Optimizing Dynamic Data Center Provisioning through Speed Scaling: A Primal-Dual Perspective.

A significant proportion of energy consumed in modern data centers and clouds is dedicated to provisioning idle servers for maintaining Quality of Service guarantees. Various studies have been conducted exploring dynamic provisioning in data centers with the objective of reducing overall energy consumption. However, many of these studies assume a fixed energy cost per operating server where each server can only handle one job within a given time slot. In this paper, we address a new and practical problem that involves speed scaling of multiple servers within a data center. Specifically, we consider a scenario where each server can handle multiple jobs simultaneously, and the energy consumed is a piece-wise convex function that depends on processing speed. In addition, turning on a server incurs a substantial energy cost. To tackle this problem, we develop a new online primal-dual fitting framework. By leveraging this framework, we have found that the straightforward LIF algorithm, which allocates new workloads to servers based on their minimal idle times, attains a bounded competitive ratio in comparison to the optimal offline solution. Building upon this finding, we have designed a novel algorithm called BDST . BDST dynamically updates server provisioning based on a long-term evaluation of the trade-off between the cost of maintaining high-speed for current servers and the cost of powering on additional servers. One critical aspect of BDST is its remarkable constant competitive ratio of less than three, regardless of the shape of the energy function.