For periodic task sets on a uniprocessor, the optimal fixed-priority
scheduling algorithm is rate-monotonic scheduling (RMS). The shorter a
task's period, the higher is its priority. For simply-periodic task sets,
RMS achieves a utilization bound of 1. But this drops to the famous
Liu/Layland bound of ca. 0.69 in the general case.
The Burchard test calculates a refined utilization bound based on the
period configuration. This test uses linear range of so-called S values for
describing period compatibility. It will be shown how a change to circular
range can ensure the natural requirement of scale invariance, give higher
sensitivity, and -- as a side effect -- simplify the Burchard test formula.
Using circular range for a more precise description of period compatibility for
rate-monotonic schedulability tests