Survivable Lightpath Routing: A New Approach to the Design of WDM –Based Networks

1. Survivable Lightpath Routing: A New Approach to the Design of WDM –Based Networks Jared Strickland, Stephanie Kinsella, Travis Grosch, Sean Lunsford, Mohammad Alsawwaf

2. Introduction: What is the problem? • The paper discusses the problem of embedding logical topologies on a WDM physical topology so that in the event of a physical link failure, the network remains connected.

3. Problem Formulation

4. Integer Linear Programming Formulation • ILP formulation • requires that not all logical links can be carried n a single physical link. • focus on minimizing total number of wavelengths used • solution must be survivable (failure of any physical link leaves logical link connected • used ILP, shortest-path, two relaxed versions of the constraints • ILP found solutions for networks of degree 3, 4, 5 • SP failed to find solutions for all the networks, performance improved with topologies of higher degree • relaxing integer constraint to LP provided solutions quickly, left only 10 deg-3 topologies unprotected • enforcing survivability constraints only for cut-sets less than or equal to degree of logical topology plus one found protected solutions for all topologies • computation time: • ILP longest, relaxations much shorter

5. Ring Logical Topologies • The study only focused on bidirectional ring topology • Meaning data can travel in both directions • Corollary 1: a bidirectional logical ring is survivable if and only if no two logical links share the same physical link • Since no two lightpaths can share a physical link, the objective of minimizing the total number of physical links and that of minimizing the total number of wavelengths*links used are in fact the same

6. Necessary conditions for survivable routing • Not always possible to route a logical topology on a given physical topology in a manner that preserver the survivability of the logical topology • In some instances lightpaths will have to share a physical link and the ring would not be survivable • Theorem 3 says that for all cuts of the physical topology, the number of physical links in the cut set must be greater than or equal to twice the number of nodes on the smaller side of the cut

7. Logical ring Results • Notice that there are 120 (5!) 6-node logical ring topologies and 362,880 (9!) 10-node logical ring topologies • To make sure the results were survivable they would remove a light path if it was already used in order to protect survivability at the cost of shortest path • The more nodes they added the harder it was for them to maintain survivability • Once they hit 10 nodes a little under 10 percent were left unprotected

8. Conclusion • With the formulation of conditions necessary for survivable routing of the logical topology, they came up with an ILP formulation. • This ILP formulation allowed them to find survivable routings for a variety of network topologies. • The results show that the new approach offers a higher degree of protection compared to shortest path routing.

9. Conclusion cont. • Because solving ILP for large scale networks is usually difficult, they examined relaxations to the ILP formulation that find survivable routings with reducing complexity. • The basic idea behind these relaxations is to enforce only a subset of the constraints. • They found that this approach creates survivable routings with very high probability, especially for densely connected networks.