Tight necessary feasibility analysis for recurring real-time tasks on a multiprocessor

One of the important design issues for time-critical embedded systems is to derive necessary conditions that meet all job deadlines invoked by a set of recurring real-time tasks under a computing resource (called feasibility). To this end, existing studies focused on how to derive a tight lower-bound of execution requirement (i.e., demand) of a target set of real-time tasks. In this paper, we address the following question regarding the supply provided by a multiprocessor resource: is it possible for a real-time task set to always utilize all the provided supply? We develop a systematic approach that i) calculates the amount of supply proven unusable, ii) finds a partial schedule that yields a necessary condition to minimize the amount of unusable supply, and iii) uses the partial schedule to further reclaim unusable supply. While the systematic approach can be applied to most (if not all) recurring real-time task models, we show two examples how the approach can yield tight necessary feasibility conditions for the sequential task model and the gang scheduling model. We demonstrate the proposed approach finds a number of additional infeasible task sets which have not been proven infeasible by any existing studies for the task models.