 
Summary: A Schedulable Utilization Bound for the Multiprocessor EPDF Pfair
Algorithm
UmaMaheswari C. Devi and James H. Anderson
Department of Computer Science, The University of North Carolina, Chapel Hill, NC
Abstract
The earliestpseudodeadlinefirst (EPDF) Pfair scheduling algorithm is less expensive than some other known
Pfair algorithms, but is not optimal for scheduling recurrent realtime tasks on more than two processors. In prior
work, sufficient pertask weight (i.e., utilization) restrictions were established for ensuring that tasks either do
not miss their deadlines or have bounded tardiness when scheduled under EPDF. Implicit in these restrictions is
the assumption that the total system utilization may equal the total available processing capacity (i.e., the total
number of processors). This paper considers an orthogonal issue, namely, determining a sufficient restriction on the
total utilization of a task set for it to be schedulable (i.e., a schedulable utilization bound) 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 value represents the worstcase for EPDF, but we do provide a counterexample that shows
that it cannot be improved to exceed 86% of the total processing capacity. The schedulable utilization bound we
derive 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 .
