Summary: Fair Scheduling of Real­time Tasks on Multiprocessors
James Anderson, Philip Holman, and Anand Srinivasan
Department of Computer Science, University of North Carolina at Chapel Hill
1 Introduction
There has been much recent interest in fair scheduling algorithms for real­time 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 1 on multiprocessors could be solved on­line in polynomial time
by using Pfair scheduling algorithms. Pfair scheduling di#ers from more conventional real­time
scheduling approaches in that tasks are explicitly required to execute at steady rates. In most real­
time 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 at an approximately uniform rate by breaking it
into a series of quantum­length subtasks. Time is then subdivided into a sequence of (potentially
overlapping) subintervals of approximately equal lengths, called windows. To satisfy the Pfairness
1 A periodic task T is characterized by a phase T.#, an execution requirement T.e, and a period T.p: a job release
(i.e., task invocation) occurs at time T.# + (k - 1) · T.p for each integer k # 1 and the k th job must receive T.e units
of processor time by the next release (at time T.# + k · T.p). A periodic task system is synchronous if each task in

Source: Anderson, James - Department of Computer Science, University of North Carolina at Chapel Hill

Collections: Computer Technologies and Information Sciences