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Dual-Failure Restorability of Meta-Mesh Networks Authors: Andres Castillo-Lugo, Tetsu Nakashima, John Doucette March 10 th , 2014 10th International Workshop on Resilient Networks Design and Modeling, Longyearbyen, Svalbard, Norway August 27,

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

March 10th, 2014

Dual-Failure Restorability

  • f Meta-Mesh Networks

Authors: Andres Castillo-Lugo, Tetsu Nakashima, John Doucette 10th International Workshop on Resilient Networks Design and Modeling,

Longyearbyen, Svalbard, Norway August 27, 2018

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

  • Introduction

✓ Background ✓ Introduction to span-restorable meta-mesh network

  • Experimental Setup

✓ Network family ✓ Experimental networks and tools

  • Studies Performed

✓ High restorability meta-mesh capacity design

  • Conclusions

✓ Experimental Results and Discussion ✓ Final Remarks

2

Outline

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

  • Alternative path segments restore all working channels of the failed

span.

– Local restoration between the end nodes of the failed span – Multiple restoration routes are possible per span – Restoration path segments for different spans can share spare capacity

3

Introduction

Background: Span Restoration Principle

Service path

A B Span 1 A B Span 1

Restoration Routes

A B Span 1

Loop backs when restoring full paths

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

  • Special interest on chains
  • f degree-2 nodes.

4

Introduction (2)

Introduction to Span-Restorable Meta-Mesh Network

A B C D Node C Node D Node B Node A

Anchor node Anchor node

Node C Node D Node B Node A

Anchor node Anchor node 𝑋𝑝𝑠𝑙𝑗𝑜𝑕 = 80 𝑋𝑝𝑠𝑙𝑗𝑜𝑕 = 70 Spare = 80 Spare = 70 Spare = 80 𝑋𝑝𝑠𝑙𝑗𝑜𝑕 = 60

𝒙𝑼𝑷𝑼 = 60 𝒙𝑼𝑷𝑼 = 80 𝒙𝑼𝑷𝑼 = 70 wLOC = 25 wEXP = 35 wLOC = 45 wEXP = 35 wLOC = 35 wEXP = 35

  • Inefficient spare capacity allocation in span restoration

due to loopback in chains

  • Meta-mesh breakdown of working capacity:

local (LOC) and express (EXP) flow

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

5

Introduction (3)

Introduction to Span-Restorable Meta-Mesh Network (2)

Node C Node D Node B Node A

Anchor node Anchor node

𝒙𝑭𝒀𝑸 = 35

Node C Node D Node B Node A

OXC OXC

Logical Chain Bypass Span

Anchor node Anchor node

Spare = 45 Spare = 35 Spare = 45

1

Improved spare capacity in sparse network topologies

2

Up to 35% reduction in spare capacity in prior work[1]

3

Only meta-mesh nodes require full OXC functionality

Meta-mesh benefits:

𝒙𝑴𝑷𝑫 = 45

  • Spare capacity requirements in a chain using the meta-

mesh restoration model

  • Logical bypass span in the meta-mesh design

[1] W. D. Grover, J. Doucette “Design of a Meta-Mesh of Chain Subnetworks: Enhancing the Attractiveness of Mesh-Restorable WDM Networking on Low Connectivity Graphs,” IEEE Journal on Selected Areas in Communications, vol. 20, no. 1, pp. January 2002 .

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

6

Introduction (4)

Introduction to Span-Restorable Meta-Mesh Network (3)

Meta-mesh network

The meta-mesh of the Sprint Communications’ USA backbone network[4]

Original network 257 nodes, 305 spans ҧ 𝑒 = 2.37 Lower bound redundancy = 73% Meta-Mesh network 77 nodes, 123 spans ҧ 𝑒 = 3.21 Lower bound redundancy = 45%

Original network

Sprint Communications’ USA backbone network[2]-[3] (used with permission)

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

  • Introduction

✓ Background ✓ Introduction to span-restorable meta-mesh network

  • Experimental Setup

✓ Network family ✓ Experimental networks and tools

  • Studies Performed

✓ High restorability meta-mesh capacity design

  • Conclusions

✓ Experimental Results and Discussion ✓ Final Remarks

7

Next…

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

8

Experimental Setup

Network Family

  • Each network family is created from an initial master network (e.g., 20-node network family).

