We present a compositional framework for the specification and analysis of hierarchical scheduling systems (HSS). Firstly we provide a generic formal model, which can be used to describe any type of scheduling system. The concept of Job automata is introduced in order to model job instantiation patterns. We model the interaction between different levels in the hierarchy through the use of state-based resource models. Our notion of resource model is general enough to capture multi-core architectures, preemptiveness and non-determinism.