Editing Rate-monotonic scheduling (section)

=== Upper bound for harmonic task sets ===

Liu and Layland noted that this bound may be relaxed to the maximum possible value of 1.0, if for tasks <math>{T_m}</math>, <math>{T_i}</math> where <math>{T_m} {>} {T_i}</math> and <math>i = 1...m-1</math>, <math>{T_m}</math> is an integer multiple of <math>{T_i}</math>, which is to say that all tasks have a period that is not just a multiple of the shortest period, <math>{T_1}</math>, but instead that any task's period is a multiple of all shorter periods.  This is known as an [[Harmonic Task Set|harmonic task set]].  An example of this would be:  <math>[{T_1},{T_2},{T_3},{T_4}] = [1, 3, 6, 12]</math>.  It is acknowledged by Liu and Layland that it is not always feasible to have a harmonic task set and that in practice other mitigation measures, such as buffering for tasks with soft-time deadlines or using a dynamic priority assignment approach may be used instead to allow for a higher bound.