Data center networks provide the physical infrastructure that hosts Internet-related services and cloud computing. Designing data center networks properly is imperative for Internet-related service and cloud computing providers to gain competitive edges through cost efficiency and service quality. In this paper, we formulate a mathematical programming model to address the data center network design problem, in which the objective is to minimize total operating cost and the service delay penalty by optimizing data center location, footprint allocation, and resource provisioning decisions, while incorporating essential features, such as latency, power, multiple resources, configuration limits, and interdependent footprints.
We employ a queueing model to approximate the service latency and provide tractable reformulations. To enhance computational efficiency for large-scale problems, we further develop Lagrangian relaxation methods and generate strengthening cuts by exploiting the structural properties of the problem. Our numerical studies demonstrate that the proposed model, which jointly optimizes location, allocation, and resource provisioning, can achieve significant cost reductions and improvements in service quality compared with a hierarchical approach that optimizes these decisions sequentially. Moreover, our proposed solution methods outperform state-of-the-art commercial software in terms of computational efficiency. Based on real-world datasets, the proposed model selects data centers that have been chosen by major cloud computing infrastructure providers. We also draw managerial insights that can be used as design guidelines in practice.