Quantifying the Effect of Period Ratios on Schedulability of Rate Monotonic

In this paper, we study the effect of period ratio and utilization of the tasks on the schedulability of rate monotonic (RM) in uni-processor systems with preemptive periodic or sporadic tasks. By quantifying this effect, we show that there exist other task sets (other than harmonic tasks in which each period is an integer multiple of the smaller periods) which are RM-friendly, i.e., they can be scheduled by RM up to 100% utilization. Furthermore, in order to quantify non-RM-friendly task sets, we derive a necessary schedulability test for RM. Our results can be used as a set of design hints for system designers during the parameter assignment phase where periods are assigned. We also show how our results can be used to reduce the computational cost of the schedulability analysis if particular properties hold between the periods. From theoretical perspective, our work improves the understanding about outputs of different random task set generation methods. We provide examples to show how the hidden effect of period ratio may lead to an inaccurate judgment about RM schedulability.