IP Restoration on WDM Optical Networks

Hwajung Lee*, Hongsik Choi, Hyeong-Ah Choi

The George Washington University

Department of Computer Science

Contents

TerminologyProblem FormulationMain ResultsLemma 1Lemma 2Theorem

ConclusionFurther Work

Terminology

WDM : Wavelength Division MultiplexingIP 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

IPWDM

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.

Example of the Problem

Fault Propagation on IP over WDM

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Example of a Solution

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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.

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

MaxeE(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.

Proof of Lemma 1IP Layer

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Mw=Maxe E(G0){# of wavelengths on an edge}

Mw=3 Mw=2

Proof of Lemma 1(Cont.)

OK

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.

Example of Lemma 2

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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.

Mapping Example

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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.

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.

Thank You.