A Schedulable Utilization Bound for Aperiodic Tasks

In this paper, we derive a utilization bound on schedulability of apriodic tasks with arbitrary arrival times, execution times, and deadlines. To the author's knowledge, this is the rst time a utilization bound is derived for the aperiodic task model. It allows constructing an O(1) admission test for aperiodic tasks. Earlier admission tests are at best O(n). We show that deadline-monotonic scheduling is the optimal xed-priority scheduling policy for aperiodic tasks in the sense of maximizing the schedulable utilization bound. We prove that the optimal bound is 5=8. Our result is an extension of the well-known Liu and Layland's bound of ln 2 (derived for periodic tasks). The new bound is shown to be tight. We brieey generalize our results to tasks with multiple resource requirements and multiple processors. Dynamic priority scheduling (EDF) of aperiodic tasks is shown to have the same schedulability bound as for periodic tasks. Our ndings are especially useful for an emerging category of soft real-time applications, such as online trading and e-commerce, where task (request) arrival times are arbitrary, task service times are unknown, and service has to be performed within a given deadline. Our result provides theoretical grounds for guaranteeing deadlines of individual aperiodic requests by observing only the aggregate utilization conditions which simpliies achieving real-time assurances in such applications.