In this paper, we prove that a simplified variant of the PD P fair algorithm, called PD{sup}2, is optimal for scheduling any mix of early-release and non-early-release asynchronous tasks on a multiprocessor. This result breaks new ground by incorporating both early-release and non-early-release tasks under a common framework. In addition, all prior work on optimal multiprocessor P fair scheduling algorithms has been limited to synchronous periodic task systems.
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