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We present our ongoing work on synchronization in hierarchical scheduled real-time systems, where tasks are scheduled using fixed-priority pre-emptive scheduling. In this paper, we show that the original local schedulability analysis of the synchronization protocol SIRAP  is very pessimistic when tasks of a subsystem access many global shared resources. The analysis therefore suggests that a subsystem requires more CPU resources than necessary. A new way to perform the schedulability analysis is presented which can make the SIRAP protocol more efficient in terms of calculated CPU resource needs.