參考Yue等論文，我們延續探討在通訊網路中對於非及時Available Bit Rate(ABR)資料與及時Variable Bit Rate(VBR)資料共同使用一條傳輸的等候模型。假設及時VBR資料傳輸較非及時ABR資料傳輸有優先權，我們建立與分析資料在離開過程之模型。本論文研究在非強制性優先權策略下之一般等候模型，藉由ABR資料的等候區域設立檢查點來控制流入量，在離開過程中推導VBR資料與ABR資料的離去時間的數學關係式，以及調查他們的數值模擬的表現。在此數學推導中需要藉MMBP關係，從ABR資料的等候區域觀點製造Markov矩陣算出穩定狀態下的機率分量、生成函數以及閒置時間的函數。結果發現檢查點影響兩者的離去時間並不顯著，但是VBR資料流入的速度卻會造成影響。 / Following the work by Yue et al., this thesis considers the departure of a multi-traffic network system for a popular communication network where a transmission link is shared by an Available Bit Rate (ABR) application for non-real time traffic and a Variable Bit Rate (VBR) application for real time traffic. It is assumed that the VBR traffic has a higher transmission priority than the ABR traffic. In this thesis, we establish a tractable analytical model of departure processes for such a system. The departure process is characterized by a general queueing model with a non-preemption policy for which the inter-departure times of VBR and ABR are derived, respectively. Since the VBR traffic is only affected when ABR is in service, the analysis is given to describe the departures of ABR, and VBR traffics. Numerical results are conducted to illustrate the system performance with input control of ABR traffic.

在本文中，我們主要研究的目標是Ｅm/Ｅk/１模型的離去過程之相關性。 在此之前，不少學者作了很多有關M/G/1模型和G/M/1模型離去過程的相關性研究，但當等候理論中的“失憶性”(memoryless)這個重要的性質不再適用後，會產生什麼結果呢？ 為了解Ｅm/Ｅk/１的相關性，我們引入N-階段離去時間分配”(N-step interdeparture time distribution)的方法。藉由這個方法，我們可以計算出系統中離去間隔時間的期望值，E(DN)，二階期望值， E(D2N)，變異數，Var(DN)，共變異數，Cov(D1,DN)，和相關係數，Corr(D1,DN)。 / In this thesis, our goal is to study the correlation coefficients of the departure process in the E_m/E_k/1 model. Many authors conduct a lot of researches about the correlation coefficients of M/G/1 models and G/M/1 models. But what if the property of “memoryless" fails ? To realize the correlation coefficient of E_m/E_k/1, we derive the methodology of N-step interdeparture time distribution which was presented by Luh in 1999. By adopting it, we can calculate the expectation, E(D_N), second order expectation, E(D_N^2), variance, Var(D_N), covariance, Cov(D_1,D_N), and correlation coefficients, Cov(D_1,D_N) of the system.