Energy‐efficient task scheduling on heterogeneous computing systems by linear programming

The continually increasing energy consumption represents a critical issue in modern heterogeneous computing systems. With the aid of dynamic voltage frequency scaling (DVFS), task scheduling is considered an effective software‐based technique for reducing the total energy consumption and minimizing the overall schedule length (makespan). A natural solution is to reclaim the slack time in a given time‐efficient schedule, which is also referred to as a “two‐pass” method or a “rescheduling” method. A number of studies have focused on slack reclamation to achieve energy reductions through heuristics; although, these methods offer suboptimal solutions. In this article, the rescheduling optimization problem is formulated as a linear program for minimizing an energy objective function subject to precedence and deadline constraints implied in the given schedule. Two types of decision variables, ie, frequency duty factors and task intervals, are defined to set up the linear model. Consequently, an optimal solution to the problem can be provided in a straightforward manner by a linear programming solver, which suggests that such a rescheduling problem belongs to the P (polynomial time) class. The experimental results show the effectiveness of the proposed approach and demonstrate that the performance is superior to that of other competitive algorithms in terms of both energy saving and runtime efficiency.