由於光訊號難以儲存和轉發，因此通過光交換機和光纖延遲線(SDL) 引導光封包是一種
無需將光封包轉換為其他形式即可存儲光封包的方法。我們所使用SDL 結構是由一個光
交換機和多個光學的先進先出多工器所組成的一個回授系統。在先前的研究中已經證明了
此結構可以作為一優先權光佇列運作，並且已經具備了很多建造SDL 結構的充分條件。
在這篇論文裡，我們提出了光優先隊列的兩個充分條件。具體來說，我們首先推導出了使
用我們的新條件下所建造出來的結構，光纖延遲線的使用會變成原有條件下所建造出結構
的一半，因此成本和復雜度可以大幅度的降低。接著，我們總結出了制定光學的先進先出
多工器容量上限的條件可以擴增為原有上限加一，因此我們可以在我們的系統中存儲更多
的封包。

Since photons cannot be easily stored, and forwarded, directing optical packets through optical Switches and fiber Delay Lines (SDL) is a way to store optical packets without converting them into other media. We use a SDL constructions which is a feedback system consisting of an optical switch and multiple optical FIFO multiplexers with delay one. The construction has been proved that it can be operated as an optical priority queue in previous work, and
there have already been many sufficient conditions for the SDL construction.
In this thesis, we propose two sufficient conditions of optical priority queues. Specifically, we first deduce that the use of fiber delay lines with our new condition could become one-half
of the use fiber delay lines with the original condition, thus, the cost and complexity are much lower than the constructions with original condition. Later, we conclude that the upper bound
of a conditions for specifying buffersize of FIFO multiplexers with delay one can become larger by 1, hence we can store more packets in our system.

Abstract i
Contents iii
1 Introduction 1
2 Definitions of Priority Queues and FIFO Multiplexers 5
3 The Simulation and the Main Result 9
4 Conclusion 19
Bibliography 21

[1] J. Cheng, S.-H. Yang, C.-Y. Wang, H.-H. Tang, and B. Tang, ”On Efficient Constructions
of optical priority queues,” submitted for publication
[2] A. D. Sarwate and V. Anantharam, “Exact emulation of a priority queue with a switch
and delay lines,” Queueing Systems: Theory and Applications, vol. 53, pp. 115–125,
July 2006.
[3] H.-C. Chiu, C.-S. Chang, J. Cheng, and D.-S. Lee, “Using a single switch with O(M)
inputs/outputs for the construction of an optical priority queue with O(M3) buffer,”
in Proceedings IEEE International Conference on Computer Communications (INFOCOM’
07 Minisymposium), Anchorage, AK, USA, May 6-12, 2007.
[4] A. Datta, “Construction of polynomial-size optical priority queues using linear switches
and fiber delay lines,” IEEE/ACM Transactions on Networking, vol. 25, pp. 974–987,
April 2017.
[5] B. Tang, X. Wang, C.-T. Nguyen, B. Ye, and S. Lu, “Construction of subexponential-size
optical priority queues with switches and fiber delay lines,” IEEE/ACM Transactions on
Networking, vol. 28, pp. 336–346, February 2020.