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.

Abstract-A multiprocessor scheduling algorithm named U-EDF, was presented in [1] for the scheduling of periodic tasks with implicit deadlines. It was claimed that U-EDF is optimal for periodic tasks (i.e., it can meet all deadlines of every schedulable task set) and extensive simulations showed a drastic improvement in the number of task preemptions and migrations in comparison to state-of-the-art optimal algorithms. However, there was no proof of its optimality and U-EDF was not designed to schedule sporadic tasks.In this work, we propose a generalization of U-EDF for the scheduling of sporadic tasks with implicit deadlines, and we prove its optimality. Contrarily to all other existing optimal multiprocessor scheduling algorithms for sporadic tasks, U-EDF is not based on the fairness property. Instead, it extends the main principles of EDF so that it achieves optimality while benefiting from a substantial reduction in the number of preemptions and migrations.

Over the past two decades, numerous optimal scheduling algorithms for real-time systems on multiprocessor platforms have been proposed for the Liu & Layland task model. However, recent studies showed that even if optimal algorithms can theoretically schedule any feasible task set, suboptimal algorithms usually perform better when executed on real computation platforms. This can be explained by the runtime overheads that such optimal algorithms induce.We have observed that all current optimal online multiprocessor real-time scheduling algorithms are (completely or partially) based on the notion of fairness. The respect of this fairness can be the cause of numerous preemptions and migrations.We therefore propose a new algorithm -named U-EDFwhich releases the property of fairness and instead use an EDFlike scheduling policy.The simulation results are really encouraging since they show that, in average, U-EDF produces less than one preemption and one migration per job released during the schedule. Furthermore, we strongly believe in the optimality of our algorithm since all tested task sets were correctly scheduled under U-EDF.

Scheduling stochastic workloads is a difficult task. In order to design efficient scheduling algorithms for such workloads, it is required to have a good in-depth knowledge of basic random scheduling strategies. This paper analyzes the distribution of sequential jobs and the system behavior in heterogeneous computational grid environments where the brokering is done in such a way that each computing element has a probability to be chosen proportional to its number of CPUs and (new from the previous paper) its relative speed. We provide the asymptotic behavior for several metrics (queue sizes, slowdowns, etc.) or, in some cases, an approximation of this behavior. We study these metrics for a variety of workload configurations (load, distribution, etc.). We compare our probabilistic analysis to simulations in order to validate our results. These results provide a good understanding of the system behavior for each metric proposed. This will enable us to design advanced and efficient algorithms for more complex cases.

Energy-efficient real-time task scheduling has been actively explored in the past decade. Different from the past work, this paper considers schedulability conditions for stochastic real-time tasks. A schedulability condition is first presented for frame-based stochastic real-time tasks, and several algorithms are also examined to check the schedulability of a given strategy. An approach is then proposed based on the schedulability condition to adapt a continuous-speed-based method to a discrete-speed system. The approach is able to stay as close as possible to the continuous-speed-based method, but still guaranteeing the schedulability. It is shown by simulations that the energy saving can be more than 20% for some system configurations.