  In this paper, we propose a novel dynamic decision method by applying the
sensitivity-based optimization theory to find the optimal energy-efficient
policy of a data center with two groups of heterogeneous servers. Servers in
Group 1 always work at high energy consumption, while servers in Group 2 may
either work at high energy consumption or sleep at low energy consumption. An
energy-efficient control policy determines the switch between work and sleep
states of servers in Group 2 in a dynamic way. Since servers in Group 1 are
always working with high priority to jobs, a transfer rule is proposed to
migrate the jobs in Group 2 to idle servers in Group 1. To find the optimal
energy-efficient policy, we set up a policy-based Poisson equation, and provide
explicit expressions for its unique solution of performance potentials by means
of the RG-factorization. Based on this, we characterize monotonicity and
optimality of the long-run average profit with respect to the policies under
different service prices. We prove that the bang-bang control is always optimal
for this optimization problem, i.e., we should either keep all servers sleep or
turn on the servers such that the number of working servers equals that of
waiting jobs in Group 2. As an easy adoption of policy forms, we further study
the threshold-type policy and obtain a necessary condition of the optimal
threshold policy. We hope the methodology and results derived in this paper can
shed light to the study of more general energy-efficient data centers.
