A distinctive feature of cloud computing is that it enables customers to dynamically summon server instances. Service providers facing uncertain demand patterns may exploit this feature by setting automatic provisioning rules for right-sizing the capacity contracted from the cloud. This situation can be modeled by a queueing system where the numbers of both jobs and servers evolve in time, the latter subject to delays in creation and deletion. We study in this context different feedback rules with the objective of efficiently matching capacity and load, while simultaneously providing a high quality of service.

These rules are analyzed by means of fluid and diffusion limits for Markov chains. In particular we develop suitable extensions of the classical literature on this topic, required to accommodate non-homogeneous intensity scalings and non-differentiable drift fields. With these tools, our final proposal is shown to exhibit properties akin to the Halfin–Whitt regime, achieved automatically without knowledge of the system load. We further investigate by simulation its behavior under time-varying load, demonstrating the capabilities of our design to provide quality and efficiency in highly dynamic scenarios.

云计算的一个显着特点是它使客户能够动态地召唤服务器实例。面临不确定的需求模式的服务提供商可以通过设置自动配置规则来对从云签约的容量进行适当调整来利用此功能。这种情况可以通过排队系统建模，其中作业和服务器的数量随时间变化，后者在创建和删除时会出现延迟。我们在此背景下研究不同的反馈规则，目的是有效匹配容量和负载，同时提供高质量的服务。

这些规则通过马尔可夫链的流体和扩散限制进行分析。特别是我们开发了关于这个主题的经典文献的适当扩展，需要适应非均匀强度缩放和不可微的漂移场。使用这些工具，我们的最终建议显示出类似于哈芬-惠特机制的特性，在不了解系统负载的情况下自动实现。我们通过模拟其在时变负载下的行为进一步研究，展示了我们的设计在高动态场景中提供质量和效率的能力。