在全光封包交換網路的主要問題裡，其中之一便是並沒有光封包的暫存器的存在，為了達到暫存封包的目的，目前已知可行的一種方法是利用光交換機將光封包導引進光纖延遲線中，等到適當的時機再將它釋放到適當的地點，以模擬暫存器的效果。在這篇論文裡，我們考慮以光交換機及光纖延遲線建造成的具有繞行次數限制之光佇列。會有這樣的問題產生其實是來自實作上可行性的考量。我們證明了光學線性壓縮器和光學線性解壓縮器(兩種特別的光佇列)的建造問題在簡單的繞行方案及有繞行次數的限制下可以被等價地轉換成一個有相對應限制條件的整數表示問題。具體來說，光學線性壓縮器/解壓縮器的有效最大延遲量等於最大可表示整數B(d_1^M;k)(定義於第一章(1.4)式)，其中d_1^M=(d_1, d_2,..., d_M)為在我們的架構中M條光纖延遲線的延遲量形成之序列，而k為一個封包的最大繞行次數。

給定M與k後，找出最佳建造方式以達到線性壓縮器/解壓縮器最大延遲量的問題等價於在A_M中找出最佳序列使得其對應的最大可表示整數達到最大值，其中A_M是所有被允許構造成線性壓縮器/解壓縮器的光纖延遲線延遲量序列的集合。在這篇論文當中，我們考慮在論文[16]提出的雙輸入埠與單輸出埠之先進先出多工器貪婪建造方式，並且推廣到線性壓縮器/解壓縮器的貪婪建造方式。我們證明每個最佳的建造方式必定是一個貪婪建造方式。

給定M與k後，找出最佳建造方式以達到線性壓縮器/解壓縮器最大延遲量的問題等價於在A_M中找出最佳序列使得其對應的最大可表示整數達到最大值，其中A_M是所有被允許構造成線性壓縮器/解壓縮器的光纖延遲線延遲量序列的集合。在這篇論文當中，我們考慮在論文[16]提出的雙輸入埠與單輸出埠之先進先出多工器貪婪建造方式，並且推廣到線性壓縮器/解壓縮器的貪婪建造方式。我們證明每個最佳的建造方式必定是一個貪婪建造方式。

One of the main problems in all-optical packet-switched networks is the lack of optical buffers, and one feasible technology for the constructions of optical buffers is to use optical crossbar Switches and fiber Delay Lines (SDL). In this thesis, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines. Such a problem arises from practical feasibility considerations. We show that the constructions of optical linear compressors and optical linear decompressors (special types of optical queues) under a simple packet routing scheme and under the constraint of a limited number of recirculations can be transformed into equivalent integer representation problems under a corresponding constraint. Specifically, we show that the effective maximum delay of a linear compressor/decompressor in our constructions is equal to the maximum representable integer B(d_1^M;k) with respect to d_1^M and k (defined in (1.4) in Chapter 1), where d_1^M=(d_1, d_2,..., d_M) is the sequence of the delays of the M fibers used in our
constructions and k is the maximum number of times that a packet can be routed through the M fibers.
Given M and k, therefore, the problem of finding an optimal construction, in the sense of maximizing the maximum delay, among our constructions of linear compressors/decompressors is equivalent to the problem of finding an optimal sequence in A_M, where A_M is the set of all sequences of fiber delays allowed in our constructions
of linear compressors/decompressors. In this thesis, we consider the class of greedy constructions of 2-to-1 FIFO multiplexers proposed in [16], and extend this class of greedy constructions for the constructions of linear compressors/decompressors. We show that every optimal construction must be a greedy construction.

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