On-line routing and wavelength assignment for dynamic traffic in WDM ring and torus networks

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, k ₂, ..., k_N], and node i, 1≤i≤N, can transmit at most k_i wavelengths and receive at most k_i wavelengths. Both algorithms support the changing traffic in a rearrangeably nonblocking fashion. Our first algorithm, for a bidirectional ring, uses ┌(Σ_i=1^Nk_i)/3┐ wavelengths in each ring direction 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 k_is 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 designed for the special case with all the k_is equal to k. For a square torus network with N nodes, the algorithm uses ┌k√N/2┐ wavelengths in each fiber, which is shown to be at most two times a lower bound obtained by assuming full wavelength conversion at all nodes. In addition, the algorithm requires at most √N-1 lightpath rearrangements per new session request regardless of the amount of traffic k.