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 non-asymptotic 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集群的能效（以平均每作业能耗衡量），该集群包含多种存储和/或计算组件，被建模为并行的抽象服务器。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和能耗速率。服务器异构性与多功率模式的耦合使优化问题复杂化，最优解通常难以求得。基于惠特尔松弛技术，我们提出一种近似最优且可扩展的作业分配策略。在与服务器服务速率和能耗速率相关的温和条件下，我们证明了所提策略在整个系统规模趋于无穷时趋近最优性，即具有渐近最优性。针对非渐近场景，数值仿真表明该策略优于所有测试基线，且我们通过数值实验验证了其对重尾作业尺寸分布的鲁棒性。