A Stretching Algorithm for Parallel Real-time DAG Tasks on Multiprocessor Systems
Manar Qamhieh, Laurent George, Serge Midonnet · 2014
Parallelism 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.