On-line scheduling on uniform multiprocessors

Abstract

Each processor in a uniform multiprocessor machine is characterized by a speed or computing capaciQ, with the interpretation that a job executing on a processor with speed s for t time units completes (s x t ) units of execution. The on-line scheduling of hard-real-time systems, in which all jobs must complete by specijied deadlines, on uniform multiprocessor machines is considered. It is known that online algorithms tend to perform very poorly in scheduling such hard-real-time systems on multiprocessors; resourceaugmentation techniques are presented here that permit online algorithms to perform better than may be expected given the inherent limitations. Results derived here are applied to the scheduling of periodic task systems on uniform multiprocessor machines.A taxonomy of multiprocessor platforms. In much previous work concerning hard-real-time scheduling on multiprocessors, it has been assumed that all processors are identical. However, scheduling theorists distinguish between at least three different kinds of multiprocessor machines: Identical parallel machines: These are multiprocessors in which all the processors are identical, in the sense that they have the same computing power. Uniform parallel machines:By contrast, each processor in a uniform parallel machine is characterized by its own computing capacity, with the interpretation that a job that executes on a processor of computing capacity s for t time units completes s x t units of execution. (Observe that identical parallel machines are a special case of uniform parallel machines, in which the computing capacities of all processors are equal.) 183 0-7695-1420-0101 $17.00 0 2001 IEEE

Competitive Analysis of Partitioned Scheduling on Uniform Multiprocessors

“…it holds that : there is at least one task assigned to processor p. (9) We have that Fact 1 is true.…”

“…A speed competitive ratio has already been proven for scheduling real-time tasks on uniform multiprocessors [9,6]; one of the algorithms has a speed competitive ratio of two [9]. In addition it has the advantage of being proven not just for the sporadic task model but for the more generic model of aperiodic jobs where the scheduling algorithm has no knowledge of jobs arriving in the future.…”

Multi-core real-time scheduling for generalized parallel task models

“…Since our model is a generalization of theirs, this lower bound still holds for our tasks. Since conventional utilization bound approaches are not useful for schedulability analysis of parallel tasks, we (like [4]) use the resource augmentation bound approach, originally introduced in [7]. We first consider global scheduling where tasks are allowed to migrate among processor cores.…”

A General Framework for Parameterized Schedulability Bound Analysis of Real-Time Systems

“…The most notable results are for periodic tasks, including 69 percent (and extensions) for the Rate/Deadline Monotonic scheduler (RMS/DMS) [2], [3], [4], [5], [6], [7], [8]; 100 percent for Earliest Deadline First scheduler (EDF) [5]; 33 percent for the Timed Token Protocol (TTP) [9], [10], [11]; etc. Utilization bounds of RMS/DMS in multiprocessor systems have also been derived in [12], [13], [14], [15], [16], [17]. Some important utilization bounds for nonperiodic systems are derived in [18], [19], [20], [21].…”