On energy conservation in data centers

We formulate and study an optimization problem that arises in the energy management of data centers and, more generally, multiprocessor environments. Data centers host a large number of heterogeneous servers. Each server has an active state and several standby/sleep states with individual power consumption rates. The demand for computing capacity varies over time. Idle servers may be transitioned to low-power modes so as to rightsize the pool of active servers. The goal is to find a state transition schedule for the servers that minimizes the total energy consumed. On a small scale, the same problem arises in multicore architectures with heterogeneous processors on a chip. One has to determine active and idle periods for the cores so as to guarantee a certain service and minimize the consumed energy. For this power/capacity management problem, we develop two main results. We use the terminology of the data center setting. First, we investigate the scenario that each server has two states: An active state and a sleep state. We show that an optimal solution, minimizing energy consumption, can be computed in polynomial time by a combinatorial algorithm. The algorithm resorts to a single-commodity minimum-cost flow computation. Second, we study the general scenario that each server has an active state and multiple standby/sleep states. We devise a τ -approximation algorithm that relies on a two-commodity minimum-cost flow computation. Here, τ is the number of different server types. A data center has a large collection of machines but only a relatively small number of different server architectures. Moreover, in the optimization, one can assign servers with comparable energy consumption to the same class. Technically, both of our algorithms involve nontrivial flow modification procedures. In particular, given a fractional two-commodity flow, our algorithm executes advanced rounding and flow packing routines.