Abstract
This paper investigates the task scheduling problem in the oontext of reservation-based real-time systems that provide quality of service (QoS) guarantees. In such a system, each incoming task specifies a rate of progress requirement on the task's execution that must be met by the system in order for the computation to be deeemed usable. A new metric, called granularity, is introduced that quantifies both the maximum slowdown and the variance in execution rate that the task allows. This metric generalizes the stretch metric used in recent research on task scheduling. An online preemptive scheduling algorithm is presented that achieves a competitive ratio of g(1 - r) for every set of tasks with maximum rate r and minimum granularity g. This result generalizes a previous result based on the stretch metric that showed that a competitive ratio of (1 - r) is achievable for the case when g = 1.
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