Generating Bounded Task Periods for Experimental Schedulability Analysis

Schedulability analysis models in embedded and real-time systems are experimentally validated using synthetic task sets, which are generated using random or pseudo-random selection algorithms. Validation of these schedulability models generally requires analyzing release of all jobs of tasks within a defined interval called the feasibility interval of the task set. The length of this interval is dependent on the hyper-period, which is the least common multiple of task periods. Hence, the time taken in experimental validations is directly proportional to the value of hyper-period, apart from the number and size of task sets. Currently, if tasks period values with low hyper-period are required, the only way to generate them is using manual or ad-hoc methods. In this paper, we present a structured method of selecting task period values from within a user-specified bounded range such that the hyper-period values of these task sets is minimized. Formula to compute maximum number of task sets of different sizes that can be generated is also derived. Finally, comparisons of hyper-period values generated from a bounded range using random selection and our method are presented.