We present our ongoing work on synchronization in hierarchicalscheduled real-time systems, where tasks arescheduled using fixed-priority pre-emptive scheduling. Inthis paper, we show that the original local schedulabilityanalysis of the synchronization protocol SIRAP is verypessimistic when tasks of a subsystem access many globalshared resources. The analysis therefore suggests that asubsystem requires more CPU resources than necessary. Anew way to perform the schedulability analysis is presentedwhich can make the SIRAP protocol more efficient in termsof calculated CPU resource needs.