Designing physical topologies that enable survivable routing of logical rings

In a WDM-based network, a single physical link failure may correspond to multiple logical link failures. As a result, 2-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. 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 of size K . We show that when K≥4 the physical topology must have at least 4N/3 links, when K≥6 it must have 3N/2 links, and when K≥N-1, it must have at least 2N-4 links. We design a topology that meets the above bounds for K=N-2 using a dual-hub architecture. Finally, we observe, through simulation experiments, 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 over-design of the physical topology.