Energy-Aware Multiserver Queueing Systems with Setup Times: Structural Properties, Exact Analysis, and Asymptotic Performance

Abstract

Energy consumption of today's data-centers is a constant concern from the standpoints of monetary and environmental costs. An intuitive solution to address these immense energy demands is to turn servers off to incur less costs. 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. What policy the model should employ, or rather when each server should be turned on and off is far from a trivial question. A specific policy is often examined, but determining which policy to study can be a difficult process and is often a product of intuition. Moreover, while a specific policy may do comparatively well against another, in general it may be far from optimal. This problem is further accentuated when one considers the case that a policy may do well or even be optimal under a specific cost function, but far from optimal under another. To address this issue this thesis studies the structural properties of the optimal policy under a wide range of cost functions, allowing for a significant reduction in the search space; then leverages these structural properties to intelligently select three families of policies to study further. An exact analysis of these policies is given, alongside offering insights, observations, and implications for how these systems behave. In particular, results are found which grant insight into the question of the number of servers that should remain on at all times under a general cost function. The model is then analysed under a fixed-load, many-server asymptotic regime, i.e. C approaches infinity, while the load remains fixed, where it is shown that not only are many of the 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.