Energy-aware Scheduling: Models and Complexity Results

This paper presents several energy-aware scheduling algorithms whose design is optimized for different speed models. Dynamic Voltage and Frequency Scaling (DVFS) is a model frequently used to reduce the energy consumption of a schedule, but it has negative effect on reliability. While the reliability of a schedule can sometimes be neglected (battery powered systems such as cell-phones or personal computers), it becomes extremely important when considering massively parallel architectures (petascale, exascale). In this work, we consider the problem of minimizing the energy within a make span constraint. Additionally, we consider two models, one that takes into account a reliability constraint, and one that does not. We assume that the mapping is given, say by an ordered list of tasks to execute on each processor, and we aim at optimizing the energy consumption while enforcing a prescribed bound on the execution time. While it is not possible to change the allocation of a task, it is possible to change its speed. Rather than using a local approach such as backfilling, we consider the problem as a whole and study the impact of several speed variation models on its complexity. To improve the reliability of a schedule while reducing the energy consumption, we allow for the re-execution of some tasks. We present several results in that framework, as well as future research plans.