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In this paper, we consider variants of Pfair and ERfair scheduling in which subtasks may be released late, i.e., there may be separation between consecutive windows of the same task. We call such tasks intra-sporadic tasks. There are two main contributions of this paper. First, we show the existence of a Pfair (and hence ERfair) schedule for any intra-sporadic task system whose utilization is at most the number of available processors. Second, we give a polynomial-time algorithm that is optimal for scheduling intra-sporadic tasks in a Pfair or ERfair manner on systems of one or two processors.

In this paper, we prove that a simplified variant of the PD Pfair algorithm, called PD', 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 Pfair scheduling algorithms has been limited to synchronous periodic task systems.