數據中心具備強大的運算能力、龐大的儲存空間來提供使用者的資料以及提供工具讓使用者來處理他們的資料。
可用性(availability)一直以來是數據中心的一個主要的議題，近日以來，不中斷(always-on)服務的需求不斷增加，使得數據中心的穩定性變得更加重要。
然而，在數據中心裡，在機器上執行的虛擬機器(virtual machine, VM)有時會遇到硬體發生的錯誤，這對於虛擬機器所提供的不中斷服務而言是個挑戰。
在數據中心建立備份虛擬機器是提升數據中心的穩定性一種方法。
執行中的虛擬機器需要定期更新在其他機器上的備份虛擬機器(backup VM)，以便在硬體發生錯誤時，啟動在其他機器上的備份繼續提供使用者服務。
在這篇論文中，我們提出一個嶄新的虛擬機器備份的問題，並且證明這個問題是NP-hard。根據我們所提出的問題，我們提出一個啟發式演算法(heuristic algorithm)來擺放備份虛擬機器。
我們使用一個數據中心網路結構和累計超過三年的虛擬機器建立請求的紀錄，並且加入一些合成的資料，來將我們的演算法與一些貪心演算法做比較。
從模擬的結果來說，我們的演算法勝過其他的貪心演算法。

Data centers have powerful processing capabilities, large storage, and backup power supplies to store the users' data and provide tools that enable users to process their data.
Availability is one of the main issues in data center. Recently, the raising of always-on online services has made the availability of data center more important.
However, the virtual machines (VMs) running in sites inside a data center are under the risk of hardware failure.
This made the challenge to make the service always-on.
Backing up VM is one way to improve the availability of data center.
Live VMs have to periodically update itself to remote sites to keep backups up to date.
When a live VM is down due to hardware failure, then one of the backup VMs in the other sites will be turned on to keep the service going on.
Due to the fact that the used network bandwidths of VMs are seldom to reach the requested network bandwidths of VMs at the same time, we can minimize backup cost by increasing the network bandwidth oversubscription.
In this thesis, we introduce a novel minimum non-metric costcost VM backup problem with network bandwidth oversubscription.
Next, we prove the introduced problem is NP-hard.
Due to the fact underlying the network bandwidth-oversubscription model is that statistically few users will attempt to fully utilize their requested network bandwidth simultaneously, we propose a heuristic adaptive bandwidth-oversubscription algorithm to backup live VMs.
We conduct simulations, using the semisynthetic data to compare the proposed algorithm with some greedy-based heuristics.
The simulation results show that the proposed algorithm outperforms these heuristics.

中文摘要 i
Abstract ii
Contents iv
List of Figures v
1 Introduction 1
2 Related Works 5
3 Problem Definition 7
3.1 The Problem 7
3.2 The Hardness 8
4 The Proposed Algorithm 10
5 Performance Evaluation 13
6 Conclusion 18
Bibliography 19

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