Using a graph-theoretic formulation, a grooming in a SONET ring network may be interpreted as a decomposition of an undirected simple graph , where V corresponds to the n nodes in the ring, and each edge represents the traffic requirements for the primitive ring . In , the decomposition of G, each subgraph specifies a set of primitive rings assigned to the same wavelength. If the maximum size set is c then G is a c-grooming. In this paper, bounding the maximum throughput of a c-grooming G is addressed, subject to each node being equipped with a limited number l of add–drop multiplexers (ADMs). Naturally, restricting the number of ADMs limits the achievable throughput. For all l, precise determinations of maximum throughput for grooming ratios , 3, and 4 are given. These underlie substantially improved bounds for larger grooming ratios.
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