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The increasing acceptance of the Earliest Deadline First (EDF) scheduling algorithm in industrial environments, together with the continued usage of Fixed Priority (FP) scheduling is leading to heterogeneous systems with different scheduling policies in the same distributed system. Schedulability analysis techniques usually consider the entire system as a whole (holistic approach), with only one preestablished scheduling policy in all the resources. In this work, composition mechanisms will be presented that enable us to combine different FP and EDF response-time analysis techniques for checking the schedulability of heterogeneous systems. Additionally, priority and scheduling deadline assignment techniques will be combined into a new algorithm called HOSPA (Heuristic Optimized Scheduling Parameters Assignment), for optimizing the assignment of priorities and scheduling deadlines to tasks and messages in heterogeneous distributed hard real-time systems.