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Over the years, many multiprocessor locking protocols have been designed and analyzed. However, the performance of these protocols highly depends on how the tasks are partitioned and prioritized and how the resources are shared locally and globally. This paper answers a few fundamental questions when realtime tasks share resources in multiprocessor systems. We explore the fundamental difficulty of the multiprocessor synchronization problem and show that a very simplified version of this problem is N P -hard in the strong sense regardless of the number of processors and the underlying scheduling paradigm. Therefore, the allowance of preemption or migration does not reduce the computational complexity. For the positive side, we develop a dependency-graph approach, that is specifically useful for framebased real-time tasks, in which all tasks have the same period and release their jobs always at the same time. We present a series of algorithms with speedup factors between 2 and 3 under semi-partitioned scheduling. We further explore methodologies and tradeoffs of preemptive against non-preemptive scheduling algorithms and partitioned against semi-partitioned scheduling algorithms. The approach is extended to periodic tasks under certain conditions.

This paper considers the scheduling of parallel realtime 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.

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