The master network

ҧ 𝑒 = 4.0 ҧ 𝑒 = 3.9 ҧ 𝑒 = 3.8 ҧ 𝑒 = 3.7 ҧ 𝑒 = 3.6 ҧ 𝑒 = 3.5 ҧ 𝑒 = 3.4 ҧ 𝑒 = 3.3 ҧ 𝑒 = 3.2 ҧ 𝑒 = 3.1

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

9

Experimental Setup (2)

Experimental Networks and Tools

20 nodes 40 spans 25 nodes 50 spans 30 nodes 60 spans

Computational aspects

Mathematical modeling software

  • AMPL v2.9

Optimization solver

  • Gurobi v6.5

58 experimental networks

  • Topology of master networks in the 3 network families
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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

  • Introduction

✓ Background ✓ Introduction to span-restorable meta-mesh network

  • Experimental Setup

✓ Network family ✓ Experimental networks and tools

  • Studies Performed

✓ High restorability meta-mesh capacity design

  • Conclusions

✓ Experimental Results and Discussion ✓ Final Remarks

10

Next…

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

11

Studies Performed

Meta-Mesh ILP model

𝐷

𝑘 ∙ 𝑡 𝑘 + 𝑥 𝑘 𝑘 ∈ 𝐓

(1) 𝑕𝑠,𝑟 = 𝑒𝑠

𝑟 ∈ 𝐑𝑠

∀𝑠 ∈ 𝐄 (2) 𝑥

𝑘 = 𝜂𝑘 𝑠,𝑟 ∙ 𝑕𝑠,𝑟 𝑟 ∈ 𝐑𝑠 𝑠 ∈ 𝐄

∀𝑘 ∈ 𝐓 (3) 𝑔

𝑗 𝑞 = 𝑥𝑗 𝑞 ∈ 𝐐𝑗

∀𝑗 ∈ 𝐓 (4) 𝑡

𝑘 ≥ 𝜀𝑗,𝑘 𝑞 ∙ 𝑔 𝑗 𝑞 𝑞 ∈ 𝐐𝑗

∀𝑗 ∈ 𝐓𝑒 ∀𝑘 ∈ 𝐓|𝑗 ≠ 𝑘 (5) 𝑡

𝑘 ≥ 𝜀𝑗,𝑘 𝑞 ∙ 𝑔 𝑗 𝑞 𝑞 ∈ 𝐐𝑗

+ 𝜀𝑙𝑗,𝑘

𝑞

∙ 𝑔

𝑙𝑗 𝑞 𝑞 ∈ 𝐐𝑙𝑗

∀𝑗 ∈ 𝐓𝑑 ∀𝑘 ∈ 𝐓|𝑗 ≠ 𝑘 ≠ 𝑙𝑗 (6) Minimizing total cost

Original single-failure meta-mesh ILP model[1]

Satisfying demand requirement Ensuring enough working capacity Ensuring single-failure restorability Ensuring enough amount of spare capacity in direct spans Ensuring enough amount of spare capacity in chain spans

Minimize Subject to:

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

12

Studies Performed (2)

Average Dual-Failure Restorability

The original single-failure meta-mesh ILP model[1] responds to a dual-span failure scenario with the exception of dual-failure scenarios in degree-2 nodes.

0.5 0.6 0.7 0.8 0.9 1.0 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75

  • Ave. Dual Failure Restorability R2

Network Average Nodal Degree

Benchmark

25 nodes and 50 spans network family

0.5 0.6 0.7 0.8 0.9 1.0 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75

  • Ave. Dual Failure Restorability R2

Network Average Nodal Degree

Benchmark

30 nodes and 60 spans network family

  • These results demonstrate how the redistribution of spare capacity in meta-mesh networks enhance

the achievable dual-failure restorability.

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

13

Studies Performed (3)

Topology Considerations

Disconnected network area

Eliminating infeasible solutions

(a) Original network (b) Meta-mesh 𝐓d x 𝐓c (d) Meta-mesh 𝑻c x 𝑻c (d) Meta-mesh 𝑻d x 𝑻d

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

14

Studies Performed (4)

Meta-Mesh Dual-Failure Minimum Capacity Model

𝑔

𝑗,𝑘 𝑞 = 𝑥𝑗 𝑞∈𝑸𝑗

∀(𝑗, 𝑘) ∈ 𝑻𝒆

𝟑 | 𝑗 ≠ 𝑘

(1) 𝑔

𝑗,𝑘 𝑞 = 𝑥𝑗 𝑞∈𝑸𝑗 | 𝜀𝑗,𝑙

𝑞 =0

∀ 𝑗, 𝑘 ∈ 𝑻𝒅𝑦𝑻𝒆 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙(𝑗) (2) 𝑔

𝑘 ,𝑗 𝑞 = 𝑥 𝑘 𝑞∈𝑸𝑘 | 𝜀𝑘,𝑙

𝑞 =0

∀ 𝑗, 𝑘 ∈ 𝑻𝒅𝑦𝑻𝒆 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙(𝑗) (3) 𝑔

𝑙,𝑘 𝑞 = 𝑥𝑙 𝑞∈𝑸𝑙 | 𝜀𝑙,𝑗

𝑞 =0

∀ 𝑗, 𝑘 ∈ 𝑻𝒅𝑦𝑻𝒆 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙(𝑗) (4) 𝑔

𝑗,𝑘 𝑞 = 𝑥𝑗 𝑞∈𝑸𝑗 | 𝜀𝑗,𝑙

𝑞 =0 ,𝜀𝑗,𝑚 𝑞 =0

∀ 𝑗, 𝑘 ∈ 𝑻𝒅

𝟑 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙 𝑗 , 𝑚 = 𝑚(𝑘)

