We aim to maximize the energy efficiency, gauged as average energy cost per job, in a large-scale server farm with various storage or/and computing components modeled as parallel abstracted servers. Each server operates in multiple power modes characterized by potentially different service and energy consumption rates. The heterogeneity of servers and multiple power modes complicate the maximization problem, where optimal solutions are generally intractable. Relying on the Whittle relaxation technique,we resort to a near-optimal, scalable job-assignment policy. Under a mild condition related to the service and energy consumption rates of the servers, we prove that our proposed policy approaches optimality as the size of the entire system tends to infinity; that is, it is asymptotically optimal. For the nonasymptotic regime, we show the effectiveness of the proposed policy through numerical simulations, where the policy outperforms all the tested baselines, and we numerically demonstrate its robustness against heavy-tailed job-size distributions.

翻译：我们旨在最大化大规模服务器群组的能源效率（以每任务平均能耗衡量）。该服务器群组包含多种存储/计算组件，建模为并行抽象服务器。每台服务器可在多种功率模式下运行，不同模式具有差异化的服务速率与能耗速率特性。服务器异构性与多功率模式交织使最优化问题复杂化，其最优解通常难以求解。基于Whittle松弛技术，我们提出一种接近最优的可扩展任务分配策略。在关于服务器服务速率与能耗速率的温和条件下，我们证明所提策略随系统规模趋于无穷大时趋近最优性，即具有渐近最优性。针对非渐近场景，通过数值仿真验证了策略有效性：该策略优于所有测试基线，且数值实验表明其对重尾任务规模分布具有鲁棒性。