在這篇論文裡，我們推廣了論文[5]中使用光交換機與光纖延遲線建造優先權光佇列之方式。詳細而言，我們證明了，可以使用一個由[(2k-1)4m+2]×[(2k-1)4m+2]的光交換機與2k-1組先進先出光學多工器組成的回授系統與一種基於封包優先權的控制方式，建造一個容量為B^*=(r+1)r^{k-1}-2的優先權光佇列。其中，k>=1、r>=2、m=r(r-1)+1，而每一組先進先出光學多工器是由m個容量相同（由(1.1)式給定）且平行設置的4對1先進先出光學多工器組成。

In this thesis, we present a generalization of the Switched-Delay-Lines (SDL) construction of an optical priority queue in [5].
Specifically, we show that by using a feedback system consisting of a [(2k-1)4m+2]×[(2k-1)4m+2] (bufferless) optical crossbar switch and 2k-1 groups of FIFO multiplexers, an optical priority queue with buffer size B^*=(r+1)r^{k-1}-2 can be achieved under a priority-based routing policy, where k>=1, r>=2, m=r(r-1)+1, and the i^{th} group has m parallel 4-to-1 FIFO multiplexers with the same buffer size B_i that is given by (1.1) for 1<=i<=2k-1.

Abstract
Contents
1 Introduction 1
2 Definitions of Priority Queues and FIFO Multiplexers 3
3 The Generalization and the Main Result 7
4 Conclusion 13
Bibliography 15

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[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(M^3) 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.

[6] J. Cheng, C.-Y. Wang, and B. Tang, “Constructions of optical priority queues under a priority-based routing policy,” in Proceedings IEEE International Conference on Computer and Communications (ICCC’19), Chengdu, China, December 6–9, 2019.