1. IP Restoration on WDM Optical Networks Hwajung Lee*, Hongsik Choi, Hyeong-Ah Choi The George Washington University Department of Computer Science

2. Contents Terminology Problem Formulation Main Results Lemma 1 Lemma 2 Theorem Conclusion Further Work

3. Terminology WDM : Wavelength Division Multiplexing IP over WDM Optical Network : Network structure with IP protocol as an upper layer and WDM Optical Network as a lower layer. Lightpath : Transfer Path from Source to Sink in Optical Networks IP WDM

4. Problem Formulation Given: IP Topology G, and WDM Topology G 0 Objective: To find mappings f and h, where f maps each vertex of V(G) into a vertex in G 0 and h maps each link of E(G) into a lightpath in G 0, which that, for any source-sink pair s and t, if G has two link-disjoint paths from s to t, there exist two sequences of link- disjoint paths from s to t in G 0. For any nodes u, v  V(G), f(u)  f(v) in any mapping f.

5. Example of the Problem Fault Propagation on IP over WDM IP Layer WDM Layer c a b d f e a b a c d b e f a c d b ab c a b d f e a b a c d b e f a c d b ab

6. b Example of a Solution a c d b e f IP Layer WDM Layer a c d bab c a b f e b a d c a b d f e a b Vs.

7. Overview of Main Results Lemma 1: Any vertex mappings are acceptable in case of 3-edge-connected. Lemma 2: Given G is 2-edge-connected, G is tolerant to single link faults of G 0 iff edge cuts of size two of G are mapped with a vertex mapping f and an edge-to-path mapping h, under the condition of Lemma 2. Theorem: Given G is 2-edge-connected and G 0 is a ring, G is tolerant to single link faults of G 0.

8. Lemma 1 If G is 3-edge-connected, for any vertex mapping f:V(G)  V(G 0 ),  an edge-to-path mapping h: E(G)  P(G 0 ) ensuring that G is tolerant to single link faults of G 0.   a mapping h of Max e  E(G 0 ) {# of wavelengths on an edge}  2 There must be at least one live path in the case of single link faults causing at most 2 edge disable.

9. Proof of Lemma 1 IP Layer WDM Layer a d a X Y Mw=Max e  E(G0) {# of wavelengths on an edge} Mw=3 Mw=2

10. Proof of Lemma 1(Cont.) OK

11. Lemma 2 Suppose G is 2-edge-connected. Let f: V(G)  V(G 0 ), and h: E(G)  P(G 0 ) be mappings such that G is tolerant to single link faults, iff, for any edge cuts of size two {e i =(a, b), e j =(c,d)} in G if there exists any, ordering of vertices in G 0 is not f(a)-f(c)-f(b)- f(d) in the clockwise or counterclockwise direction.

12. Example of Lemma 2 IP Layer WDM Layer c a b d f e a b a c d b e f a c d b ab a c d b e f c a b b f e a c d b ab a d

13. Theorem Given G is 2-edge-connected and G 0 is a ring, G is tolerant to single link faults of G 0.  It is obtained based on the Lemma 1 and Lemma 2.

14. Mapping Example d b l k h f a c j i e g f a c j i e g k l b d h a c i e j g IP Layer WDM Layer

15. Conclusion Lemma 1: Any vertex mappings are acceptable in case of 3-edge-connected. Lemma 2: Given G is 2-edge-connected, G is tolerant to single link faults of G 0 iff edge cuts of size two of G are mapped with a vertex mapping f and an edge-to-path mapping h, under the condition of Lemma 2. Theorem: Given G is 2-edge-connected and G 0 is a ring, G is tolerant to single link faults of G 0.

16. Further Work Consider a mesh Topology as the underlying WDM structures. Consider Load Balancing issues Minimize Max e  E(G0) {the number of wavelengths on an edge}. Set up Lightpath based on # of available wavelengths & Integrate it into MPLamdaS.

17. Thank You.