Abstract: In the cloud computing environment, due to complex state of virtual machine normal operation, a novel method, processor running state is thought as hardware/software series repairable system and normal operation is described by Weibull distribution, is proposed to remit serious energy problems. The correlation model among processor utilization, energy and given task completion time is structured by a semi-Markov process which formulated for virtual machine operation, Laplace-Stielties transform which used to simplify numerical calculation, and Bayesian theorem which used to remove restricted condition. Combined with repairable system lifetime distribution theory, probability density function of VMs normal operation is changed. It can obtain processor operation energy consumption and a given task completion time under different shape parameter of Weibull distribution. The implied relationship among shape parameter, processor utilization, energy and performance is analyzed to give some rational proposal in order to effectively reduce energy consumption. Numerical examples results show that increasing shape parameter is superior to improving processor utilization about reducing energy consumption. Increasing shape parameter by improving processor configuration not only can significantly reduce energy consumption, and can avoid depletion of system performance.

Key words: cloud computing, energy consumption, Weibull distribution, shape parameter, semi-Markov process

摘要： 针对云计算环境中复杂的虚拟机正常运行状态，提出将虚拟机运行看成由硬软件串联的可修复系统，用威布尔分布描述虚拟机硬软件正常运行的方法来建模缓解云计算高能耗问题。运用半马尔科夫过程刻画虚拟机运行过程、Laplace-Stielties变换简化数值计算、Bayesian定理去除限制条件，构建处理器利用率与能耗、性能的关系模型。再结合可修复系统寿命分布理论，调整虚拟机正常运行的威布尔分布函数，得到不同形状参数下处理器运行能耗以及给定任务完成时间，最终分析形状参数、处理器利用率与能耗-性能隐含关系并给出有效降低处理器运行能耗的合理化建议。数值分析表明：增大形状参数比提高利用率更显著降低处理器运行能耗；优化虚拟机配置使得形状参数变大，可以明显降低处理器运行能耗，同时避免云系统性能过度损耗。

关键词: 云计算, 能耗, 威布尔分布, 形状参数, 半马尔科夫过程