Performance Analysis for Segment Stretch Transformation of Parallel Real-time Tasks

The Segment Stretch Transformation (SST) is an algorithm that transforms parallel Fork-Join (FJ) tasks into sequential tasks on multiprocessor systems when possible, in order to increase the schedulability of the tasksets of this model. SST is based on Task Stretch Transformation (TST) which is a transformation for the same model of tasks, but it uses segment migrations while SST eliminates their use. In this paper, we prove that SST transformation has the same performance of TST transformation by providing a detailed analysis based on Demand Bound Function (DBF) and by showing that SST has a resource augmentation bound of 3.42, same as TST, which means that if a taskset is feasible on m speed processors, then it is schedulable using the transformation on m processors that are 3.42 times faster.

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