Research On Energy-efficient Management And Optimal Dynamic Energy-efficient Policies In Data Centers

During the last two decades,considerable attention has been paid to studying the energy-efficient management in data centers.As the number and size of data centers increase rapidly,tremendous energy consumption becomes a significant operation expense of data centers.On the other hand,data centers have become a core part of the IT infrastructure for today's Internet services,in which hundreds of thousands of servers are deployed in a data center to provide ubiquitous computing environments.Therefore,finding optimal energy-efficient policies and designing optimal energy-efficient mechanism are both the research directions with theoretical challenges and application values.Most of the previous works applied the vacation and the setup queues to provide static optimal policies for energy-efficient management in data centers.In this thesis,an energy-efficient evaluation index system is given by Group-Server Queues,and dynamic energy-efficient policies are provided by using Markov decision process and the sensitivity-based optimization theory for energy-efficient management in data centers.The main results of this thesis are as follows:Firstly,by analyzing energy-efficient management of data centers,we propose and develop a class of important Group-Server Queues.Not only analyzing and summarizing the research problems,research methods,and theoretical difficulties for general group-server queues,but also establishing two representative group-server queues through loss mechanism and impatient customers,respectively.Furthermore,simple mathematical discussion is provided for such two group-server queues,and an energy-efficient index system is established.Finally,some numerical examples are made to show how the performance measurement depends on the key parameters for such group-server queues in energy-efficient data centers.Secondly,a novel dynamic decision method is proposed by applying the sensitivity-based optimization theory to find the optimal energy-efficient policy of a data center with two groups of heterogeneous servers.To find the optimal energy-efficientpolicy,we set up a policy-based Poisson equation,and provide explicit expressions for its unique solution of performance potentials by means of the RG-factorization.Based on this,we characterize monotonicity and optimality of the long-run average profit with respect to the policies under different service prices.We prove that the bang-bang control is always optimal for this optimization problem.As an easy adoption of policy forms,we further study the threshold-type policy and obtain a necessary condition of the optimal threshold policy.Thirdly,we establish a block-structured continuous-time Markov process under an asynchronous energy-efficient policy in a data center with two groups of heterogeneous servers,a finite buffer,and a fast setup process.For such a data center,we establish the block-structured asynchronous energy-efficient policy-based continuous-time Markov process,and introduce the state transition relations and the infinitesimal generator in detail.Based on this,we compute the stationary probability vector of the Markov process by means of the UL-type RG-factorization.Fourthly,the optimal asynchronous energy-efficient policy in the data center is analyzed by sensitivity-based optimization theory.We establish the asynchronous energy-efficient policy-based block-structured Poisson equation to compute the unique solution by means of the RG-factorization.Based on this,we discuss the monotonicity and optimality of the long-run average profit of the data center with respect to the asynchronous dynamic policy under different service prices.Furthermore,we provide the optimal asynchronous energy-efficient policy and prove that the bang-bang control is always optimal for this optimization problem.For a threshold-type optimal asynchronous energy-efficient policy,we compute the maximal long-run average profit.Fifthly,this thesis takes the data center A in Qinhuangdao as an example.According to some actual situations of energy-efficient management in this data center,we evaluate the energy-efficient indices by comparing the analytical and numerical results,and discuss optimal energy-efficient policies under different service prices through some numerical experiments.