在這篇論文裡，我們提出建造N對1可變長度封包叢組之輸出緩衝先進先出光學多工器的方法。我們利用一個由光交換機與光纖延遲線組成的多層級前饋式架構來建造N對1可變長度封包叢組之輸出緩衝先進先出光學多工器。由於封包所需的延遲時間在封包到達時就是已知的，我們參考論文[28]的作法，將封包的延遲時間拆解成r進位表示式，接著讓封包在前饋式架構中依據r進位表示式做自我繞行(self-routing)的動作，並且在繞行時滿足下列三個限制: (i) 封包碰撞限制: 在任意時間裡不能有超過一個封包被繞行到光交換機的同一個輸入端 (ii) 因果關係限制: 任何封包叢組都不能夠在其到達輸入端之前被排程 (iii) 嚴格連續性限制: 在同一個叢組裡的封包會連續地依循相同路徑被傳送到此延遲路徑的光纖延遲線裡。為了滿足封包碰撞限制，在這樣的前饋式架構裡，我們為每一個延遲時間提供了許多的路徑。為了使我們的建造方式能被操作成一個N對1可變長度封包叢組之輸出緩衝先進先出光學多工器，在前饋式架構中每個層級所需的光纖延遲線數目上，我們獲得了一個充分條件。由於叢組內封包的排程滿足嚴格連續性限制，所以不需要執行叢組的分割與重組，因此建造的複雜度與繞行的複雜度可以被大幅縮減，這是我們所提出之建造方式的一大優點。

In this thesis, we propose the constructions of N-to-1 output-buffered first-in first-out (FIFO)
multiplexers for variable length bursts. We consider a multistage feedforward network con-
sisting of optical crossbar Switches and ‾ber Delay Lines (SDL) for the constructions of
N-to-1 output-buffered FIFO multiplexers for variable length bursts. Since the delay of a
packet (in a burst) is known upon its arrival for N-to-1 output-bu®ered FIFO multiplexers
with variable length bursts, as in the previous work [28] we use the r-ary representation of
the packet delay for the self-routing of a packet through such a feedforward network, and
we schedule the bursts so that the following three constraints are satis‾ed: (i) Con°ict con-
straint: no more than one packet can be scheduled at the same input/output port of any
crossbar switch at the same time. (ii) Causality constraint: no burst can be scheduled before
its arrival. (iii) Strong contiguity constraint: packets in the same burst should be routed
through any ‾ber delay line contiguously. To satisfy the con°ict constraint, we provide
multiple delay paths in such a feedforward network for each delay. We obtain a su±cient
condition on the number of ‾ber delay lines in each stage of the feedforward network for the
constructions of N-to-1 output-bu®ered FIFO multiplexers for variable length bursts. Since
we schedule the bursts so that the strong contiguity constraint is satis‾ed, there is no need to
perform burst segmentation and reassembly, which is a great advantage of our constructions
as both the construction complexity and the routing complexity can be greatly reduced.

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