在這一篇文章中，我們探討Banyan型網路在干擾限制下的多重傳送可重排性．令n,x,j,p 和 c 是非負整數且滿足0leq xleq n,0leq jleq n+1 和 n,pgeq1．B_{n}(x,p,c)是一個有2^{n+1}輸入端和2^{n+1}輸出端和額外加x層的Banyan型網路且滿足每一個輸入端至多連接到f=2^{j}個輸出端和每一個連通包含至多c個連接器受到干擾．(註:兩個訊息進入相同的連接器，我們稱為干擾) 我們給予Banyan型網路B_{n}(x,p,c)在干擾限制下的多重傳送可重排性的充分必要條件．以下是我們獲得的一些結果:

(a) B_{n}(0,p,0)是多重傳送可重排不阻塞若且為若
pgeq2^{lceil frac{n+j+1}{2}
ceil}．

(b) 當1leq cleq n+1, B_{n}(0,p,c)是多重傳送可重排不阻塞若且為若 pgeq2^{lfloor frac{n+j+1}{2}
floor}．

(c) 當jleq n, B_{n}(x,p,0)是多重傳送可重排不阻塞若且為若pgeq max {2^{j+1},2^{lceil frac{n+j-x+1}{2} rceil}}．

(d) 當j=n+1, B_{n}(x,p,0)是多重傳送可重排不阻塞若且為若pgeq2^{n+1}．

(e) B_{n}(x,p,n+x+1)是多重傳送可重排不阻塞若且為若
pgeq max {2^{j},2^{lfloor frac{n+j-x+1}{2} rfloor}}．

(f) 當1leq cleq n+x, B_{n}(n,p,c)是多重傳送可重排不阻塞若且為若
pgeq left {
2^{j} & 當n+1geq jgeq n.
2^{lceil frac{j+1}{2}rceil} & 當lfloor frac{j+1}{2} rfloor geq jgeq0.

(g) 當1leq cleq n+x 和 1leq x^{prime}leq n-1, B_{n}(x^{prime},p,c)是多重傳送可重排不阻塞若且為若
pgeq left {
2^{j} & 當n+1geq jgeq n.
2^{lfloor frac{n+j-x+1}{2} rfloor} & 當lfloor frac{n+j-x+1}
{2} rfloor geq jgeq0.

In the thesis, we study the f-cast rearrangeability of the Banyan-type network with crosstalk constraint. Let n, j, x and c be nonnegative integers with 0leq jleq n+1, 0leq xleq n and f=2^{j}. B_{n}(x,p,c) is the Banyan-type network with, 2^{n+1} inputs, 2^{n+1} outputs, x extra-stages, and each connection containing at most c crosstalk switches. We give the necessary and sufficient condictions for f-cast rearrangeable Banyan-type networks B_{n}(x,p,c). We show that
(a) B_{n}(0,p,0) is f-cast rearrangeable nonblocking if and only if pgeq2^{lceil frac{n+j+1}{2} rceil}.
(b) B_{n}(0,p,c) is f-cast rearrangeable nonblocking if and only if pgeq2^{lfloorfrac{n+j+1}{2} rfloor} for 1leq cleq n+1.
(c) B_{n}(x,p,0) is f-cast rearrangeable nonblocking if and only if pgeqmax{2^{j+1}, 2^{lceil frac{n+j-x+1}{2} rceil}} for 0leq jleq n.
(d) B_{n}(x,p,c) is 2^{n+1}-cast rearrangeable nonblocking if and only if pgeq2^{n+1} for 0leq cleq n+x+1.
(e) B_{n}(x,p,n+x+1) is f-cast rearrangeable nonblocking if and only if pgeqmax{2^{j}, 2^{lfloor frac{n+j-x+1}{2}
rfloor}}.
(f) B_{n}(n,p,c) is f-cast rearrangeable nonblocking if and only if pgeqleft{
2^{j} & if n+1geq jgeq n.
2^{lceil frac{j+1}{2} rceil} & if lfloor frac{j+1}{2}
rfloorgeq jgeq0.
for 1leq cleq n+x.
(g) B_{n}(x^{prime},p,c) is f-cast rearrangeable nonblocking if and only if pgeqleft{
2^{j} & if n+1geq jgeq n.
2^{lfloor frac{n+j-x+1}{2} rfloor} & if lfloor frac{n+j-x+1}{2} rfloorgeq jgeq0.
for 1leq cleq n+x and 1leq x^{prime}leq n-1.

Contents
1 Introduction 2
2 Preliminaries 8
3 The main results 13
4 Conclusions and future works 40

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