Period Fitting for Rate-monotonic Scheduling Using a Circular Similarity Measure

For Rate-monotonic Scheduling (RMS) on uniprocessor, there is a steady transition between the two extremes Liu/Layland worst case and simply periodic task set (best case) in terms of utilization bound. The degree of harmonicity is only based on period ratios. Hence, scale invariance is a required property of an appropriate period similarity measure. A standard approach to describe harmonicity is based on the linear range ß of S values, the fractional parts of period logarithms [1]. But linear range is not scale-invariant. We suggest to replace it by circular range in order to obtain better and more consistent utilization bounds.