A Stretching Algorithm for Parallel Real-time DAG Tasks on Multiprocessor Systems

International audienceParallelism is becoming more important nowadays due to the increasing use of multiprocessor systems. In this paper, we study the problem of scheduling periodic parallel real-time Directed Acyclic graph (DAG) tasks on m homogeneous multiprocessor systems. A DAG task is an example of inter-subtask parallelism. It consists of a collection of dependent subtasks under precedence constraints. The dependencies between subtasks make scheduling process more challenging. We propose a stretching algorithm applied on each DAG tasks to transform them into a set of independent sequential threads with intermediate offsets and deadlines. The threads obtained with the transformation are two types, (i) fully-stretched master threads with utilization equal to 1 and (ii) constrained-deadline independent threads. The fully-stretched master threads are assigned to dedicated processors and the remaining processors m' ≤ m, are scheduled using global EDF scheduling algorithm. Then, we prove that preemptive global EDF scheduling of stretched threads has a resource augmentation bound equal to (3+ √ 5)/2 for all tasksets with n < ϕ * m , where n is the number of tasks in the taskset and ϕ is the golden ratio 1

Global EDF scheduling of directed acyclic graphs on multiprocessor systems

International audienceIn this paper, we study the problem of real-time scheduling of parallel tasks represented by a Directed Acyclic Graph (DAG) on multiprocessor architectures. We focus on Global Earliest Deadline First scheduling of sporadic DAG tasksets with constrained-deadlines on a system of homogeneous processors. Our contributions consist in analyzing DAG tasks by considering their internal structures and providing a tighter bound on the workload and interference analysis. This approach consists in assigning a local offset and deadline for each subtask in the DAG. We derive an improved sufficient schedulability test w.r.t. an existing test proposed in the state of the art. Then we discuss the sustainability of this test

Global EDF Scheduling for Parallel Real-Time Tasks

As multicore processors become ever more prevalent, it is important for real-time programs to take advantage of intra-task parallelism in order to support computation-intensive applications with tight deadlines. In this thesis, we consider the Global Earliest Deadline First (GEDF) scheduling policy for task sets consisting of parallel tasks. Each task can be represented by a directed acyclic graph (DAG) where nodes represent computational work and edges represent dependences between nodes. In this model, we prove that GEDF provides a capacity augmentation bound of 4-2/m and a resource augmentation bound of 2-1/m. The capacity augmentation bound acts as a linear-time schedulability test since it guarantees that any task set with total utilization of at most m/(4-2/m) where each task\u27s critical-path length is at most 1/(4-2/m) of its deadline is schedulable on m cores under GEDF. In addition, we present a pseudo-polynomial time fixed-point schedulability test for GEDF; this test uses a carry-in work calculation based on the proof for the capacity bound. Finally, we present and evaluate a prototype platform --- called PGEDF --- for scheduling parallel tasks using GEDF. PGEDF is built by combining the GNU OpenMP runtime system and the LITMUS_RT operating system. This platform allows programmers to write parallel OpenMP tasks and specify real-time parameters such as deadlines for tasks. We perform two kinds of experiments to evaluate the performance of GEDF for parallel tasks. (1) We run numerical simulations for DAG tasks. (2) We execute randomly generated tasks using PGEDF. Both sets of experiments indicate that GEDF performs surprisingly well and outperforms an existing scheduling techniques that involves task decomposition

Capacity Augmentation Bound of Federated Scheduling for Parallel DAG Tasks

We present a novel federated scheduling approach for parallel real-time tasks under a general directed acyclic graph (DAG) model. We provide a capacity augmentation bound of 2 for hard real-time scheduling; here we use the worst-case execution time and critical-path length of tasks to determine schedulability. This is the best known capacity augmentation bound for parallel tasks. By constructing example task sets, we further show that the lower bound on capacity augmentation of federated scheduling is also 2 for any m \u3e 2. Hence, the gap is closed and bound 2 is a strict bound for federated scheduling. The federated scheduling algorithm is also a schedulability test that often admits task sets with utilization much greater than 50%m

Reservation-Based Federated Scheduling for Parallel Real-Time Tasks

This paper considers the scheduling of parallel real-time tasks with arbitrary-deadlines. Each job of a parallel task is described as a directed acyclic graph (DAG). In contrast to prior work in this area, where decomposition-based scheduling algorithms are proposed based on the DAG-structure and inter-task interference is analyzed as self-suspending behavior, this paper generalizes the federated scheduling approach. We propose a reservation-based algorithm, called reservation-based federated scheduling, that dominates federated scheduling. We provide general constraints for the design of such systems and prove that reservation-based federated scheduling has a constant speedup factor with respect to any optimal DAG task scheduler. Furthermore, the presented algorithm can be used in conjunction with any scheduler and scheduling analysis suitable for ordinary arbitrary-deadline sporadic task sets, i.e., without parallelism

Energy-Efficient Multi-Core Scheduling for Real-Time DAG Tasks

In this work, we study energy-aware real-time scheduling of a set of sporadic Directed Acyclic Graph (DAG) tasks with implicit deadlines. While meeting all real-time constraints, we try to identify the best task allocation and execution pattern such that the average power consumption of the whole platform is minimized. To the best of our knowledge, this is the first work that addresses the power consumption issue in scheduling multiple DAG tasks on multi-cores and allows intra-task processor sharing. We first adapt the decomposition-based framework for federated scheduling and propose an energy-sub-optimal scheduler. Then we derive an approximation algorithm to identify processors to be merged together for further improvements in energy-efficiency and to prove the bound of the approximation ratio. We perform a simulation study to demonstrate the effectiveness and efficiency of the proposed scheduling. The simulation results show that our algorithms achieve an energy saving of 27% to 41% compared to existing DAG task schedulers