Steady-state approximations of dynamic speed-scaling in data centers

Dynamic speed-scaling, which varies the server speed with the number of tasks, has been proposed to balance energy and delay costs in data-centers. The direct numerical computation of these costs under the optimal speed-scaling policy does not give much insight into their behavior. By making an analogy with the Erlang-C model, we propose approximations for the mean energy consumed per task and the mean delay in systems with dynamic speed-scaling. These approximations are related to those by Halfin and Whitt for the Erlang-C system. The applicability of these approximations is illustrated with the help of comparison with the exact optimal routing policy in data-centers.