Energy-aware capacity scaling in virtualized environments with performance guarantees

We investigate the trade-off between performance and power consumption in servers hosting virtual machines running IT services. The performance behavior of such servers is modeled through Generalized Processor Sharing (GPS) queues enhanced with a green speed-scaling mechanism that controls the processing capacity to use depending on the number of active virtual machines. When the number of virtual machines grows large, we show that the stochastic evolution of our model converges to a system of ordinary differential equations for which we derive a closed-form formula for its unique stationary point. This point is a function of the capacity and the shares that characterize the GPS mechanism. It allows us to show that speed-scaling mechanisms can provide large reduction in power consumption having only small performance degradation in terms of the delays experienced in the virtual machines. In addition, we derive the optimal choice for the shares of the GPS discipline, which turns out to be non-trivial. Finally, we show how our asymptotic analysis can be applied to the dimensioning and service partitioning in data-centers. Experimental results show that our asymptotic formulas are accurate even when the number of virtual machines is small.