  In this paper, we use a Markov decision process to find optimal asynchronous
policy of an energy-efficient data center with two groups of heterogeneous
servers, a finite buffer, and a fast setup process at sleep state. Servers in
Group 1 always work. Servers in Group 2 may either work or sleep, and a fast
setup process occurs when server's states are changed from sleep to work. In
such a data center, an asynchronous dynamic policy is designed as two
sub-policies: The setup policy and the sleep policy, which determine the switch
rule between the work and sleep states for the servers in Group 2. To analyze
the optimal asynchronous dynamic policy, we apply the Markov decision process
to establish a policy-based Poisson equation, which provides expression for 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 the
bang-bang control is always optimal for this optimization problem, and supports
a threshold-type dynamic control in the energy-efficient data center. We hope
that the methodology and results derived in this paper can shed light to the
study of more general energy-efficient data centers.
