Nonutilization Bounds and Feasible Regions for Arbitrary Fixed-Priority Policies

Prior research on schedulability bounds focused primarily on bounding utilization as a means to meet deadline constraints. Nontrivial bounds were found for a handful of scheduling policies in which utilization is directly related to the ability of the policy to meet deadlines. Examples include rate-monotonic, deadline-monotonic, and EDF scheduling. For most other scheduling policies, however, utilization is not correlated with schedulability. For example, shortest-job-first can miss deadlines at an arbitrarily low utilization. This raises the question of whether or not some other nonutilization-based metric might be more indicative of schedulability in those cases. This article answers the above question positively by extending the notion of schedulability bounds, in a uniform manner, to arbitrary (fixed) priorities and nonutilization metrics. We present a simple function that generates the schedulability metric to be bounded from the definition of a fixed-priority scheduling policy, and derive a nontrivial schedulability bound on that metric for aperiodic tasks. It is shown that the generated metrics and bounds are valid in that no deadline misses occur when these bounds are not violated. This result allows efficient real-time admission control to be performed in systems with arbitrary fixed-priority scheduling policies. As an example, we illustrate applying schedulability bounds for admission control to shortest-job-first and velocity-monotonic scheduling. While the proposed nonutilization bounds and feasible regions are derived for fixed-priority scheduling policies, the authors are investigating extensions of the results to dynamic-priority scheduling.