In this paper, we show that both global as well as local schedulability analysis of synchronization protocols based on the stack resource policy (SRP) and overrun without payback for hierarchical scheduling frameworks based on fixed-priority preemptive scheduling (FPPS) are pessimistic. We present tighter global and local schedulability analysis, illustrate the improvements of the new analysis by means of examples, and show that the improved global analysis is both uniform and sustainable. We evaluate the new global and local schedulability analysis based on an extensive simulation study and compare the results with the existing analysis