On Multirate Rearrangeable Clos Networks

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Abstract
In the multirate switching environment each (connection) request is associated with a bandwidth weight. We consider a three-stage Clos network and assume that each link has a capacity of one (after normalization). The network is rearrangeable if for all possible sets of requests such that each input and output link generates a total weight not exceeding one, there always exists a set of paths, one for each request, such that the sum of weights of all paths going through a link does not exceed the link capacity. The question is to determine the minimum number of center switches which guarantees rearrangeability. We obtain a lower bound of 11n/9 and an upper bound of 41n/16. We then extend the result for the three-stage Clos network to the multistage Clos network. Finally, we propose the weighted version of the edge-coloring problem, which somehow has escaped the literature, associated with our switching network problem.

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