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 ...