Nonclairvoyant sleep management and flow-time scheduling on multiple processors

Abstract

In large data centers, managing the availability of servers is often non-trivial, especially when the workload is unpredictable. Using too many servers would waste energy, while using too few would affect the performance. A recent theoretical study, which assumes the clairvoyant model where job size is known at arrival time, has successfully integrated sleep-and-wakeup management into multi-processor job scheduling and obtained a competitive tradeoff between flow time and energy [6]. This paper extends the study to the nonclairvoyant model where the size of a job is not known until the job is finished. We give a new online algorithm SATA which is, for any ε > 0, (1 + ε)-speed O( 1⁄ε2 )-competitive for the objective of minimizing the sum of flow time and energy. SATA also gives a new nonclairvoyant result for the classic setting where all processors are always on and the concern is flow time only. In this case, the previous work of Chekuri et al. [7] and Chadha et al. [8] has revealed that random dispatching can give a non-migratory algorithm that is (1 + ε)-speed O( 1⁄ε3 )-competitive, and any deterministic non-migratory algorithm is Ω(m⁄s)-competitive using s-speed processors [7], where m is the number of processors. SATA, which is a deterministic algorithm migrating each job at most four times on average, has a competitive ratio of O(1⁄ε2). The number of migrations used by SATA is optimal up to a constant factor as we can extend the above lower bound result.