Non-Schedulability Conditions for Off-line Scheduling of Real-Time Systems Subject to Precedence and Strict Periodicity Constraints

Classical off-line approaches based on preemption such as RM (rate monotonic), DM (deadline monotonic), EDF (earliest deadline first), LLF (least laxity first), etc, give schedulability conditions but most of the time assuming on the one hand that all the tasks are independent, and on the other hand, that the first instances of all tasks are released at the same time. We are interested in hard real-time systems subject to precedence and strict periodicity constraints, i.e. such that for all instances of each task, the release time and start time are equal. For such systems, it is mandatory to satisfy these constraints. In this paper we give non-schedulability conditions in order to restrict the study field of all systems of tasks to only potentially schedulable systems.