Service Rate Control of On/Off Servers

根据加拿大自然资源公司的数据，数据中心支持加拿大经济的每个部门，消耗的电力约占加拿大总用电量的1%。在调整数据中心的规模时，它们通常是为适应高峰需求而设计的。其结果是，大部分时间，绝大多数服务器处于空闲状态，但仍在消耗能量。如果人们能够确定如何有效地关闭(和打开)服务器，显然将取得重大收益，无论是在数据中心运营商的直接节省方面，还是在由于相应的温室气体排放减少而为加拿大社会带来的方面。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，则性能可能会降低(就等待时间而言)，而且频繁打开和关闭服务器可能会缩短设备的寿命。*刚才描述的数据中心问题是更一般问题的一个例子，该问题是由具有可变需求的多个资源组成的系统之一，其中可能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。这种机会可以使组织在需求低时降低成本，但如果在需求增加时延迟部署资源(例如，在任何外包决策中可能发生的情况)，则存在系统性能可能降级到不可接受的水平的风险。人们可能也不想太频繁地关闭或部署资源，因为这样的决策可能会产生大量的开销。*受控排队模型是研究此类问题的自然手段。当所有资源(服务器)都是同类的，只有一个需求流，并且决策者拥有关于系统的完美信息时，我们将首先研究这个问题。使用马尔可夫决策过程、计算稳态性能度量的最新方法和检查限制随机过程等技术的组合，我们将尽可能多地描述最优控制策略-确定应该始终保持打开的服务器数量以及如何打开和关闭剩余的服务器。当服务器是异类的并且有不同的需求流时，这些策略如何改变将被研究。*完美信息的假设在现场应用中很少实现。然而，了解最优政策的形式既为能够实现什么提供了基准，也为衡量使用较少信息的政策的效力提供了基准。更深入的洞察是可能的--在信息完备的情况下了解最优政策的行为，可能会让人在信息较少的政策中构建此类行为的近似值。将花费大量精力制定此类政策，通过构建适当的限制程序和通过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.**