Traffic Grooming in Unidirectional Wavelength-Division Multiplexed Rings with Grooming RatioC= 6

Abstract

International audienceSONET/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 $\frac{1}{6}$ of the wavelength capacity, is determined with a finite number of possible exceptions. Indeed, when the number N of sites satisfies $N \equiv 1 \pmod{3}$, the determination is complete, and when $N \equiv 2 \pmod{3}$, the only value left undetermined is N = 17. When $N \equiv 0 \pmod{3}$, a finite number of values of N remain, the largest being N = 2580. The techniques developed rely heavily on tools from combinatorial design theory

Approximations for All-to-All Uniform Traffic Grooming on Unidirectional Rings

“…Using ρ max (C) ≤ We can also give a construction analogous to Construction 21 using the optimal construction for a grooming factor C = 6 presented in [4]. The results are a little better but give the same order of approximation.…”

“…The traffic grooming problem has recently been extensively studied on unidirectional WDM rings, primarily in the context of variable traffic requirements [10,13,18,25,28], but the case of fixed traffic requirements has served as an important special case [3,4,5,6,7,8,14,16,17,19,20,22,26,29]. The problem has also been studied on the path [2].…”

“…Then a first approximation algorithm for computing the total number of ADMs with approximation factor With the all-to-all set of requests, I = K N , the extremal problem of finding the exact value of A(C, N ) is open and there is not even a conjecture for the extremal constructions. Optimal constructions for given grooming ratio C were obtained using tools of graph and design theory [7,11,12], in particular for grooming ratio C = 3 [3], C = 4 [19,8], C = 5 [5], C = 6 [4] and C ≥ N (N −1)/6 [8]. However it will be a very long and intractable task to find optimal constructions for all grooming ratio.…”

Drop Cost and Wavelength Optimal Two-Period Grooming with Ratio 4

“…In the example above with n = 4 and C = 3, solution a consists of a decomposition of K 4 into two paths with four vertices [1,2,3,4] and [2,4,1,3], while solution b corresponds to a decomposition into a triangle (1,2,3) and a star with the edges {1, 4}, {2, 4}, and {3, 4}.…”

“…With the all-to-all set of requests, optimal constructions for a given grooming ratio C have been obtained using tools of graph and design theory [10], in particular for grooming ratio C = 3 [1], C = 4 [4,21], C = 5 [3], C = 6 [2], C = 7 [11] and C ≥ N(N − 1)/6 [6].…”