We develop traffic grooming algorithms for unidirectional SONET/WDM ring networks. The objective is to assign low rate circuits to wavelengths in a way that minimizes the total cost of electronic equipment (e.g., the number of SONET add/drop multiplexers (ADMs)). When the traffic from all nodes is destined to a single node, and all traffic rates are the same, we obtain a solution that minimizes the number of ADMs. In the more general case of all-to-all uniform traffic we obtain a lower bound on the number of ADMs required, and provide a heuristic algorithm that performs close to that bound. Finally, we consider the use of a hub node, where traffic can be switched between different wavelengths, and obtain an optimal algorithm which minimizes the number of ADMs by efficiently multiplexing and switching the traffic at the hub. Moreover, we show that any solution not using a hub can be transformed into a solution with a hub using fewer or the same number of ADMs.
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