Service Rate Control of On/Off Servers

根据加拿大自然资源部的数据，数据中心支持加拿大经济的每个部门，消耗了加拿大大约1%的总电力消耗。在确定数据中心的规模时，它们通常被设计为适应峰值需求。其结果是，大部分时间，绝大多数服务器都处于空闲状态，但仍在消耗能源。如果能够确定如何有效地关闭（或打开）服务器，就数据中心运营商的直接节省而言，以及由于相应减少温室气体排放而对加拿大社会而言，显然都将取得重大收益。需要考虑的权衡是，如果需要打开服务器以应对不断增长的需求，则性能可能会下降（就等待时间而言），并且频繁打开和关闭服务器可能会减少设备的使用寿命。***刚才描述的数据中心问题是一个更普遍的问题的例子，它是一个由需求可变的多个资源组成的系统，在这种情况下，可能会出现关闭或移除资源的机会，同时仍然有效地满足当前提供的需求。这个机会可能允许组织在需求较低时降低成本，但是如果在需求增加时部署资源有一些延迟（例如，可能发生在任何外包决策中），则存在系统性能可能降低到不可接受水平的风险。人们可能也不希望过于频繁地关闭或部署资源，因为这样的决策可能会带来巨大的开销。控制排队模型是研究这类问题的自然方法。当所有的资源（服务器）都是同质的，有一个单一的需求流，并且决策者有关于系统的完美信息时，我们将首先研究这个问题。使用包括马尔可夫决策过程在内的技术组合，计算稳态性能度量的最新方法和检查限制随机过程，我们将尽可能多地描述最优控制策略-确定应该始终保持多少服务器以及如何打开和关闭剩余的服务器。当服务器是异构的，并且存在不同的需求流时，这些策略如何变化将被研究。***在该领域的应用中很少实现完全信息的假设。然而，了解最优策略的形式为可以实现的目标提供了一个基准，以衡量使用较少信息的策略的有效性。更深入的见解是可能的——了解具有完美信息的最优策略的行为，可能允许人们在信息较少的情况下，将这种行为的近似值构建到策略中。将在制定此类政策上花费大量精力，并通过构建适当的限制过程和模拟对这些政策进行分析评估

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.**