近幾年來，光佇列的建造在學術界引起了很多注意，這個研究主題主要是起因於在全光網路中我們並沒有可以存放光封包的隨機存取記憶體，為了達到儲存光封包的目的，除了將光封包轉換成電的形式以外，目前已知的唯一方法是利用光交換機將光封包導進光纖延遲線中，等到適當的時機再將它從適當的地點釋放出來，以達到模擬存放光封包的效果。關於如何利用光交換機與光纖延遲線建造各種光佇列，目前在文獻上已經有一些理論研究成果的發表，包括輸出緩衝儲存交換機、先進先出光學多工器、先進先出光佇列，後進先出光佇列、優先權光佇列、光學線性壓縮器、光學不超越延遲線、以及可調變光纖延遲線等等。
在這篇論文裡，我們專注於證明有容錯能力之雙輸入埠與單輸出埠先進先出光學多工器的已知建造方式之最佳漸進建構效率(亦即使其緩衝區容量為最大)。這樣的容錯能力是來自現實世界中光纖可能損壞的考量。雙輸入埠與單輸出埠之先進先出光學多工器可以由一個具有M+2輸入埠與M+2輸出埠的光交換機以及 條光纖延遲線建造出來。在此架構下，鄭傑教授已提出一組建構方式，能使原本的回溯架構具備允許最多F (F為容錯能力)條光纖損壞後，剩下的光纖依舊可以操作成一個雙輸入埠與單輸出埠先進先出之光學多工器，並且從這一組建構裡面找出其中的最佳建構方式(亦即使其緩衝區容量為最大)。我們在這篇論文裡的主要貢獻，是證明出在最佳的建造方式中，所有長度為 之光纖的數目 所形成之序列在k夠大的時候會具有週期性，並且我們證明此最佳建造方式的漸進建構效率可以表示成一個簡單明確的數學表達式。

In this thesis, we consider a class of constructions of fault-tolerant optical 2-to-1 first-in
first-out (FIFO) multiplexers that was studied in one of the authors’ previous work. Such
constructions use a feedback network consisting of an (M + 2) × (M + 2) optical crossbar
switch and M fiber delay lines with delays d1, d2, . . . , dM and can tolerate up to F broken
fibers, where d1, d2, . . . , dM satisfy the condition in (A2) in Chapter 1 and 0 <= F <= M − 1.
We show some properties of the fiber delays in an optimal (in the sense of maximizing the
buffer size) construction among this class of construction. We also obtain a closed-form
expression for the asymptotic construction efficiency of an optimal construction among this
class of construction.

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