Optimal Asynchronous Dynamic Policies in Energy-Efficient Data Centers

In this paper, we apply a Markov decision process to find the optimal asynchronous dynamic policy of an energy-efficient data center with two server groups. Servers in Group 1 always work, while servers in Group 2 may either work or sleep, and a fast setup process occurs when the server's states are changed from sleep to work. The servers in Group 1 are faster and cheaper than those of Group 2 so that Group 1 has a higher service priority. Putting each server in Group 2 to sleep can reduce system costs and energy consumption, but it must bear setup costs and transfer costs. For such a data center, an asynchronous dynamic policy is designed as two sub-policies: The setup policy and the sleep policy, both of which determine the switch rule between the work and sleep states for each server in Group 2. To find the optimal asynchronous dynamic policy, we apply the sensitivity-based optimization to establish a block-structured policy-based Markov process and use a block-structured policy-based Poisson equation to compute the unique solution of the performance potential by means of the RG-factorization. Based on this, we can characterize the monotonicity and optimality of the long-run average profit of the data center with respect to the asynchronous dynamic policy under different service prices. Furthermore, we prove that a bang-bang control is always optimal for this optimization problem. We hope that the methodology and results developed in this paper can shed light on the study of more general energy-efficient data centers.