Survivable Logical Topology Design in WDM Optical Ring

Networks

Hwajung Lee, Hongsik Choi,

Suresh Subramaniam, and Hyeong-Ah Choi*

The George Washington University

Supported in part by

DARPA under grant #N66001-00-18949

(Co-funded by NSA)

DISA under NSA-LUCITE Contract

NSF under grant ANI-9973098

Outline

Introduction – Network SurvivabilityMotivationProblem Formulation Problem ComplexityHeuristic AlgorithmNumerical ResultsConcluding Remarks

Network Survivability

To guarantee for users to use the network service without any interruption.

Each layers have their own fault recovery functions.

Fault propagation

ATM

ATM

IP

IP

IP IP

WDM Optical Network

Physical Fiber Plant

SONET/SDH

SONET/SDH

Introduction

Logical topology (Upper Layer) is called survivable if it remains connected in the presence of a single optical link failure.

Faulty Model : Single optical link failure.

Survivable Logical TopologyMotivations

Survivable Logical Topology

Survivable

Electronic layer is connected even when a single optical link fails

Map each connection requestto an optical lightpath.

1

3

52

4

0

1

2

34

5

0

1

2

34

5

0

Motivations

Upper Layer= Logical Topology

Optical Layer= Physical Topo.

Not Survivable

Desirable!

Sometimes, there is no way to have a Survivable

Logical Topology Embedding

on a Physical Topology.

Survivable Logical Topology

e1

e2

…

…a

c

b

d …

…

…

…

d

b

c

a

Motivations

Electronic Layer= Logical Topology

Optical Layer= Physical Topo.

2-Edge Connected

Survivable Logical Topology Design Problem(SLTDP)

Given a physical topology, and a logical topology = a set of connection requests.

Objectives Find a route of lightpath for each connection

request, such that the logical topology remains connected after a single link failure if possible.

Otherwise, determine and embed the minimum number of additional lightpaths to make the logical topology survivable.

Problem Formulation

Problem Complexity Survivable LT design possible

Completely connected (i.e., (n-1)-edge connected) NO survivable LT design when logical topology G is

2-edge connected 3-edge connected 4-edged connected

Degree Constraints

Survivable LT design possible when min.degree >= No survivable LT design for min. degree <= ( -1)

2n 3 n

2

Problem Complexity

1

43

525

3 4

2

1

Complete Graph: Survivable

Problem Complexity

k

a 2

b 1

f

e h

b 2

i

a 1

d 1

c 1

g

c 2

l

jd 2

C 1

C 2

C 3C 4

a 1

f

b 2

a 2

e

b 1

k

3-edge Connected Graph: not Survivable

Problem Complexity

b1

b3

b2

b4

c1

c3

c2

c4

d1

d3

d2

d4

e1

e3

e2

e4

a1

a3

a2

a4

C1

C2

C3

C4

a1

a4

a2

a3

e2

e1

e4

e3

c4

c2

c3

c1

b4

b3b2

b1

d3

d1

d4

d2

4-edge Connected Graph: not Survivable

Problem Complexity

n-10

n/4+1

n/3-1

n/4

n/2n/2-1 2n/3

n/2+j

L R

Number of Nodes = b Number of Nodes = b

j n-j-1...

... ...

.... . .

...

...

...

si +i (L); si - I + n -1(R)

t: highest index in L smallest_component4 cases: t -1; t ; t -2; t= -1

n 6

n 6

n 4

n 3

n 4

n 3

n 3

Shortest Path Routing: Survivable if (minimum d ) 2n

3

Problem Complexity

: Vodd

: Veven

Kn/2-1 Graphn-1Kn/2-1 Graph 0

0 n-1

... .........

...

Shortest Path Routing: not Survivable if (minimum d -1 )

n 2

Problem Complexity

Heuristic Algorithm Heuristic Algorithm

based on Shortest Path Routing

Assign logical links to lightpaths.Cut each optical link

and Calculate the # of Components.Find an optical link (x,y) with the maximum #

of components.Add an additional lightpath without using (x,y).Repeat the above procedure

until the logical topology being survivable.

Numerical Results# of Simulations = 1000

n = 100

0

5

10

15

20

25

0.02

80.

040.

060.

08 0.1

0.2

link probability p

aver

age

# o

f ad

dit

ion

al l

igh

tpat

hs

2 edge-connected

arbitrary

22.953

7.037

1.8611.938

0.0080.0023.357

Numerical Results

Numerical Results# of Simulations = 1000

n = 200

0123456789

10

0.02

80.

040.

060.

08 0.1

0.2

link probability p

aver

age

# o

f ad

dtio

nal

lig

htp

ath

s

2 edge-connected

arbitrary

8.889

0.4940.549 0.023

0.027

4.632

Numerical Results

Numerical Results# of Simulations = 1000

n = 300

-1

1

3

5

7

9

11

0.02

80.

050.

070.

090.

110.

130.

15

link probability p

aver

age

# o

f ad

dti

on

al l

igh

tpat

hs

2 edge-connected

arbitrary

10.293

0.533

5.585

0.814

0.0270.027

Numerical Results

Concluding RemarksSurvivable LT design in WDM ring networkDetermine if survivable design possible from G

Degree constraint : -1, Edge-connectivity constraint

Heuristic algorithm: almost optimal Further Research

Tighter bounds WDM mesh topology Reconfiguration of Survivable Logical Topology

2n 3

n 2

Concluding Remarks