minimally interacting with each other. This structure makes embedded systems amenable to compositional system design. Compositional design of real-time embedded systems can be done using hierarchical systems which consist of real-time components arranged in a scheduling hierarchy. Each component consists of a real-time workload and a scheduling policy for the workload. To simplify schedulability analysis of hierarchical systems, analysis can be done compositionally using interfaces that abstract the timing requirements of components. Associative composition will facilitate analysis of systems in which components are modified on the fly. In this paper, we propose efficient algorithms to abstract the resource requirements of components in the form of periodic resource models. Each component interface consists of a set of periodic resource models for different values of period, which allows the selection of a periodic interface that minimizes the collective real-time requirements of hierarchical components. We also describe an interface composition algorithm which accounts for context switch overheads incurred by components and is associative.