多樣少量的生產型態乃是傳統式工廠於１９８０年代所面臨的最大衝擊之一，而彈性 製造系統則是傳統式工廠舒解其困境並獲致競爭優勢之最佳武器，一般而言，彈性製 造系統包括綜合加工中心、物料搬運系統及電腦控制三大子系統，而根據統計顯示工 件實際在機器上加工作業之時間僅佔其在系統中總時間之３５％左右，其耗費在等待 、搬運及儲存之時間卻高達６５％，故物料搬運系統影響系統作業績效之巨，由此可 見一斑，本研究之研究目的即針對以無人搬運車構成彈性製造系統之自動搬運系統時 ，探討搬運系統之設計與控制原則，藉此使廠商能有較進一步的認識，並可作為日後 規劃與設計之依據。許多文獻報告都採用等候理論、數學規劃等技術來進行這方面之 研究，雖然其優點在於簡單、迅速可求得最佳研究，但卻無法反應系統的真車狀況， 故本研究方法仍使用非連續－事件（Discrete-Event）模擬技術模擬自動搬運系統， 來評估系統各種設計與控制方案之作業績效，以推導出一般之原則，雖然模擬較為複 雜及耗時，不過其較能符合實際之要求。本研究首先依據已知之機器佈置、機器數目 、工件的加工條件與加工時間以及工件之到達率等條件，找出無人搬運車之最適搬運 路徑（Routes），然後決定搬運車應有之數目與速度，以及無人搬運車所配備充電電 池之最低容量（Capacity）需求，最後並透過模據評估無人搬運車各項派車方式對系 統績效之影響。本研究發現第一、無人搬運車之路徑選擇影響系統之作業績效甚巨， 而其路徑之決定原則不只在使搬運車承載工件之搬運總長度最小，尚要考慮搬運車空 車行走之總長度，第二、搬運車之數目與速度對系統之產出有顯著之影響，第三、無 人搬運車之最低電池容量可由模擬中搬運車每次生，產週期之平均利用率推算出，如 此可避免電池容量超出所需之成本增加，同時也能防止搬運車於生產過程中耗盡電池 ，而需更換電池或充電之時間浪費，第四、搬運車之派工方式對系統績效有顯著之影 響。

本論文針對隨機數位網路提出一套可行的計算機制，以提供網路管理者進行資源分配與壅塞管理的分析工具。我們研究兩種利潤最佳化模型，探討在預算控制下的頻寬分配方式。因為資源有限，網路管理者無法隨時提供足夠頻寬以滿足隨機的網路需求，而量測網路連結成功與否的阻塞機率(Blocking Probability)為評估此風險之一種指標。我們利用頻寬分配、網路需求量和虛擬端對端路徑的數量等變數，推導阻塞機率函數，並證明阻塞機率的單調性(Monotonicity)和凸性(Convexity)等數學性質。在不失一般性之假設下，我們驗證阻塞機率是(1)隨頻寬增加而變小；(2)在特定的頻寬分配區間內呈凸性；(3)隨網路需求量增加而變大；(4)隨虛擬路徑的數量增加而變小。 本研究探討頻寬分配與阻塞機率之關係，藉由推導單調性和凸性等性質，提供此兩種利潤模型解的最適條件與求解演算法。同時，我們引用經濟學的彈性概念，提出三種模型參數對阻塞機率變化量的彈性定義，並分別進行頻寬分配、網路需求量和虛擬路徑數量對邊際利潤函數的敏感度分析。當網路上的虛擬路徑數量非常大時，阻塞機率的計算將變得複雜難解，因此我們利用高負荷極限理論(Heavy-Traffic Limit Theorem)提供阻塞機率的估計式，並分析其漸近行為(Asymptotic Behavior)。本論文的主要貢獻是分析頻寬分配與阻塞機率之間的關係及其數學性質。網路管理者可應用本研究提出的分析工具，在總預算限制下規劃寬頻網路的資源分配，並根據阻塞機率進行網路參數的調控。 / This thesis considers the problem of bandwidth allocation on communication networks with multiple traffic classes, where bandwidth is determined under the budget constraint. Due to the limited budget, there exists a risk that the network service providers can not assert a 100% guaranteed availability for the stochastic traffic demand at all times. We derive the blocking probabilities of connections as a function of bandwidth, traffic demand and the available number of virtual end-to-end paths for all service classes. Under general assumptions, we prove that the blocking probability is directionally (i) decreasing in bandwidth, (ii) convex in bandwidth for specific regions, (iii) increasing in traffic demand, and (iv) decreasing in the number of virtual paths. We also demonstrate the monotone and convex relations among those model parameters and the expected path occupancy. As the number of virtual paths is huge, we derive a heavy-traffic queueing model, and provide a diffusion approximation and its asymptotic analysis for the blocking probability, where the traffic intensity increases to one from below. Taking the blocking probability into account, two revenue management schemes are introduced to allocate bandwidth under budget control. The revenue/profit functions are studied in this thesis through the monotonicity and convexity of the blocking probability and expected path occupancy. Optimality conditions are derived to obtain an optimal bandwidth allocation for two revenue management schemes, and a solution algorithm is developed to allocate limited budget among competing traffic classes. In addition, we present three elasticities of the blocking probability to study the effect of changing model parameters on the average revenue in analysis of economic models. The sensitivity analysis and economic elasticity notions are proposed to investigate the marginal revenue for a given traffic class by changing bandwidth, traffic demand and the number of virtual paths, respectively. The main contribution of the present work is to prove the relationship between the blocking probability and allocated bandwidth under the budget constraint. Those results are also verified with numerical examples interpreting the blocking probability, utilization level, average revenue, etc. The relationship between blocking probability and bandwidth allocation can be applied in the design and provision of broadband communication networks by optimally choosing model parameters under budget control for sharing bandwidth in terms of blocking/congestion costs.