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 [k/sub 1/, k /sub 2/, ..., k/sub N/], and node i, 1/spl les/i/spl les/N, can transmit at most k/sub i/ wavelengths and receive at most k/sub i/ wavelengths. Both algorithms support the changing traffic in a rearrangeably nonblocking fashion. Our first algorithm, for a bidirectional ring, uses /spl lceil/(/spl Sigma//sub i=1//sup N/k/sub i/)/3/spl rceil/ 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/sub i/s are equal to k, the algorithm uses /spl lceil/kN/3/spl rceil/ 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/sub i/s equal to k. For a square torus network with N nodes, the algorithm uses /spl lceil/k/spl radic/N/2/spl rceil/ 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 /spl radic/N-1 lightpath rearrangements per new session request regardless of the amount of traffic k.