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

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Each processor in a uniform multiprocessor machine is characterized by a speed or computing capacity, with the interpretation that a job executing on a processor with speed s for t time units completes (s × t) units of execution. The scheduling of systems of periodic tasks on uniform multiprocessor platforms using the rate-monotonic scheduling algorithm is considered here. A simple, sufficient test is presented for determining whether a given periodic task system will be successfully scheduled by algorithm upon a particular uniform multiprocessor platform-this test generalizes earlier results concerning rate-monotonic scheduling upon identical multiprocessor platforms.

Abstract-These last years, we have witnessed a dramatic increase in the number of cores available in computational platforms. Concurrently, a new coding paradigm dividing tasks into smaller execution instances called threads, was developed to take advantage of the inherent parallelism of multiprocessor platforms. However, only few methods were proposed to efficiently schedule hard real-time multi-threaded tasks on multiprocessor.In this paper, we propose techniques optimizing the number of processors needed to schedule such sporadic parallel tasks with constrained deadlines. We first define an optimization problem determining, for each thread, an intermediate (artificial) deadline minimizing the number of processors needed to schedule the whole task set. The scheduling algorithm can then schedule threads as if they were independent sequential sporadic tasks. The second contribution is an efficient and nevertheless optimal algorithm that can be executed online to determine the thread's deadlines. Hence, it can be used in dynamic systems were all tasks and their characteristics are not known a priori. We finally prove that our techniques achieve a resource augmentation bound of 2 when the threads are scheduled with algorithms such as U-EDF, PD 2 , LLREF, DP-Wrap, etc.

We investigate the global scheduling of sporadic, implicit deadline, real-time task systems on multiprocessor platforms. We provide a task model which integrates job parallelism. We prove that the time-complexity of the feasibility problem of these systems is linear relatively to the number of (sporadic) tasks for a fixed number of processors. We propose a scheduling algorithm theoretically optimal (i.e., preemptions and migrations neglected). Moreover, we provide an exact feasibility utilization bound. Lastly, we propose a technique to limit the number of migrations and preemptions.