(5) 𝑔

𝑙,𝑘 𝑞 = 𝑥𝑙 𝑞∈𝑸𝑙 | 𝜀𝑙,𝑗

𝑞 =0 ,𝜀𝑙,𝑚 𝑞 =0

∀ 𝑗, 𝑘 ∈ 𝑻𝒅

𝟑 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙 𝑗 , 𝑚 = 𝑚(𝑘)

(6) 𝑔

𝑚,𝑗 𝑞 = 𝑥𝑚 𝑞∈𝑸𝑚 | 𝜀𝑚,𝑘

𝑞 =0 ,𝜀𝑚,𝑙 𝑞 =0

∀ 𝑗, 𝑘 ∈ 𝑻𝒅

𝟑 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙 𝑗 , 𝑚 = 𝑚(𝑘)

(7) 𝑔

𝑗,𝑘 𝑞 = 0 𝑞∈𝑸𝑗 | 𝜀𝑗,𝑘

𝑞 =1

∀(𝑗, 𝑘) ∈ 𝑻𝒆

𝟑 | 𝑗 ≠ 𝑘

(8) 𝑔

𝑗,𝑘 𝑞 = 0 𝑞∈𝑸𝑗 | 𝜀𝑗,𝑘

𝑞 =1

∀ 𝑗, 𝑘 ∈ 𝑻𝒅𝑦𝑻𝒆 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙(𝑗) (9) 𝑔

𝑘,𝑗 𝑞 = 0 𝑞∈𝑸𝑘 | 𝜀𝑘,𝑗

𝑞 =1

∀ 𝑗, 𝑘 ∈ 𝑻𝒅𝑦𝑻𝒆 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙(𝑗) (10) 𝑔

𝑙,𝑘 𝑞 = 0 𝑞∈𝑸𝑙 | 𝜀𝑙,𝑘

𝑞 =1

∀ 𝑗, 𝑘 ∈ 𝑻𝒅𝑦𝑻𝒆 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙(𝑗) (11) 𝑔

𝑗,𝑘 𝑞 = 0 𝑞∈𝑸𝑗 | 𝜀𝑗,𝑘

𝑞 =1

∀ 𝑗, 𝑘 ∈ 𝑻𝒅

𝟑 | 𝑗 ≠ 𝑘,

𝑙 = 𝑙 𝑗 , 𝑚 = 𝑚(𝑘) (12) 𝑔

𝑙,𝑘 𝑞 = 0 𝑞∈𝑸𝑙 | 𝜀𝑙,𝑘

𝑞 =1

∀ 𝑗, 𝑘 ∈ 𝑻𝒅

𝟑 | 𝑗 ≠ 𝑘,

𝑙 = 𝑙 𝑗 , 𝑚 = 𝑚(𝑘) (13) 𝑔

𝑚,𝑗 𝑞 = 0 𝑞∈𝑸𝑚 | 𝜀𝑚,𝑗

𝑞 =1

∀ 𝑗, 𝑘 ∈ 𝑻𝒅

𝟑 | 𝑗 ≠ 𝑘,

𝑙 = 𝑙 𝑗 , 𝑚 = 𝑚(𝑘) (14) 𝑡𝑥 ≥ 𝜀𝑗,𝑥

𝑞 ∙ 𝑔 𝑗,𝑘 𝑞 + 𝑞∈𝑸𝑗

𝜀

𝑘,𝑥 𝑞 ∙ 𝑔 𝑘,𝑗 𝑞 𝑞∈𝑸𝑘

∀ 𝑗, 𝑘 ∈ 𝑻𝒆

𝟑 𝑦 𝑻 |

𝑗 ≠ 𝑘 (15) 𝑡𝑥 ≥ 𝜀𝑗,𝑥

𝑞 ∙ 𝑔 𝑗,𝑘 𝑞 + 𝑞∈𝑸𝑗

𝜀

𝑘,𝑥 𝑞 ∙ 𝑔 𝑘,𝑗 𝑞 𝑞∈𝑸𝑘

+ 𝜀𝑙,𝑥

𝑞

∙ 𝑔

𝑙,𝑘 𝑞 𝑞∈𝑸𝑙

∀ 𝑗, 𝑘 ∈ 𝑻𝒅𝑦𝑻𝒆𝑦𝑻 | 𝑗 ≠ 𝑘, 𝑙 = 𝑙(𝑗) (16) 𝑡𝑥 ≥ 𝜀𝑗,𝑥

𝑞 ∙ 𝑔 𝑗,𝑘 𝑞 + 𝑞∈𝑸𝑗

𝜀

𝑘,𝑥 𝑞 ∙ 𝑔 𝑘,𝑗 𝑞 𝑞∈𝑸𝑘

+ 𝜀𝑙,𝑥

𝑞

∙ 𝑔

𝑙,𝑘 𝑞 𝑞∈𝑸𝑙

+ 𝜀𝑚,𝑥

𝑞 ∙ 𝑔 𝑚,𝑗 𝑞 𝑞∈𝑸𝑚

∀ 𝑗, 𝑘 ∈ 𝑻𝒅

𝟑𝑦𝑻 |

𝑙 = 𝑙 𝑗 , 𝑚 = 𝑚(𝑘) (17)

Subject to:

Our proposed DFMC ILP design model follows from the meta-mesh ILP design model, and carries forward the objective function and all of the constraints from that prior model. Added constraints are:

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

  • Introduction

✓ Background ✓ Introduction to span-restorable meta-mesh network

  • Experimental Setup

✓ Network family ✓ Experimental networks and tools

  • Studies Performed

✓ High restorability meta-mesh capacity design

  • Conclusions

✓ Experimental Results and Discussion ✓ Final Remarks

15

Next…

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

16

Conclusions

Experimental Results and Discussion: MM-DFMC

1.0 2.0 3.0 4.0 5.0 6.0 2.00 2.25 2.50 2.75 3.00 3.25 3.50

Normalized Spare Capacity Cost Network Average Nodal Degree SR-DFMC MM-DFMC Benchmark

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75

Normalized Spare Capacity Cost Network Average Nodal Degree SR-DFMC MM-DFMC Benchmark

25 nodes and 50 spans network family 20 nodes and 40 spans network family

  • Results demonstrate that the price of assuring dual-failure restorability in meta-mesh is moderately high.
  • The meta-mesh dual-failure design considerably improves the spare capacity requirements relative

