Dynamic routing and wavelength assignment with optical bypass using ring embeddings

We consider routing and wavelength assignment in ring, torus, and tree topologies with the twin objectives of minimizing wavelength usage and maximizing optical bypass. The P-port traffic assumption is used, which allows each node to send and receive at most P calls. For rings we show that [PN/4] wavelengths are necessary and sufficient, and provide a 4-hub ring architecture that requires only half of these wavelengths to be locally processed. We extend this approach to a torus by embedding virtual rings within the topology. For an R × C torus, we embed R + C rings onto the torus and provide an approach to RWA and banding based on solving disjoint RWA/banding problems for each ring. Our RWA algorithm is more wavelength-efficient than any currently known algorithm and uses the minimum number of wavelengths for R > 2C. Finally, we give a RWA for trees that embeds a single virtual ring and uses the ring to obtain a RWA that requires no more than [PN/2] total wavelengths; this figure is shown to be optimal for balanced binary trees. Banding can be used for both the torus and the tree to further allow half the wavelengths to bypass all non-hub nodes.