Sleep management on multiple machines for energy and flow time

In large data centers, determining the right number of operating machines is often non-trivial, especially when the workload is unpredictable. Using too many machines would waste energy, while using too few would affect the performance. This paper extends the traditional study of online flow-time scheduling on multiple machines to take sleep management and energy into consideration. Specifically, we study online algorithms that can determine dynamically when and which subset of machines should wake up (or sleep), and how jobs are dispatched and scheduled. We consider schedules whose objective is to minimize the sum of flow time and energy, and obtain O(1)-competitive algorithms for two settings: one assumes machines running at a fixed speed, and the other allows dynamic speed scaling to further optimize energy usage. Like the previous work on the tradeoff between flow time and energy, the analysis of our algorithms is based on potential functions. What is new here is that the online and offline algorithms would use different subsets of machines at different times, and we need a more general potential analysis that can consider different match-up of machines.