Quantifying the sub-optimality of uniprocessor fixed-priority scheduling

There are sporadic task systems schedulable by EDF, which no fixed-priority (FP) algorithm can schedule successfully. For instance, it is known that while all implicit-deadline sporadic task systems with utilization at most one are EDF-schedulable on a unit-capacity uniprocessor, there are implicit-deadline sporadic task systems that are not schedulable by any FP algorithm, and have utilization exceeding ln 2 (approx. 0.69) by an arbitrarily small amount. A quantitative metric of the relative effectiveness of fixed-priority scheduling of constrained-deadline sporadic task systems is derived here, which generalizes this well-known 0.69 utilization bound for implicit-deadline systems.