On non-preemptive scheduling of period and sporadic tasks

This paper examines a fundamental problem in the theory of real-time scheduling, that of scheduling a set of periodic or sporadic tasks on a uniprocessor without preemption and without inserted idle time. We exhibit a necessary and sufficient set of conditions C for a set of periodic or sporadic tasks to be schedulable for arbitrary release times of the tasks. We then show that any set of periodic or sporadic tasks that satisfies conditions C can be scheduled with an earliest deadline first (EDF) scheduling algorithm. We also address the question of schedulability of a set of tasks with specified release times. For sets of sporadic tasks with specified release times, we show that the conditions C are again necessary and sufficient for schedulability. However, for sets of periodic tasks with specified release times, the conditions C, while sufficient, are not necessary. In fact, we show that determining whether a set of periodic tasks with specified release times is schedulable is intractable (i.e., NP-hard in the strong sense). Moreover, we show that the existence of a universal algorithm for scheduling periodic tasks with specified release times would imply that P = NP.