Abstract
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.
Highlights
Compared with Ma et al [31], this paper considers more practical factors in the energy-efficient data centers such that the policy-based Markov process is block-structured, which makes solving the block-structured Poisson equation more complicated
The third contribution of this paper is to provide a unified framework for applying the sensitivity-based optimization to study the optimal asynchronous dynamic policy of the energy-efficient data center
For Group 2, we introduce an asynchronous dynamic policy, which is related to two dynamic actions: from sleep to work and from work to sleep
Summary
Over the last two decades considerable attention has been given to studying energy- efficient data centers. The first contribution is to apply the sensitivity-based optimization (and the MDPs) to study a more general energy-efficient data center with key practical factors, for example, a finite buffer, a fast setup process, and transferring some incomplete service jobs to the idle servers in Group 1 or to the finite buffer, if any. The third contribution of this paper is to provide a unified framework for applying the sensitivity-based optimization to study the optimal asynchronous dynamic policy of the energy-efficient data center For such a more complicated energy-efficient data center, we first establish a policy-based block-structured Markov process as well as a more detailed cost and reward structure, and provide an expression for the unique solution to the block-structured Poisson equation by means of the RG-factorization. Three appendices are given, both for the state-transition relation figure of the policy-based block-structured continuous-time Markov process and for the block entries of its infinitesimal generator
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