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As the complexity of software for Cyber-Physical Systems (CPS) rapidly increases, multi-core processors and parallel programming models such as OpenMP become appealing to CPS developers for guaranteeing timeliness. Hence, a parallel task on multi-core processors is expected to become a vital component in CPS such as a self-driving car, where tasks must be scheduled in real-time.

In this paper, we extend the fork-join parallel task model to be scheduled in real-time, where the number of parallel threads can vary depending on the physical attributes of the system. To efficiently schedule the proposed task model, we develop the task stretch transform. Using this transform for global Deadline Monotonic scheduling for fork-join real-time tasks, we achieve a resource augmentation bound of 3.73. In other words, any task set that is feasible on m unit-speed processors can be scheduled by the proposed algorithm …