Editing Rate-monotonic scheduling (section)

=== Generalization to harmonic chains ===

Kuo and Mok<ref>{{cite book|author=T.-W. Kuo |author2=A.K. Mok |title=&#91;1991&#93; Proceedings Twelfth Real-Time Systems Symposium |chapter=Load adjustment in adaptive real-time systems |year=1991|pages=160–170|doi=10.1109/REAL.1991.160369|isbn=0-8186-2450-7|s2cid=31127772}}</ref> showed that for a task set made up of {{mvar|K}} harmonic task subsets (known as ''harmonic chains''), the least upper bound test becomes:
:<math>U = \sum_{i=1}^{n} \frac{C_i}{T_i} \leq K({2}^{1/K} - 1)</math>
In the instance where for each task, its period is an exact multiple of every other task that has a shorter period, the task set can be thought of as being composed of {{mvar|n}} harmonic task subsets of size 1 and therefore <math>{K}{=}{n}</math>, which makes this generalization equivalent to Liu and Layland's least upper bound.  When <math>{K}{=}{1}</math>, the upper bound becomes 1.0, representing full utilization.