Service Rate Control of On/Off Servers

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According to Natural Resources Canada, data centres support every sector of the Canadian economy and consume roughly one percent of the total electricity consumed in Canada. When sizing data centres, they are typically designed to accommodate peak demand. A consequence is that much of the time, the vast majority of servers are idle yet still consuming energy. If one could determine how to effectively turn servers off (and on), there are clearly significant gains to be made, both in terms of direct savings for data centre operators, but also for Canadian society due to the corresponding reduction in greenhouse gas emissions. The tradeoff to consider is that performance may decrease (in terms of waiting times) if servers need to be turned on to cope with rising demand, and that frequently turning servers on and off may reduce the lifetime of the equipment. ***The data centre problem just described is an example of a more general problem, one of systems consisting of multiple resources with variable demand, where the opportunity may present itself to shut down or remove resources while still effectively satisfying the current offered demand. This opportunity may allow an organization to reduce costs when demand is low, but if there is some delay to deploy resources when the demand increases (as may occur in any outsourcing decision, for example), there is a risk that the performance of the system may degrade to an unacceptable level. One may also not want to shut down or deploy resources too frequently, as there may be significant overhead associated with such decisions.***Controlled queueing models are a natural means to study such problems. We will first study this problem when all resources (servers) are homogeneous, there is a single demand stream, and the decision maker has perfect information about the system. Using a combination of techniques including Markov Decision Processes, recent approaches to computing steady-state performance measures and examining limiting stochastic processes, we will characterize as much as possible optimal control policies - determining how many servers should always remain on and how to turn on and off the remaining servers. How these policies change when servers are heterogeneous and there are differing demand streams will then be studied.***The assumption of perfect information is rarely achieved in applications in the field. However, knowing the form of optimal policies provides both a benchmark for what can be achieved, to measure the efficacy of policies which use less information. Deeper insights are possible - knowing the behaviour of optimal policies with perfect information may allow one to build an approximation of such behaviour into policies with less information. Significant effort will be spent on developing such policies, where they will be evaluated both analytically by constructing appropriate limiting processes and through simulation.**