IP Restoration on WDM Optical Networks

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. IP WDM 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

4. Problem Formulation • Given: IP Topology G, and WDM Topology G0 • Objective: To find mappings f and h, where f maps each vertex of V(G) into a vertex in G0 and h maps each link of E(G) into a lightpath in G0, 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 G0. For any nodes u, vV(G),f(u)f(v) in any mapping f.

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

6. a a a b b b e c c a d d b f a d f e a b c b Example of a Solution IP Layer a b WDM Layer f e d b c 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 G0 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 G0 is a ring, G is tolerant to single link faults of G0.

8. Lemma 1 • If G is 3-edge-connected, for any vertex mapping f:V(G)  V(G0), an edge-to-path mapping h: E(G)  P(G0) ensuring that G is tolerant to single link faults of G0.  a mapping h of MaxeE(G0){# 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 Y X a a d Mw=2 Mw=3 WDM Layer Mw=Maxe E(G0){# of wavelengths on an edge}

10. Proof of Lemma 1(Cont.) OK

11. Lemma 2 • Suppose G is 2-edge-connected. Let f: V(G)  V(G0), and h: E(G) P(G0) be mappings such that G is tolerant to single link faults, iff, for any edge cuts of size two {ei=(a, b), ej=(c,d)} in G if there exists any, ordering of vertices in G0 is not f(a)-f(c)-f(b)-f(d) in the clockwise or counterclockwise direction.

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

13. Theorem • Given G is 2-edge-connected and G0 is a ring,G is tolerant to single link faults of G0.  It is obtained based on the Lemma 1 and Lemma 2.

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

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 G0 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 G0 is a ring, G is tolerant to single link faults of G0.

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

17. Thank You.