There has been much recent interest in fair scheduling algorithms for real-time multiprocessor systems. The roots of much of the research on this topic can be traced back to the seminal work of Baruah et al. on Proportionate fairness (Pfairness) [6]. This work proved that the problem of optimally scheduling periodic tasks on multiprocessors could be solved on-line in polynomial time by using Pfair scheduling algorithms. Pfair scheduling differs from more conventional real-time scheduling approaches in that tasks are explicitly required to execute at steady rates. In most realtime scheduling disciplines, the notion of a rate is implicit. For example, in a periodic schedule, a task T executes at a rate defined by its required utilization (T.e/T.p) over large intervals. However, T's execution rate over short intervals, e.g., individual periods, may vary significantly. Hence, the notion of a rate under the periodic task model is a bit inexact. Under Pfair scheduling, each task is executed...

The supertask approach was proposed by Moir and Ramamthy as a means of supporting non-migratory tasks in Pfair-scheduled systems. In this approach, tasks bound to the same processor are combined into a single server task, called a supertask, which is scheduled as an ordinary Pfair task. When a supertask is scheduled, one of its component tasks is selected for execution. In previous work, Holman et al. showed that component-task deadlines can be guaranteed by inflating each supertask’s utilization. In addition, their experimental results showed that the required inflation factors should be small in practice. Consequently, the average inflation produced by their rules is much greater than that actually required by the supertasks. In this paper, we first propose a notion of Transient Behavior Prediction for supertasks, which predicts the latest possible finish time of subtasks that belong to supertasks. On the basis of the notion, we present an efficient schedulability algorithm for Pfair supertasks in which the deadlines of all component tasks can be guaranteed. In addition, we propose a task merging process which combines the unschedulable supertasks with some Pfair tasks; hence, a newly supertask can be scheduled in the system. Finally, we propose the new reweighting functions that can be used when the previous two methods fail. Our reweighting functions produce smaller inflation factor than the previous work does. To demonstrate the efficacy of the supertasking approach, we present the experimental evaluations of our algorithm, which decreases substantially a number of reweights and the size of inflation when there are many supertasks in the Pfair-scheduled systems.