Embedded systems are complex as a whole but consist of smaller independent modules interacting with each other. This structure makes embedded systems amenable to compositional design. Real-time embedded systems consist of real-time workloads having temporal deadlines. Compositional design of real-time embedded systems can be done using systems consisting of real-time components arranged in a scheduling hierarchy. Each component consists of some real-time workload and a scheduling policy for the workload. To simplify schedulability analysis for such systems, analysis can be done compositionally using interfaces that abstract the timing requirements of components. To facilitate analysis of dynam- ically changing real-time systems, the framework must support incremental analysis. In this paper, we summarize our work [19, 6] on schedulability analysis for hierarchical real-time systems. We describe a compositional analysis technique that abstracts resource requirements of components using periodic resource models. To support incremental analysis and resource bandwidth minimization, we describe an extension to this interface model. Each extended interface consists of multiple periodic resource models for different periods. This allows the selection of a periodic model that can schedule the system using minimum bandwidth. We also account for context switch overheads in these interfaces. We then describe an associative composition technique for such interfaces that supports incremental analysis.