Schedulable Utilization Bounds for EPDF Fair Multiprocessor Scheduling

The earliest-pseudo-deadline-first (EPDF) algorithm is less expensive than other known Pfair algorithms, but is not optimal for scheduling recurrent real-time tasks on more than two processors. Prior work established sufficient per-task weight (i.e., utilization) restrictions that ensure that tasks either do not miss their deadlines or have bounded tardiness when scheduled under EPDF. Implicit in these restrictions is the assumption that total system utilization may equal the total available processing capacity (i.e., the total number of processors). This paper considers an orthogonal issue — that of determining a sufficient restriction on the total utilization of a task set for it to be schedulable under EPDF, assuming that there are no per-task weight restrictions. We prove that a task set with total utilization at most 3M+1 4 is correctly scheduled under EPDF on M processors, regardless of how large each task’s weight is. At present, we do not know whether this bound is tight. However, we provide a conterexample that shows that it cannot be improved to exceed 86% of the total processing capacity. Our schedulability test is expressed in terms of the maximum weight of any task, and hence, if this value is known, may be used to schedule task sets with total utilization greater than 3M+1 4 . ∗Work supported by NSF grants CCR 9988327, ITR 0082866, CCR 0204312, and CCR 0309825.