Abstract |
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. |