在能夠控制封包延遲之情況下，我們將提出多級架構之類似電路交換機來進行討論。在輸入訊務符合峰值平穩 ((r, T)-smooth) 的限制條件之下，也就是在一定的時間區間之內，每一個流量的訊務量確保一定在某一個已知的最大訊務量之下。基於此種假設，增加一層負載平衡的 Birkhoff-von Neumann 類似電路交換機，可以達到傳輸速率保證的服務，也就是能夠控制封包的延遲時間。因為不會產生封包順序混亂的情形，此架構不需要在輸出端增加一個重新排序的暫存器。

此類似電路交換的架構雖然可以達到傳輸速率保證的服務，但是當交換機的架構擴大時，其最大封包延遲時間也同時增加。同時，也提高了硬體設計的複雜度。為此，我們提出一個多級架構之類似電路交換機，以 Banyan 網路為基礎的系統，用多個硬體設計複雜度低的 類似電路交換機完成一個大的交換機網路。此架構同樣具有傳輸速率的保證。當中的每一個交錯式交換機的變更週期與碼框的大小相同，不需要做另外的計算以降低複雜度。我們將證明在交換機的架構大於 時，Banyan-based類似電路交換機相較於加一層負載平衡的Birkhoff-von Neumann 類似電路交換機，具有較低的最大封包延遲時間，與較佳的統計特性。與Benes類似類似電路交換機比較，我們可以證明在碼框小於某些邊界值時，Banyan-based類似電路交換機具有較低的最大封包延遲時間與平均封包延遲時間。

In this thesis, we propose the multi-stage architecture for quasi-circuit switching to discuss. In the previous work, we have assumed that all input flows are (r, T)-smooth. Furthermore, it is assumed that the all inputs of an switch satisfy the no overbooking condition. Load balanced Birkoff-von Neumann quasi-circuit switch is one of quasi-circuit switches. It can provide guaranteed rate services and all the packets would be transmitted their destinations without lost.

Although this quasi-circuit switch can offer quality of services, the maximum delay becomes larger and the hardware complexity increases as the size of switch fabric is large. Therefore, we propose a multi-stage architecture for quasi-circuit switch, called Banyan-based scheme. It is composed of some quasi-circuit switches. Each of crossbar fabrics has one-cycle permutation matrix and changes its matrix every frame time. We will prove that the Banyan-based scheme has less maximum delay than former scheme as the size of switch fabric is larger than . To compare with Benes quasi-circuit switches; the Banyan-based scheme has less maximum and average delay as the frame size is less than some values.

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