The Aperiodic Multiprocessor Utilization Bound for Liquid Tasks

Real-time scheduling theory has developed powerful tools for translating conditions on aggregate system utilization into per-task schedulability guarantees. The main breakthrough has been Liu and Layland’s utilization bound for schedulability of periodic tasks. In 2001 this bound was generalized by Abdelzaher and Lu to the aperiodic task case. In this paper, we further generalize the aperiodic bound to the case of multiprocessors, and present key new insights into schedulability analysis of aperiodic tasks. We consider a special task model, called the liquid task model, representative of high-performance servers with aperiodic workloads, such as network routers, web servers, proxies, and real-time databases. For this model, we derive the optimal multiprocessor utilization bound, defined on a utilization-like metric we call “synthetic utilization”. This bound allows developing constant-time admission control tests that provide utilization-based absolute delay guarantees. We show that the real utilization of admitted tasks can be close to unity even when synthetic utilization is kept below the bound. Thus, our results lead to multiprocessor systems which combine constant-time admission control with high utilization while making no periodicity assumptions regarding the task arrival pattern.