本論文提出一個由M/M/1排隊理論模型和遞迴公式所組成的數學架構去估計分時/分波多工乙太被動式光學網路系統(Ethernet Passive Optical networks,簡稱EPONs)的平均封包延遲時間和平均佇列長度。在本架構中，M/M/1排隊理論模型是用來估量不同優先權網路資料的效能，而遞迴公式則用來分析在被動式光學網路中以適應循環時間交錯詢問演算法(Interleaved Polling Adaptive Cycle Time,簡稱IPACT)為基礎的動態頻寬分配協定。該架構的重要特性為此分析架構不但可以用來分析支援品質傳輸保證的傳統乙太被動式光學網路，也可以應用於分析一個具有私有傳輸能力（即在網路中，允許光網路單元(Optical Network Unit, 簡稱ONU)可互相傳輸資料）的分波多工乙太被動式光學網路。再者，本論文藉由一系列的電腦模擬實驗去驗證所提出分析模型的正確性和準確性。經由模擬結果可發現使用分析架構所得到的數據和電腦模擬執行出來的結果互相吻合，由此可證明本分析架構可以準確的分析分時/分波多工乙太被動式光學網路的系統效能。

This thesis proposes a mathematical framework comprising an M/M/1 queuing model and a recursive formulation to derive the mean packet delay and the mean queue length for TDM/WDM EPON systems. The M/M/1 queuing model is used to analyze the performance of different traffic priorities while the recursive formulation is applied to model the polling behavior of IPACT-based protocols employed in EPON-based networks. Importantly, the analytical framework can be used to analyze the performance not only for conventional EPON networks with QoS support but also for WDM EPON systems with private networking capability, i.e., the ONUs are allowed to communicate directly with one another. Furthermore, the correctness and accuracy of the proposed framework is verified by performing a series of computer simulations. The analytical results derived using this model for the mean packet delay and mean queue length are found to be in good agreement with those obtained from computer simulations.

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