The Space of Feasible Execution Times for Asynchronous Periodic Task Systems Using Definitive Idle Times

Sensitivity analysis for real-time systems provides efficient methods to determine feasibility conditions in the case of changes in task parameters, such as different WCET values when porting a system to a different platform. The C-space defines the space of execution times for which a system is feasible, which can help system designers to more easily check if a task set is feasible on a set of candidate platforms. This paper extends previous works generalizing the description of the C-space for Earliest Deadline First scheduling to systems with initial task offsets. The feasibility gain offered by offsets is then expressed as the volume ratio between the C-space of an asynchronous system and its corresponding synchronous system when offsets are randomly chosen. The problem requires solving multiple similar instances of the Chinese Remainder Problem, for which an efficient algorithm in this context is provided. We show that even for random offsets, the gain can reach 15%.