Deriving period restrictions from a given utilization bound under RMS

We propose a new method to compute period choice restrictions based on a given maximum number of tasks in a task set, some pre-set period values, and a goal utilization bound ensuring the meeting of all deadlines under preemptive Rate-monotonic Scheduling (RMS) on a uniprocessor. The new approach is motivated by demonstrating that a safe utilization bound can be significantly increased by taking period configuration data into account. The two well-known approaches of the period-independent Liu/Layland bound and the harmonic chain method restriction which enforces new periods to be integer multiples or parts of pre-set periods are discussed. It will turn out that our new approach can serve as a trade-off balancing the two goals of a weak period choice restriction and a high utilization bound. Subsequently, we justify and demonstrate it by several examples and derive some rules of thumb.