Survivability of lightwave networks - Path lengths in WDM protection scheme

In the protection scheme of fault management in a WDM optical network, corresponding to every source-destination path used for data transmission, a backup path is maintained in a stand-by mode. In the case of a failure (either due to a fiber cut or due to equipment failure) in the primary path, data transmission is quickly switched to the backup path. In order to tolerate any single fault, the backup path must be edge (or node) disjoint from the primary path. Most often a shortest path between the source and the destination is chosen as the primary path. To obtain a link (node) disjoint backup (or secondary) path, the links (nodes) of the primary path are removed from the graph and then a shortest path in the modified graph is chosen as the backup path. The attractive feature of this scheme is its simplicity. However, the scheme has a severe drawback. Due to the choice of a shortest path as the primary path, the length of a link disjoint secondary path may be unacceptably large. In this paper, we propose a novel way of choosing the primary and the secondary paths so that the lengths of both the paths are small. Unfortunately, the problem of choosing primary and secondary paths in this way turns out to be NP-complete. We provide the NP-completeness proof of both the edge disjoint and the node disjoint version of the problem. We provide an approximation algorithm for the problem with a guaranteed performance bound of 2 and a mathematical programming formulation for the exact solution of the problem. Though the approximate solution provides a performance bound of 2, through extensive experimental evaluation, we find that the approximate solution is very close to the optimal solution and the ratio between the approximate to the optimal solution never exceeds 1.2. Although we discuss the single fault scenario in this paper, the algorithms discussed here, can be used equally effectively for the multiple fault scenario also. Finally, we discuss other variations of the disjoint path problem relevant to the lightwave networks.