An energy-constrained makespan optimization framework in fine-to coarse-grain partitioned multicore systems

In today's multicore systems, depending on an application's computational demand, cores are either operated individually at different Voltage/Frequency (V/F) levels or grouped into multiple Voltage-Frequency Islands (VFIs) to reduce system energy consumption. This paper formulates a task scheduling and VFI partitioning problem whose optimization goal is to minimize the task set (application) execution time (makespan) for a given energy budget. First, the combinatorial optimization problem is formulated with Integer Linear Programming (ILP) to obtain per-core, per-task dynamic V/F levels in a fine-grain VFI-based system with single-core islands. Next, static task scheduling on coarse-grain VFI-based systems, where an island can contain several cores operated at the same V/F level, is formulated with Mixed Integer Linear Programming (MILP), considering the energy budget and task set's precedence constraints. The experimental results show that under different energy budget constraints, fine-grain, dynamic task allocations provide on average 1.35x speedup over static coarse grain scheduling and partitioning methods.