Asymptotic Performance of an Energy-Aware G/G/C Queue with General Setup Times

Abstract

An intuitive solution to address the immense energy demands of datacentres is to turn servers off to incur less costs. However, when to turn a specific server off and when to then turn that server back on are far from trivial questions. As such, many different authors have modeled this problem as an M/M/C queue where each server can be turned on with an exponentially distributed setup time or turned off instantaneously. Due to the complexity of the model analysis, authors often examine a specific policy. Moreover, different authors examine different policies under different cost functions. This in turn causes difficulties when making statements or drawing conclusions regarding competing policies. We analyse this well established model under the asymptotic regime where the number of servers approaches infinity, i.e. , while the load remains fixed, i.e. . Furthermore, we relax the assumptions regarding the underlying exponential distributions. That is, we consider a G/G/C queue that has generally distributed setup times. To address the issue of comparing competing policies, it is shown that under the aforementioned asymptotic regime and generality, not only are many of the policies in the literature equivalent, but they are also optimal under any cost function which is non-decreasing in the expected energy cost and response time.