A common problem in optical networking is that the large quantity of raw bandwidth available in such networks is often difficult to access. We show that time-division multiplexing (TDM) can be used to operate bus and ring architectures in a manner akin to a switch. We consider a time-varying approach, akin to that used in switching theory, instead of the static approach, related to the knapsack problem, often associated with fixed allocation of traffic onto circuits, often termed the grooming

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... oblem. Our approach is probabilistic in nature, and requires significant generalization beyond the Birkhoff-von Neumann statistical multiplexing approaches have that have been successful in switching theory. Our techniques rely on decompositions of