於即時系統(Real-Time System)中，回饋機制排程法提供了一個較具彈性的模型，回饋機制排程法與許多現實上的應用程式相似，如多媒體應用程式及反覆定義型的演算法。回饋機制工作由兩個部分組成，分別是主要部分工作(Mandatory Part)和次要部分工作(Optional Part)，次要部分工作必需要在主要部分工作完成後，才能開始執行。而每一個次要部分工作都伴隨了一個回饋函式，回饋函式定義了當次要部分工作執行了某段時間後，它所能得到的回饋值，在多數的研究中，回饋函式常為凹面型(cancave)回饋函式或直線型(linear)回饋函式。此兩種函式被認為是最接近於實際應用程式的函式，因此，論文中的回饋函式，也以此兩種函式為依歸。傳統上的回饋機制排程演算法專注於如何使系統整體的回饋值達到最大值。也因為如此，這些回饋機制排程演算法常常造成系統工作所收到的回饋值不平衡。有些工作可能會得到極高的回饋值，而有些工作可能會得到極低的回饋值。在這篇論文中，我們將提出一個最佳化的回饋平衡演算法，使每個工作能得到相同的回饋品質率。首先，我們將討論當回饋函式是可逆且漸增的時候，我們將利用數學的方式解決。接下來，我們對於一般函式或不可逆函式發展另一套演算法。最後，我們將利用實驗以證明我們的排程演算法是有效率並且有好的效用。實驗結果證明，我們的確發展出一套有效率並且有效用的演算法。

Reward-based scheduling provides graceful degradation for real-time systems such as multimedia applications and iterative-refinement numerical algorithms. A reward-based task is composed of a mandatory part and an optional part which only executes after completion of the mandatory part. Traditional reward-based scheduling algorithms address on maximizing the total reward in a system. Such an algorithm may result in an unbalanced system where some tasks receive results of superior quality while other tasks only receive minimal acceptable results. In this paper, we present an optimal balanced-reward algorithm such that each task receives the same quality ratio. We first discuss the case where each reward function is strictly increasing and invertible. A mathematical approach is presented to determine the optimal quality ratio. We next develop an efficient generic solution for general cases where some reward functions are not invertible. We conducted experiments to compare our algorithm with a set of other reward-based algorithms to demonstrate its effectiveness. The experimental results show that our algorithm effectively and efficiently develops an optimal balanced-reward schedule.

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