The Number of Rearrangements in a 3-stage Clos Network Using an Auxiliary Switch

Abstract

We consider the problem raised by Bassalygo: “What is the maximum number of rearrangements required by a rearrangeable 3-stage Clos network when there is an auxiliary middle switch carrying a light load?” For a 3-stage Clos network with an auxiliary middle switch carrying s connections, he claimed that the maximum number of rearrangements ϕ₁ (n,n,r;s) 1 is less than $s + \sqrt {2s } + 1$. In this paper, we give a lower bound 3×⌊s/2⌋ and an upper bound 2s + 1, where the lower bound shows that the upper bound given by Bassalygo does not hold in general.