我們以公平頻寬配置考慮網路上多重等級與多重服務品質的效用函數， 利用權重效用函數提出兩種數學最佳化模型。 這兩個模型的目標都是要尋找權重效用函數總和值的最大值。 本篇論文特別以權重為決策變數， 研究最佳權重的行為模式， 並求得最佳權重分佈公式。 我們發現模型I的總權重效用只看重某個效用值最大的等級， 完全忽略其他效用值較小的等級； 即最大效用函數的最佳權重為1，其他效用較小的最佳權重為0。 在最佳化過程中， 模型II的數值資料呈現出最佳權重架構為：最佳權重中的每個權重均相等，且總和為1。 我們隨後證明這些結果，並利用GAMS軟體來呈現數值資料。 / We propose two mathematical models with weighted utility functions for the fair bandwidth allocation and QoS routing in communication networks which offer multiple services for several classes of users. The formulation and numerical experiments are carried out in a general utility-maximizing framework. In this work, instead of being fixed, the weight for each utility function is taken as a free variable. The objective of this thesis is to find the structure of optimal weights that maximize the weighted sum of utilities of the bandwidth allocation for each class. We solve it by proposing two models in terms of fairness. Model I and II are constructed to compare different choices for optimal weights. For Model I, the structure of optimal weights form a vector which consists of one for a class and zero otherwise. For Model II, the form of optimal weights is that each weight of utility function is equally assigned. The results are proved and illustrated by software GAMS numerically.

面對通訊與資訊科技的大幅進步，通訊網路正在進行一個巨大的變革，要將電信網路與數據網路整合成一個單一的All-IP網路以支援所有網路應用服務。欲達到整合型網路的理想，仍有許多困難尚待克服，而服務品質問題是其中最關鍵的問題之一。因為受限於封包交換網路之原有的特性，All-IP網路有影響服務品質的三項因素：過長的延遲時間、抖動以及封包遺失。首先，我們利用了達成度函數(achievement function)來處理單位的轉換，使得能夠同時考量此三項不同單位的因素。接著，本文中提出一套方法來解決All-IP網路上端對端(end-to-end)的資源配置及路徑規劃問題。在分配資源時，我們企圖提供一種成比例的公平性給各個不同等級。此公平性的精神是要使得所有網路使用者的滿足程度相當，而非各個不同等級的使用者分配到相同的資源。我們將以預算方式控制端對端品質管理以追求使用者之整體最大滿意程度。 本論文的規劃概念是將網路規劃分成兩個階段。第一階段是在一筆給定的總預算底下，以成比例的方式去分配資源給各個不同等級，並建置網路上的頻寬，使各等級能依其需求拿到適當的頻寬，確保滿足程度相當。 接下來第二階段則是在第一部份已完成的規劃基礎下，做路徑規劃，指派新進入的使用者到一條較好的路徑，在滿足此使用者的延遲時間要求下，使此系統的壅塞程度越小越好。路徑規劃的概念為如何挑選最佳網路路徑，以規劃具服務品質之端對端路徑，並可達到資源之最有效利用。網路營運者將可運用此套方法來調校自身所營運的網路以追求使用者最高滿意度。 / We present an approach for the fair resource allocation problem and QoS routing in All-IP networks that offer multiple services to users. The objective of the optimization problem is to determine the amount of required bandwidth for each link and each class to maximize the sum of the users' utility. In this work, we focus on approaches that, while allocating bandwidth, attempt to provide a proportionally fair treatment of all the competing classes. First, we will show that an achievement function can map different criteria subject to various utility onto a normalized scale. It may be interpreted as a measure of QoS (Quality of Service) on All-IP networks. Using the bandwidth allocation model, we can find a Pareto optimal allocation of bandwidth on the network under a limited available budget. This allocation can provide the so-called proportional fairness to every class, that is, this allocation can provide the similar satisfaction to each user. Next, we present a routing scheme under consideration of the delay. Such an optimal path provides the end-to-end QoS guarantees to each user. Finally, a numerical example is given to illustrate how to solve the fair resource allocation problem and how to modify the nonlinear parts.