論文摘要
這篇文章我們提出了一個以配對作為原則適用在異質環境下的排程演算法，我們的演算法與其他演算法所不同的是我們的演算法除了可以用在一般的異質環境下，更可以進一步地使用在機器的處理能力隨時間而變動的狀況下。
我們的方法是將每一台機器視為一類，依處理能力分由小到大分類，再將工作量以同樣由小到大的方式，按照各台機器處理能力所佔總處理能力的比例，將工作也做分類，再將各類機器的處理能力代入相對應類別的節點以求得每一工作節點的時間計算成本。對於每一個工作節點的執行優先等級，我們將其執行時的預期時間成本及其在工作圖上直接相連之子節點等級總和，和最大子節點之總和做為該節點點排列優先等級的依據，總和大的先做。另外在工作分配給機器時，我們採取動態分配的方式，意即在機器處理能力無任何變動時，我們按照分類大小比較與最早完成工作時間的方式來做為排程的依據，但若機器未按照預定的排程時間完成工作時，我們便認定其處理能力改變，則我們的演算法將重新進行工作排程。
我們將實驗分為動態與靜態的異質環境，在機器處理能力不變的環境，我們稱為靜態的異質環境;機器處理能力隨時間改變的環境我們稱為動態的異質環境。並與DLS（Dynamic Level Scheduling）[12]，HNF（Heavy Node First）[6]
WLA(Weighted Leanth Algorithm)[6]比較其效能，證明了我們的演算法不管在機器處理能力變動的或不變的狀況下相對於它們而言，都有著較佳的效能，且在機器處理能力標準差大時效能越顯著，除此外我們和DPS(Dynamic Priority Scheduling)演算法[18]比較，在機器處理能力不變的狀況下於效能上我們的演算法是和DPS差不多的，但在時間複雜度上，DPS是 而我們的演算法在時間複雜度上為只要 ，於機器處理能力變動的狀況下則有著較好的效能，證明了我們的演算法同時適用於動態與靜態的異質環境。

Abstract
In this thesis we propose a match_based scheduling algorithm for heterogeneous environment. The major difference of our algorithm from other researches is that it considers the variation of computing power with time.

In our algorithm the each host is regarded as a group, their computing powers are sorted in ascending way and the ratio of each computing power with the total computing power is calculated. Similarly, the workload of tasks is classified and is sorted to the relative computing power in ascending way, then is assigned to one of host groups depending on the balance of computing power. The execution cost for each node of the task group is calculated from the task load and the computing power of host been assigned. In order to determine the priority of execution, the rank of each task is calculated from the total of the execution costs, maximum execution cost of its immediate successor, and the summation of ranks of all immediate successors.

Experiment results show that the proposed algorithm has better performance than DLS (Dynamic Level Scheduling)[12], HNF (Heavy Node First)[6], WLA (Weighted Length Algorithm)[6] and DPS (Dynamic Priority Scheduling)[18], especially, for heterogeneous environment.

1動機及背景知識
1.1研究動機
1.2背景知識
2問題定義及模型
3相關演算法
3.1 DLS (Dynamic Level scheduling )
3.2 HNF (Heavy Node First)
3.3 WLA (Weighted Length Algorithm）
3.4 DPS (Dynamic Priority scheduling)
4演算法
4.1動機來源及演算法基本構想
4.2演算法相關之符號及定義
4.3演算法描述
4.4演算法實例
5 效能評估
5.1測試案例的產生
5.2實驗結果
5.3結果討論
6結論
參考文獻

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