Some New Problems In Nonblocking Switching Networks

Switching networks have been widely used in telecommunication, data communication, satellite communication and etc. The nonblocking condition of switching networks arouses great interests since it can significantly reduce the hardware cost. Several nonblocking concepts are proposed, including strictly nonblocking, wide-sense nonblocking and rearrangeable. Several switching networks have been widely used, including Clos, selfrouting network, Benes, Cantor, BY_d^-l{n,k) and Log_d(N.m,p). In this dissertation, we solved four problems. Firstly, we constructed striclty nonblocking networks basing on BY_d^-l(n,m). Kolman constructed a point to point strictly nonblocking network basing on Benes network by keeping only a small portion of inputs and outputs. We extended his method to general BY_d^-1(n, k). When k=n-l, it is Benes network and we improved his lower bound to 1/n. When k=0, it is a self routing network. Secondly we obtained the necessary and sufficient conditions for Log_d(N, m, p) to be f-cast strictly nonblocking for every f, and thus covered the point-to-point case (f = 1) and the broadcast case (f = N) as special cases. Thirdly, we studied strictly nonblocking under multirate model. As we know, Cantor network is just Log_d(N, n — 1, p) and Chung and Ross's result was on Cantor network and it was also under the uniform model. Thus we extended their result in two directions. We tried to get a general result for Logd{N, m, p),m = 1,2,... , n — 1 at first. Then we considered the situation where links have different capacities. Fourthly, we studied the multirate stricly nonblocking condition of switching network. The current research on multirete rearrangeable networks are all focused on 3-stage Clos network. We considered using Hu's method on Log_d{N', m,p). Using the method of analyzing f-cast, we constructed a rearrangeable nonblocking network basing on Log_d(N, m, p).