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