1. On Survivable Routing of Mesh Topologies in IP-over-WDM Networks Maciej Kurant, Patrick Thiran EPFL, Switzerland Infocom 2005, March 13-17, Miami

2. 2 Mapping Logical topology G L - mesh of IP links Physical topology G Φ - mesh of physical links (fibers) Each logical link is mapped on the physical topology as a physical path called a lightpath. We assume infinite capacities of fibers Mapping M - a set of lightpaths associated with a set of logical links GLGL GΦGΦ M

3. 3 Survivability How to deal with failures? There are several methods Protection vs restoration WDM layer vs IP layer We use only the IP restoration approach: (The failures are detected at the IP layer, and a new route is found dynamically.) GLGL GΦGΦ M

4. 4 Link-survivability example GLGL GΦGΦ GLGL GΦGΦ GLGL GΦGΦ The logical topology remains conneceted after any single physical link failure The mapping is link-survivable

5. 5 Node-survivability example GLGL GΦGΦ GLGL GΦGΦ GLGL GΦGΦ The failure of node v* disconnects the remaining logical topology G L \{v*} The mapping is not node-survivable v* Connected Not connected!!

6. 6 The problem of finding a survivable mapping is not new… E. Modiano and A. Narula-Tam, Survivable lightpath routing: a new approach to the design of WDM-based networks, IEEE Journal on Selected Areas in Communications, vol. 20, no. 4, 2002 F. Giroire, A. Nucci, T. Taft, and C. Diot, Increasing the Robustness of IP Backbones in the Absence of Optical Level Protection, Proc. of IEEE INFOCOM 2003. L-W. Chen and E. Modiano, Efficient Routing and Wavelength Assignment for Recongurable WDM Networks with Wavelength Converters, Proc. of IEEE INFOCOM’03. … J. Armitage, O. Crochat, and J. Y. Le Boudec, Design of a Survivable WDM Photonic Network, Proceedings of IEEE INFOCOM 97, April 1997.

7. Our solution

8. 8 Contraction a b c e d g h f Contraction of C={a, b, c} e d g h f G C =G C G

9. 9 The SMART algorithm (link-survivability example) GLGL GΦGΦ GLGL GΦGΦ GLGL GΦGΦ GCGC GCGC GCGC A single node! Iteration 1Iteration 2Iteration 3 Theorem 1: If the contracted logical topology G C converges to a single node, then the mapping is (link/node)-survivable. a b c d f g h e a b c d f g h e a b c d f g h e a b c d f g h e f g h e d e d

10. 10 Verification of mapping existence GLGL GΦGΦ GLGL GΦGΦ GLGL GΦGΦ GCGC GCGC GCGC Iteration 1Iteration 2Iteration 3 a b c d f g h e a b c d f g h e a b c d f g h e a b c d f g h e f g h e d e d Theorem 2: A (link/node)-survivable mapping of G L on G Φ exists iff any contracted topology G C can be mapped on G Φ in a (link/node)-survivable way. A node-survivable mapping of the contracted topology G C ={e,d} does not exist. A node-survivable mapping of the logical topology G L on G Φ does not exist. Sequence of cycles does not matter!

11. 11 SMART applied to the verification of the existence of a link/node- survivable mapping Application 1

12. 12 Verification of mapping existence (2)

13. 13 Random graph on NSFNET

14. 14 SMART applied to the fixing a vulnerable topology (enabling link/node-survivable mapping) Application 2

15. 15 Where to introduce a new link? GLGL GΦGΦ GCGC a b d f g h e e d A new logical link which is a self-loop in the contracted topology G C will never help. Only a new logical link between two different nodes in G C might help. i i i i In simulations (up to 64 nodes): New logical link introduced at random rarely helped (<10%) New logical link between two different nodes in G C helped in more than 80% of cases.

16. 16 Applications of SMART (summary) The formal verification of the existence of a link/node-survivable mapping, a tool tracing and repairing the vulnerable areas in network, a fast heuristic.

17. 17 Thank you!

18. 18 SMART algorithm (main steps) 1.Pick a cycle C in G c 2.Map C in a (link/node)-survivable way 3.Contract C in G c, i.e., G c = G c C 4.Goto 1. G c – contracted logical topology Initialization: G c = Logical topology

19. 19 Random graph on f-lattice, 49 nodes

20. 20 Introduction of a new link (when link-survivable mapping impossible)