Fault-Tolerant General Benes Networks

Benes networks are well-known rearrangeable nonblocking (RNB) multistage networks. The so-called conventional Benes networks are based on 2 x 2 switches. In this paper, Benes network is a general term used to refer to an NxN n -nary Benes network. Such networks, denoted by B( n , t) , where N = n(t) and t >= 2 , are based on regular nxn switches, and are RNB as well. A Benes network is constructed recursively from a 3-stage Clos network. For an NxN RNB Clos network C( n , m , r) , where N=nr and m >= n , the maximum allowable number of non-contact faults in each single shell for realizing any permutation has been investigated in an earlier study, where shell k in a network consists of both the k th and the k th-to-last node stages. That study showed that, for a given integer N , an RNB C( n , n , r) network with larger nxn switches leads to tolerance of more non-contact faults in shell 1. In this paper, for an N x N B( n , t) network, we study the maximum allowable number, say f(k) , of non-contact faults for any permutation not only in each single shell k , but also in all shells simultaneously under the fault condition that at most f(k) non-contact faults are arbitrarily located in the switches in each shell k . We call the former the fault tolerance capability in a single shell, and the latter the fault tolerance capability of the network. We show that a larger switch size, i.e., n x n , in an N x N B( n , t) network leads to a higher fault tolerance capability of the network and a higher fault tolerance capability in each non-middle shell. An NxN Benes network B( n , t) considers only the value of N which is a power of n . To consider a flexible N with N = n(s)& sdot;q , where s >= 2 , 1 < q < n and q|n, which means that n is divisible by q, we propose in this paper an NxN RNB Benes-type network using regular nxn switches, which is called an extended Benes and denoted by B(n,s,q). Both Benes and extended Benes networks are based on regular switches, and they have better scalabilities than a Clos network. We define a network's fault tolerance rate as the ratioof the fault tolerance capability to the total crosspoints in the network. For given integersNandn, we derive that the fault tolerance capability and fault tolerance rate of an N x N Benes(or extended Benes) network are higher than or equal to those of an N x N RNB C(n,n,r)network, and the former out performs the latter in most cases.