Logical topology survivability in IP-over-WDM networks: Survivable lightpath routing for maximum logical topology capacity and minimum spare capacity requirements

The survivable logical topology mapping problem in an IP-over-WDM optical network is to map each link (u, v) in the logical topology (at the IP layer) into a lightpath between the nodes u and v in the physical topology (at the optical layer) such that failure of a physical link does not cause the logical topology to become disconnected. It is assumed that both the physical and logical topologies are 2-edge connected. For this problem two lines of investigations have been pursued in the literature: one pioneered by Modiano et al., and the other pioneered by Kurant and Thiran. Since then there have been a great deal of research on this problem. Most of the works have not considered limitations imposed on the routings by physical capacity limits. In this paper, we first introduce two concepts: weakly survivable routing and strongly survivable routing. We then provide mathematical programming formulations for two problems. Problem 1 is to design a survivable lightpath routing that maximizes the logical capacity available before and after a physical link failure. The second problem is to add spare capacities to the physical links to guarantee routability of all logical link demands before and after a physical link failure. The frameworks provided by our formulation can be used to accommodate other scenarios such as those involving load balancing and fair capacity allocation constraints. We conclude with simulations that compare the results using these formulations and those obtained by heuristics that mitigate the computational complexity of the mathematical programming formulations.