Cost Minimization for Scheduling Parallel, Single-Threaded, Heterogeneous, Speed-Scalable Processors

Abstract

We introduce an online scheduling algorithm to optimally assign a set of arriving heterogeneous tasks to heterogeneous speed-scalable processors. The goal of our algorithm is to minimize the total cost of response time and energy consumption (TCRTEC) of the tasks. We have three contributions that constitute the algorithm. First, we propose a novel task dispatching strategy for assigning the tasks to the processors. Second, we propose a novel preemptive service discipline called Smallest remaining Computation Volume Per unit Price of response Time (SCVPPT) to schedule the tasks on the assigned processor. Third, we propose a dynamic speed-scaling function that explicitly determines the optimum processing rate of each task. In our work, the processors are heterogeneous in that they may differ in their hardware specifications with respect to maximum processing rate and power functions. Tasks are heterogeneous in terms of computation volume and processing requirements. We also consider that the unit price of response time for each task is heterogeneous. Each task's unit price of response time is allowed to differ because the user may be willing to pay higher/lower unit prices for certain tasks, thereby increasing/decreasing their optimum processing rates. In our SCVPPT discipline, a task's scheduling priority is influenced by its remaining computation volume as well as its unit price of response time. Our simulation results show that SCVPPT outperforms the two known service disciplines, Shortest Remaining Processing Time (SRPT) and the First Come First Serve (FCFS), in terms of minimizing the TCRTEC performance metric. The results also show that the algorithm's dispatcher outperforms the well known Round Robin dispatcher when the processors are heterogeneous. We focus on multi-buffer, single-threading where a set of tasks is allocated to a given processor, but only one task is processed at a time until completion unless preemption is dictated by the service discipline.