Decomposition-based scheduling for parallel real-time tasks on multiprocessors

Abstract

This paper addresses the problem of multiprocessor real-time scheduling for parallel tasks modeled as directed acyclic graph (DAG). We propose a new decomposition-based scheduling algorithm to schedule parallel DAG tasks with implicit-deadlines. We prove that our algorithm has a resource augmentation bound of 2.618 for DAG tasks with implicit-deadlines when the decomposed tasks are scheduled using Global EDF scheduling, i.e., if the input set of DAG tasks is schedulable on m unit-speed processors, the proposed scheduling algorithm will always succeed on m processors with speed 2.618. This result improves the resource augmentation bound of 2.618 for tasks with special DAGs provided by Qamhieh et al. in 2019. Moreover, when using Global DM (Partitioned-DM, respectively) scheduling for the decomposed tasks, we prove a resource augmentation bound of 3.42 for DAG tasks with implicit-deadlines, which improves the resource augmentation bound of 3.73 for tasks with special DAGs (3.42 for fork-join tasks, respectively).