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) is less than s +√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.