This paper addresses the problem of jointly scheduling tasks with both hard and soft time constraints. We present a new analysis which builds upon previous research into slack stealing algorithms. Our analysis determines the maximum processing time which may be stolen from hard deadline periodic or sporadic tasks, without jeopardising their timing constraints. It extends to tasks with characteristics such as synchronization, release jitter and stochastic execution times, as well as forming the basis for a family of optimal and approximate slack stealing algorithms.
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