We consider an auto-scaling technique in a cloud system where virtual machines hosted on a physical node are turned on and off depending on the queue's occupation (or thresholds), in order to minimise a global cost integrating both energy consumption and performance. We propose several efficient optimisation methods to find threshold values minimising this global cost: local search heuristics coupled with aggregation of Markov chain and with queues approximation techniques to reduce the execution time and improve the accuracy. The second approach tackles the problem with a Markov Decision Process (MDP) for which we proceed to a theoretical study and provide theoretical comparison with the first approach. We also develop structured MDP algorithms integrating hysteresis properties. We show that MDP algorithms (value iteration, policy iteration) and especially structured MDP algorithms outperform the devised heuristics, in terms of time execution and accuracy. Finally, we propose a cost model for a real scenario of a cloud system to apply our optimisation algorithms and show their relevance.

中文翻译：

---

云端资源分配的最优控制策略：马尔可夫决策过程与启发式方法的比较

我们考虑在云系统中使用一种自动缩放技术，在该系统中，根据队列的占用情况（或阈值）打开和关闭托管在物理节点上的虚拟机，以最大程度地降低整合能耗和性能的总体成本。我们提出了几种有效的优化方法来找到最小化此全局成本的阈值：局部搜索启发式算法与马尔可夫链的聚合方法以及队列逼近技术相结合，以减少执行时间并提高准确性。第二种方法通过马尔可夫决策过程（MDP）解决了这个问题，我们将对其进行理论研究，并与第一种方法进行理论比较。我们还开发了具有滞后特性的结构化MDP算法。我们展示了MDP算法（值迭代，策略迭代），尤其是结构化的MDP算法，在时间执行和准确性方面均优于设计的启发式算法。最后，我们为云系统的实际方案提出了一种成本模型，以应用我们的优化算法并显示其相关性。