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各个部门，消耗的电力约占加拿大总消耗量的1%。在调整数据中心规模时，它们通常被设计为适应峰值需求。其结果是，大多数服务器在大部分时间都处于空闲状态，但仍在消耗能源。如果人们能够确定如何有效地关闭（和打开）服务器，显然可以取得显着的收益，无论是在数据中心运营商的直接节省方面，还是由于温室气体排放的相应减少而为加拿大社会带来的收益。需要考虑的权衡是，如果需要打开服务器以科普不断增长的需求，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缩短设备的寿命。* 刚刚描述的数据中心问题是一个更一般问题的例子，一个由具有可变需求的多个资源组成的系统，其中可能存在关闭或删除资源的机会，同时仍然有效地满足当前提供的需求。 这一机会可使组织在需求较低时降低成本，但如果在需求增加时部署资源出现一些延迟（例如，在任何外包决策中可能出现这种情况），则系统的性能可能会下降到不可接受的水平。人们可能也不想太频繁地关闭或部署资源，因为此类决策可能会产生大量开销。*受控扩散模型是研究这类问题的一种自然方法。我们将首先研究这个问题时，所有的资源（服务器）是同构的，有一个单一的需求流，决策者有完善的信息系统。使用的技术，包括马尔可夫决策过程，最近的方法来计算稳态性能指标和检查限制随机过程的组合，我们将尽可能多地表征最佳控制策略-确定有多少服务器应该始终保持打开，以及如何打开和关闭其余的服务器。然后将研究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改变。*完全信息的假设在该领域的应用中很少实现。然而，了解最优政策的形式既为可以实现的目标提供了一个基准，也为衡量使用较少信息的政策的有效性提供了一个基准。更深入的见解是可能的-知道最佳政策的行为与完美的信息可以让一个建立一个近似的这种行为的政策与较少的信息。将在制定这些政策方面投入大量精力，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.**