Complex real-time embedded systems can be developed using component based design methodologies. Timing requirements of real-time components in the system can be modeled using hierarchical frameworks to capture resource sharing among components under different schedulers. To support component based design for real-time embedded systems, we must then address schedulability analysis of hierarchical scheduling models. In this paper, we propose a generic interface algebra for compositional schedulability analysis of such models. We also define conditions under which this algebra supports incremental analysis, dynamic adaptability, and independent implementability. Furthermore, we also propose a novel periodic resource model based framework for compositional and incremental schedulability analysis of hierarchical scheduling models. This extends our earlier proposed framework with a technique that allows periodic resource models with different periods to be composed together. We formulate this framework in our proposed algebra to demonstrate ease of use of the algebra and to identify framework properties.