 
Summary: Schedulable Utilization Bounds for EPDF Fair Multiprocessor Scheduling
UmaMaheswari C. Devi and James H. Anderson
Department of Computer Science, The University of North Carolina, Chapel Hill, NC
Abstract
The earliestpseudodeadlinefirst (EPDF) algorithm is less expensive than other known Pfair algorithms, but is not
optimal for scheduling recurrent realtime tasks on more than two processors. Prior work established sufficient pertask
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 pertask 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.
1 Introduction
We consider the scheduling of recurrent (i.e., periodic, sporadic, or ratebased) realtime task systems on multiprocessor
