A New Result on Rearrangeable 3-Stage Clos Networks

Rearrangeable 3-stage Clos networks have long been studied for their theoretical interest and rich potential applicability. Although the existing connections of a rearrangeable Clos network may block a newly requested connection, this problem can be resolved by adequately rearranging some of the existing connections. The number of rearrangements needed to unblock the system poses an interesting question. In past studies, the number of rearrangements has been found only in limited cases and has not been determined for generic parameter values. This paper discovers a new bound on the number of rearrangements for a certain parameter range, which has not been considered in past studies. The underlying analysis is performed by a rearrangement algorithm that unblocks the system with the minimum number of rearrangements. The algorithm is based on the connection chain concept, which clearly and efficiently represents a sequence of connections to be rearranged.