Best-Harmonically-Fit Periodic Task Assignment Algorithm on Multiple Periodic Resources

Abstract

The periodic task set assignment problem in the context of multiple processors has been studied for decades. Different heuristic approaches have been proposed, such as the Best-Fit (BF), the First-Fit (FF), and the Worst-Fit (WF) task assignment algorithms. However, when processors are not dedicated but only periodically available to the task set, whether existing approaches still provide good performance or if there is a better task assignment approach in the new context are research problems which, to our best knowledge, have not been studied by the real-time research community. In this paper, we present the Best-Harmonically-Fit (BHF) task assignment algorithm to assign periodic tasks on multiple periodic resources. By periodic resource we mean that for every fixed time interval, i.e., the period, the resource always provides the same amount of processing capacity to a given task set. Our formal analysis indicates that if a harmonic task set is also harmonic with a resource's period, the resource capacity can be fully utilized by the task set. Based on this analysis, we present the Best-Harmonically-Fit task assignment algorithm. The experimental results show that, on average, the BHF algorithm results in $53.26$ , $42.54$ , and $27.79$ percent higher resource utilization rate than the Best-Fit Decreasing (BFD), the First-Fit Decreasing (FFD), and the Worst-Fit Decreasing (WFD) task assignment algorithms, respectively; but comparing to the optimal resource utilization rate found by exhaustive search, it is about $11.63$ percent lower.