to the span-restorable dual-failure design.

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

17

Conclusions (2)

Experimental Results and Discussion: MM-DFMC (2)

30 nodes and 60 spans network family

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75

Normalized Spare Capacity Cost Network Average Nodal Degree SR-DFMC MM-DFMC Benchmark

  • However, in some network families (large network families) the improvement relative to span-

restoration dual-failure was not significant.

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

  • We have designed and implemented a new ILP model capable of

providing dual-failure restoration in a meta-mesh design model.

– Results show that providing dual-failure in a meta-mesh design is quite expensive and in some cases exceedingly difficult (e.g., spare capacity required, design considerations). – Unfeasibility issues: network disconnection, as well as increasing the number of working and restoration routes is required. – However, the dual-failure meta-mesh model outperformed the dual-failure span- restorable model providing an attractive reduction in spare capacity in some test networks. – In addition, meta-mesh network designed to be only single failure restorable will exhibit a sizeable inherent degree of dual-failure restorability.

18

Conclusions (3)

Final Remarks

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Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

[1] W. D. Grover, J. Doucette “Design of a Meta-Mesh of Chain Subnetworks: Enhancing the Attractiveness of Mesh-Restorable WDM Networking on Low Connectivity Graphs,” IEEE Journal on Selected Areas in Communications, vol. 20,

  • no. 1, pp. January 2002 .

[2] University of Kansas, “ResiliNets Topology Map Viewer”, 2010. [Online]. Available: http://www.ittc.ku.edu/resilinets/maps/#. [Accessed: 10-Aug-2017]. [3] United States Map, Google maps. [Accessed: 20-Dec-2017]. [4] N. Spring, R. Mahajan, D. Wetherall, “Measuring ISP Topologies with Rocketfuel”, SIGCOMM, Pittsburgh, Pennsylvania, USA 2002.

19

References

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SLIDE 20

Castillo-Lugo, A., Nakashima-Paniagua, T., Doucette, J. “Dual-Failure Restorability of Meta-Mesh Networks” RNDM 2018, Longyearbyen, Norway (Aug 27-29, 2018)

March 10th, 2014

Dual-Failure Restorability

  • f Meta-Mesh Networks

Authors: Andres Castillo-Lugo, Tetsu Nakashima, John Doucette 10th International Workshop on Resilient Networks Design and Modeling,

Longyearbyen, Svalbard, Norway August 27, 2018