Schedulability of generalized multiframe task sets under static priority assignment

The multiframe task model has been proposed recently to effectively model a task whose execution times are periodically changed according to a specified pattern. Schedulability of task sets consisting of multiframe tasks or generalized multiframe tasks (GMF task) is now being investigated under various conditions. This paper discusses the necessary and sufficient condition of the schedulability of GMF task sets under a priority-based preemptive scheduling with static priority assignment. The critical instant theorem for GMF task sets is described and the necessary and sufficient condition of their schedulability is presented based on the theorem. We also introduce the maximum interference function (MIF) and propose a polynomial-time feasibility decision algorithm using the MIF.