In recent years, several synchronization protocols for resource sharing have been presented for use in a Hierarchical Scheduling Framework (HSF). An initial comparative assessment of existing protocols revealed that none of the protocols is superior to the others and that the performance of a protocol heavily depends on system parameters. In this paper, we aim at efficiency improvements of the synchronization protocol SIRAP [5] and its associated schedulability analysis, where efficiency refers to calculated CPU resource needs. The contribution of the paper is threefold. Firstly, we present an improvement of the schedulability analysis for SIRAP, which makes SIRAP more efficient. Secondly, we generalize SIRAP by distinguishing separate reso...