Improved Tardiness Bounds for Global EDF

The Earliest Deadline First scheduling algorithm (EDF) is known to not be optimal under global scheduling on multiprocessor platforms. Results have been obtained that bound the maximum tardiness– the amount of time by which deadlines may be missed– of any feasible system of implicit-deadline sporadic tasks scheduled using global EDF. However, it is known that these bounds are not tight. In this paper, we derive an algorithm for obtaining tardiness bounds that are superior to previously known bounds. In contrast to prior algorithms, which compute a single tardiness bound for all the tasks in the system, our algorithm derives a separate tardiness bound for each task. Particularly upon task systems in which the parameters of the tasks are very dissimilar, our bounds are significantly better than prior bounds. Our algorithm also yields a simple sufficient test for the tardiness verification problem: given a task system with maximum acceptable tardiness bounds per task, is the system guaranteed to be scheduled by global EDF such that these tardiness constraints are not violated?