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IP Restoration on WDM Optical Networks. Hwajung Lee*, Hongsik Choi, Hyeong-Ah Choi The George Washington University Department of Computer Science. Contents. Terminology Problem Formulation Main Results Lemma 1 Lemma 2 Theorem Conclusion Further Work. IP WDM. Terminology.

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ip restoration on wdm optical networks

IP Restoration on WDM Optical Networks

Hwajung Lee*, Hongsik Choi, Hyeong-Ah Choi

The George Washington University

Department of Computer Science

contents
Contents
  • Terminology
  • Problem Formulation
  • Main Results
    • Lemma 1
    • Lemma 2
    • Theorem
  • Conclusion
  • Further Work
terminology

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
problem formulation
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

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Example of the Problem
  • Fault Propagation on IP over WDM

IP Layer

WDM Layer

example of a solution

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Example of a Solution

IP Layer

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WDM Layer

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overview of main results
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
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.

proof of lemma 1
Proof of Lemma 1

IP Layer

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Mw=2

Mw=3

WDM Layer

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

lemma 2
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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Example of Lemma 2

IP Layer

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WDM Layer

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theorem
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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Mapping Example

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WDM Layer

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conclusion
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
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.

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