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We develop on-line routing and wavelength assignment (RWA) algorithms for WDM bidirectional ring and torus networks with N nodes. The algorithms dynamically support all k-allowable traffic matrices, where k denotes an arbitrary integer vector [k1, k2,... kN], and node i, 1 ≤ i ≤ N, can transmit at most ki wavelengths and receive at most ki wavelengths. Both algorithms support the changing traffic in a rearrangeably nonblocking fashion. Our first algorithm, for a bidirectional ring, uses [(Σi=1N ki)/3] wavelengths in each fiber and requires at most three lightpath rearrangements per new session request regardless of the number of nodes N and the amount of traffic k. When all the ki's are equal to k, the algorithm uses [kN/3] wavelengths, which is known to be the minimum for any off-line rearrangeably nonblocking algorithm. Our second algorithm, for a torus topology, is an extension of a known off-line algorithm for the special case with all the ki's equal to k. For an R × C torus network with R ≥ C nodes, our on-line algorithm uses [kR/2] wavelengths in each fiber, which is the same as in the off-line algorithm, and is at most two times a lower bound obtained by assuming full wavelength conversion at all nodes. In addition, the on-line algorithm requires at most C - 1 lightpath rearrangements per new session request regardless of the amount of traffic k. Finally, each RWA update requires solving a bipartite matching problem whose time complexity is only O (R), which is much smaller than the time complexity O(kCR2) of the bipartite matching problem for an off-line algorithm.
Date of Publication: April 2006