Compositional schedulability analysis of hierarchical scheduling frameworks is a well studied problem, as it has wide-ranging applications in the embedded systems domain. Several techniques, such as periodic resource model based abstraction and composition, have been proposed for this problem. However these frameworks are sub-optimal because they incur bandwidth overhead. In this work, we introduce the Explicit Deadline Periodic (EDP) resource model, and present compositional analysis techniques under EDF and DM. We show that these techniques are bandwidth optimal, in that they do not incur any bandwidth overhead in abstraction or composition. Hence, this framework is more efficient when compared to existing approaches.