A Schedulable Utilization Bound for the Multiprocessor EPDF Pfair Algorithm

The earliest-pseudo-deadline-first (EPDF) Pfair scheduling algorithm is less expensive than some other knownPfair algorithms, but is not optimal for scheduling recurrent real-time tasks on more than two processors. In priorwork, sufficient per-task weight (i.e., utilization) restrictions were established for ensuring that tasks either donot miss their deadlines or have bounded tardiness when scheduled under EPDF. Implicit in these restrictions isthe assumption that the total system utilization may equal the total available processing capacity (i.e., the totalnumber of processors). This paper considers an orthogonal issue, namely, determining a sufficient restriction on thetotal utilization of a task set for it to be schedulable (i.e., a schedulable utilization bound) under EPDF, assumingthat there are no per-task weight restrictions. We prove that a task set with total utilization at most 3M+14 iscorrectly scheduled under EPDF on M processors, regardless of how large each task’s weight is. At present, we donot know whether this value represents the worst-case for EPDF, but we do provide a counterexample that showsthat it cannot be improved to exceed 86% of the total processing capacity. The schedulable utilization bound wederive is expressed in terms of the maximum weight of any task, and hence, if this value is known, may be used toschedule task sets with total utilization greater than 3M+14 . ∗Work supported by NSF grants CCR 9988327, ITR 0082866, CCR 0204312, CNS 0309825, and CNS 0615197, and by ARO grantW911NF-06-1-0425. The first author was also supported by an IBM Ph.D. fellowship.