In order to analyse such an hierarchical structure for schedulability, various analysis techniques exist. The common one is compositional schedulability analysis (CSA). Component-based design decomposes a system into components allowing the reduction of a single complex system design problem into multiple single system designs. Each component is analysed separately and represented by a component interface that abstracts and hides the internal complexity. These interfaces are used for composing the system for the system analysis.
Real-time systems can benefit from component-based design, if components are assembled without violating timing properties. This requires that the component interfaces include all the timing information.
Both uses this tool:
https://rtg.cis.upenn.edu/carts/