Traffic grooming in unidirectional wavelength-division multiplexed rings with grooming ratio C = 6

SONET/WDM networks using wavelength add-drop multiplexing can be constructed using certain graph decompositions used to form a grooming, consisting of unions of primitive rings. The cost of such a decomposition is the sum, over all graphs in the decomposition, of the number of vertices of nonzero degree in the graph. The existence of such decompositions with minimum cost, when every pair of sites employs no more than 1/6 of the wavelength capacity, is determined with a finite number of possible exceptions. Indeed, when the number N of sites satisfies N ≡ 1 (mod 3), the determination is complete, and when N ≡ 2 (mod 3), the only value left undetermined is N = 17. When N ≡ 0 (mod 3), a finite number of values of N remain, the largest being W = 2580. The techniques developed rely heavily on tools from combinatorial design theory.