The Grid 2: Blueprint for a New Computing Infrastructure

Multi-core processors offer a significant performance increase over single-core processors. They have the potential to enable computation-intensive real-time applications with stringent timing constraints that cannot be met on traditional single-core processors. However, most results in traditional multiprocessor real-time scheduling are limited to sequential programming models and ignore intra-task parallelism. In this paper, we address the problem of scheduling periodic parallel tasks with implicit deadlines on multi-core processors. We first consider a synchronous task model where each task consists of segments, each segment having an arbitrary number of parallel threads that synchronize at the end of the segment. We propose a new task decomposition method that decomposes each parallel task into a set of sequential tasks. We prove that our task decomposition achieves a resource augmentation bound of 4 and 5 when the decomposed tasks are scheduled using global EDF and partitioned deadline monotonic scheduling, respectively. Finally, we extend our analysis to a directed acyclic graph (DAG) task model where each node in the DAG has a unit execution requirement. We show how these tasks can be converted into synchronous tasks such that the same decomposition can be applied and the same augmentation bounds hold. Simulations based on synthetic workload demonstrate that the derived resource augmentation bounds are safe and sufficient.

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

Multi-core processors offer a significant performance increase over single core processors. Therefore, they have the potential to enable computation-intensive real-time applications with stringent timing constraints that cannot be met on traditional single-core processors. However, most results in traditional multiprocessor real-time scheduling are limited to sequential programming models and ignore intra-task parallelism. In this paper, we address the problem of scheduling periodic parallel tasks with implicit deadlines on multi-core processors. We first consider a synchronous task model where each task consists of segments, each segment having an arbitrary number of parallel threads that synchronize at the end of the segment. We propose a new task decomposition method that decomposes each parallel task into a set of sequential tasks. We prove that our task decomposition achieves a resource augmentation bound of 2.62 and 3.42 when the decomposed tasks are scheduled using global EDF and partitioned deadline monotonic scheduling, respectively. Finally, we extend our analysis to directed a cyclic graph tasks. We show how these tasks can be converted into synchronous tasks such that the same transformation can be applied and the same augmentation bounds hold.

/pdf/multi-core-real-time-scheduling-for-generalized-parallel-qegq1ffeg7.pdf

Multi-core Real-Time Scheduling for Generalized Parallel Task Models

Recently, multi-core processors have become mainstream in processor design. To take full advantage of multi-core processing, computation-intensive real-time systems must exploit intra-task parallelism. In this paper, we address the problem of real-time scheduling for a general model of deterministic parallel tasks, where each task is represented as a directed acyclic graph (DAG) with nodes having arbitrary execution requirements. We prove processor-speed augmentation bounds for both preemptive and non-preemptive real-time scheduling for general DAG tasks on multi-core processors. We first decompose each DAG into sequential tasks with their own release times and deadlines. Then we prove that these decomposed tasks can be scheduled using preemptive global EDF with a resource augmentation bound of 4. This bound is as good as the best known bound for more restrictive models, and is the first for a general DAG model. We also prove that the decomposition has a resource augmentation bound of 4 plus a constant non-preemption overhead for non-preemptive global EDF scheduling. To our knowledge, this is the first resource augmentation bound for non-preemptive scheduling of parallel tasks. Finally, we evaluate our analytical results through simulations that demonstrate that the derived resource augmentation bounds are safe in practice.

/pdf/parallel-real-time-scheduling-of-dags-1ed3ddpvi2.pdf

Parallel Real-Time Scheduling of DAGs

A model is considered for representing recurrent precedence-constrained tasks that are to execute on multiprocessor platforms. A recurrent task is specified as a directed a cyclic graph (DAG), a period, and a relative deadline. Each vertex of the DAG represents a sequential job, while the edges of the DAG represent precedence constraints between these jobs. All the jobs of the DAG are released simultaneously and need to complete execution within the specified relative deadline of their release. The task may release jobs in this manner an unbounded number of times, with successive releases occurring at least the specified period apart. The scheduling problem is to determine whether such a recurrent task can be scheduled to always meet all deadlines upon a specified number of processors that are dedicated for the use of this task. This problem is shown to be computationally intractable, but amenable to efficient approximate solutions. EDF is shown to be a good approximate scheduling algorithm. Polynomial and pseudo-polynomial schedulability tests, of differing effectiveness, are presented for determining whether a given task can be scheduled by EDF to always meet all deadlines on a specified number of processors.

/pdf/a-generalized-parallel-task-model-for-recurrent-real-time-41qgczpx9z.pdf

A Generalized Parallel Task Model for Recurrent Real-time Processes

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.

/pdf/techniques-optimizing-the-number-of-processors-to-schedule-2g7iggh4zn.pdf

Techniques Optimizing the Number of Processors to Schedule Multi-threaded Tasks

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 enables us to design advanced and efficient algorithms for more complex cases.

https://hal.inria.fr/inria-00070508/document

On the distribution of sequential jobs in random brokering for heterogeneous computational grids

In this paper we consider the scheduling of periodic and parallel rigid tasks. We provide (and prove correct) an exact schedulability test for Fixed Task Priority (FTP) Gang scheduler sub-classes: Parallelism Monotonic, Idling, Limited Gang, and Limited Slack Reclaiming. Additionally, we study the predictability of our schedulers: we show that Gang FJP schedulers are not predictable and we identify several sub-classes which are actually predictable. Moreover, we extend the definition of rigid, moldable and malleable jobs to recurrent tasks.

Gang FTP scheduling of periodic and parallel rigid real-time tasks

Over the past two decades, numerous optimal scheduling algorithms for real-time systems on multiprocessor platforms have been proposed for the Liu \& Lay land 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-EDF -- which releases the property of fairness and instead use an EDF-like 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.

Reducing Preemptions and Migrations in Real-Time Multiprocessor Scheduling Algorithms by Releasing the Fairness

In the past decade, the development of multicore and multiprocessor platforms attracted a lot of attention in the real-time community. At first, researchers considered several ways to take advantage of this kind of platform to process sequential tasks. Over the past few years, people started considering parallel tasks to take even better profit of this new architecture, or to save energy. There are several families of parallel tasks. One of them is the “Thread” model, where threads can run (rather) independently [4]. Another one is the “Gang” family, requiring that all threads start and stop using the processors synchronously. Tasks can then be seen as rectangles, where the width represent the time, and the height the number of processors. As presented in [2], the Gang task family can be split in three sub-families: rigid tasks [2, 3], Malleable [1] and Moldable. In the latter, considered in this paper, the scheduler chooses the number of processors for each job1, and this number does not vary with time for a given job (but may be different for two jobs of the same task), we propose algorithms and sufficient schedulability conditions in this research. As far as we know, this is the first paper studying moldable tasks for real-time systems.

Gang fixed priority scheduling of periodic moldable real-time tasks

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