Physical topology design for survivable routing of logical rings in WDM-based networks

In a wavelength-division multiplexed (WDM)-based network, a single physical link failure may correspond to multiple logical link failures. As a result, two-connected logical topologies, such as rings routed on a WDM physical topology, may become disconnected after a single physical link failure. We consider the design of physical topologies that ensure logical rings can be embedded in a survivable manner. This is of particular interest in metropolitan area networks, where logical rings are in practice almost exclusively employed for providing protection against link failures. First, we develop necessary conditions for the physical topology to be able to embed all logical rings in a survivable manner. We then use these conditions to provide tight bounds on the number of physical links that an N-node physical topology must have in order to support all logical rings for different sizes K. We show that when K≥4 the physical topology must have at least 4N/3 links, and that when K≥6 the physical topology must have at least 3N/2 links. Subsequently, we generalize this bound for all K≥4. When K≥N-2, we show that the physical topology must have at least 2N-4 links. Finally, we design physical topologies that meet the above bounds for both K=4 and K=N-2. Specifically, our physical topology for embedding (N-2)-node rings has a dual hub structure and is able to embed all rings of size less than N-1 in a survivable manner. We also provide a simple extension to this topology that addresses rings of size K=N-1 and rings of size K=N for N odd. We observe that designing the physical topology for supporting all logical rings in a survivable manner does not use significantly more physical links than a design that only supports a small number of logical rings. Hence, our approach of designing physical topologies that can be used to embed all possible ring logical topologies does not lead to a significant overdesign of the physical topology.