Stochastic Modeling and Approaches for Managing Energy Footprints in Cloud Computing Service

In this paper, we formulate several stochastic optimization models for trading off between energy footprints and quality of service associated with server consolidation in cloud computing data centers. We consider finite service times with uncertain workloads at each period and minimize the expected energy consumption. Decisions include workload scheduling and switching servers on or off based on estimated loads. In models involving backlogging and penalizing unmet demand, we first incorporate zero-delay and zero-work-loss criteria, of which the latter allows backlogging but sets deadlines and penalty cost for all delays. We also formulate alternative chance-constrained programs to ensure that workload delay percentage is within a certain risk tolerance. By assuming scenario-based workload realizations, we solve each model as an mixed-integer program. For the zero-work-loss model, when all servers are homogeneous (i.e., have the same computational efficiency), we provide a heuristic approach. We also consider a benchmark two-stage stochastic program, which involves recourse scheduling decisions and is solved using the Benders decomposition. Numerical results demonstrate the computational efficacy and reduction of energy consumption for certain patterns of workload realizations. In particular, we consider instances generated from a typical daily workload pattern existing in many data centers and provide managerial insights.