Grooming traffic to maximize throughput in SONET rings

Using a graph-theoretic formulation, a grooming in a SONET ring network may be interpreted as a decomposition of an undirected simple graph G=(V,E), where V corresponds to the n nodes in the ring, and each edge {i,j}∈E represents the traffic requirements for the primitive ring {i,j}. In G={G ₁,...,G_s}, the decomposition of G, each subgraph Gi 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 tp̄(c,n,ℓ) of a c-grooming G is addressed, subject to each node being equipped with a limited number ℓ of adddrop multiplexers (ADMs). Naturally, restricting the number of ADMs limits the achievable throughput. For all ℓ, precise determinations of maximum throughput for grooming ratios c=2, 3, and 4 are given. These underlie substantially improved bounds for larger grooming ratios.