Optimal Energy-Aware Scheduling in VFI-enabled Multicore Systems

Abstract

Energy efficiency is considered a challenging problem in modern multicore systems. Partitioning the cores into multiple voltage and frequency islands (VFI) provides a compromise between simple global Dynamic Voltage Frequency Scaling (DVFS) and fine-grain per-core, per-task DVFS. This paper formulates the optimization problem of scheduling tasks statically on multiple VFIs as a Mixed Integer Linear Programming (MILP) such that for a given energy budget, the program execution time (makespan) is minimized. Our proposed solution consists of two steps. In the first step, we use an Integer Linear Programming (ILP)-based algorithm, from our previous work, to assign per-core fine-grain dynamic Voltage/Frequency (V/F) levels to each task in a task set (program) to minimize the makespan for a given energy budget. In the second step, which is the focus of this paper, we use the MILP framework to schedule this task set, with the given V/F levels provided in step one, on the islands of a VFI-enabled multicore system to again minimize the makespan subject to (1) the energy budget and (2) the task set's precedence (dependency) constraints. Together with the solutions obtained by MILP, a round-robin algorithm is used to compare these two methodologies to ILP that provides the best solution. Our experimental results show that across all the benchmarks considered, the MILP-based and round-robin makespan solutions are on average 1.2 and 2.28 times slower than the ILP-based makespan solutions, respectively.