An upper bound to the lateness of soft real-time tasks scheduled by EDF on multiprocessors

Multiprocessors are now commonplace for efficiently achieving high computational power, even in embedded systems. A considerable research effort is being addressed to schedulability analysis of global scheduling in symmetric multiprocessor platforms (SMP), where there is a global queue of ready tasks, and preemption and migration are allowed. In many soft real-time applications (as e.g. multimedia and telecommunication) a bounded lateness is often tolerated. Unfortunately, when considering priority-driven scheduling of periodic/sporadic tasks, previous results only focused on guaranteeing all deadlines, and provided worst-case utilization bounds that are lower than the maximum available computational power. In particular, until now, the existence of an upper bound on the lateness of soft real-time tasks for a fully utilized SMP was still an open problem. In this paper we do solve this problem by providing an upper bound to the lateness of periodic/sporadic tasks - with relative deadlines equal to periods/minimum inter-arrival times - scheduled by EDF on a SMP, under the only assumption that the total utilization is no higher than the total system capacity