Near-optimal constant-time admission control for DM tasks via non-uniform approximations

Admission control decisions involve determining whether a new task can be accepted by a running system such that the new task and the already running tasks all meet their deadlines. Since such decisions need to be taken on-line, there is a strong interest in developing fast and yet accurate algorithms for different setups. In this paper, we propose a constant-time admission control test for tasks that are scheduled under the Deadline Monotonic (DM) policy. The proposed test approximates the execution demand of DM tasks using a configurable number of linear segments. The more segments are used, the higher the running time of the test. However, a small number of segments normally suffice for a near-optimal admission control. The main innovation introduced by our test is that approximation segments are distributed in a non-uniform manner. We can concentrate more segments for approximating critical parts of the execution demand and reduce the number of segments where this does not change significantly. In particular, the tasks with shorter deadlines dominate the worst-case response time under DM and, hence, these should be approximated more accurately for a better performance of the algorithm. In contrast to other constant-time tests based on well-known techniques from the literature, our algorithm is remarkably less pessimistic and allows accepting a much greater number of tasks. We evaluate this through detailed experiments based on a large number of synthetic tasks and a case study.