A model has been proposed in [Baruah et al., in Proceedings of the IEEE Real-Time Systems Symposium 2012] for representing recurrent precedence-constrained tasks to be executed on multiprocessor platforms, where each recurrent task is modeled by a di
rected acyclic 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 have to be completed within some specified relative deadline. The task may release jobs in this manner an unbounded number of times, with successive releases occurring at least the specified period apart. The feasibility problem is to determine whether such a recurrent task can be scheduled to always meet all deadlines on a specified number of dedicated processors. The case of a single task has been considered in [Baruah et al., 2012]. The main contribution of this paper is to consider the case of multiple tasks. We show that EDF has a speedup bound of 2-1/m, where m is the number of processors. Moreover, we present polynomial and pseudopolynomial schedulability tests, of differing effectiveness, for determining whether a set of sporadic DAG tasks can be scheduled by EDF to meet all deadlines on a specified number of processors.
We give the first algorithm for testing the feasibility of a system of sporadic real-time tasks on a set of identical processors, solving one major open problem in the area of multiprocessor real-time scheduling [S.K. Baruah and K. Pruhs, Journal of
Scheduling, 2009]. We also investigate the related notion of schedulability and a notion that we call online feasibility. Finally, we show that discrete-time schedules are as powerful as continuous-time schedules, which answers another open question in the above mentioned survey.
