Asymptotic Performance of Energy-Aware Multiserver Queueing Systems with Setup Times

Energy demands of modern datacentres are an immense concern. An intuitive solution is to turn servers off to incur less costs. However, the control problem of when to turn a specific server off, and when to then turn that server back on, is far from trivial. 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. We analyse this well-established model under the asymptotic regime where the number of servers approaches infinity while the load per server remains fixed and show that not only are many of the control policies in the literature equivalent under this regime, but they are also optimal under any cost function which is non-decreasing in the expected energy cost and response time.