Robust Designs for WDM Routing and Provisioning

Jeff Kennington & Eli Olinick

Southern Methodist University

Augustyn Ortynski & Gheorghe Spiride

Nortel Networks

1

LTE LTE

LTE LTE

LTE LTE

… …

LTE LTE

LTE LTE

LTE LTE

… …

TE TE

TE TE

TE TE

… …

R R

R R

R R

… …

R R

R R

R R

… …

R R

R R

R R

… …

A A

A A

… …A A

A A

… …A A

A A

… …A A

A A

… …A A

A A

… …A A

A A

… …

LTE LTE

LTE LTE

LTE LTE

… …

LTE LTE

LTE LTE

LTE LTE

… …

TE TE

TE TE

TE TE

… …

R R

R R

R R

… …

R R

R R

R R

… …

R R

R R

R R

… …

A A

A A

… …A A

A A

… …A A

A A

… …A A

A A

… …

Basic Building Block for the WDM Network

Optical Amplifier

Regenerator

2

Unmet demandSatisfied demandExcess capacity

UnderprovisionedCase

Dallas Atlanta

Perfect MatchCase

LA Phoenix

OverprovisionedCase

Boston NYC

3

0

50

100

150

200

250

300

350

400

450

-12.5 -10 -7.5 -5 -2.5 0 2.5 5 7.5 10 12.5

OverprovisionedCase

UnderprovisionedCase

Perfect MatchCase

Underprovisioning Overprovisioning

Regret

4

7

4

3

1

2

5

6

Atlanta

San Francisco

Los Angeles

Dallas

Chicago Boston

New York

Example

5

ATL BOS CHI DAL LA NY SF

ATL - - 1126 1287 3540 1368 -

BOS - 1609 - - 322 -

CHI - 1448 - 1287 3540

DAL - 2253 - 2816

LA - - 644

NY - -

SF -

Distance Matrix (KM)

6

ATL BOS CHI DAL LA NY SF

ATL - 5000 3700 8800 3000 9500 -

BOS - - 8600 7100 - 7400

CHI - - - - -

DAL - - - -

LA - - -

NY - 5400

SF -

Scenario #1 Demand Matrix (DS3s)

7

ATL BOS CHI DAL LA NY SF

ATL - 15000

13700

18800

13000

19500

-

BOS - - 18600

17100

- 17400

CHI - - - - -

DAL - - - -

LA - - -

NY - 15400

SF -

Scenario #2 Demand Matrix (DS3s)

8

ATL BOS CHI DAL LA NY SF

ATL - 25000 23700 28800 23000 29500 -

BOS - - 28600 27100 - 27400

CHI - - - - -

DAL - - - -

LA - - -

NY - 25400

SF -

Scenario #3 Demand Matrix (DS3s)

9

Scenario 2Scenario 1

Scenario 3 Robust Solution

Figure 5. Solutions 10

Basic design model

Minimizecx (equip. cost)

Subject to

Ax = b (structural const)

Bx = r (demand const)

0 < x < u (bounds)

xj integer for some j (integrality)

Integer Linear Program

Decision VariablesScenarios Model

Variables Robust Model

Variables Variable

Type Description

xsp xp continuous number of DS3s assigned to path p

sn n continuous number of TEs assigned to node n

tse te continuous number of TEs assigned to link e

ase ae continuous number of optical amplifiers assigned to link e

rse re continuous number of regens assigned to link e

fse fe integer number of fibers assigned to link e

cse ce integer number of channels assigned to link e

zse ze continuous number of DS3s assigned to link e

- z+ods continuous positive infeasibility for demand (o,d) and scenario s

- z-ods continuous negative infeasibility for demand (o,d) and scenario s

ConstantsConstant Value or Range Description

Rsod 300-1500 traffic demand for pair (o,d) in scenario s in units of DS3s

MTE 192 number of DS3s that each TE can accommodate

MR 192 number of DS3s that each regen can accommodate

MA 15,360 number of DS3s that each optical amplifier can accommodate

CTE 50,000 unit cost for an TE

CR 80,000 unit cost for a regen

CA 500,000 unit cost for an optical amplifier Fe 24 max number of fibers available on link e

R 80km max distance that a signal can traverse without amplification, also called the reach

Q 5 max number of amplified spans above which signal regeneration is

required Be 2-1106 the length of link e

Routing for scenario s

(9)

(8)

rs)regenerato and amplifiers into channels andfiber (convert

(7)

(6)

channels) and fibers intocapacity link (convert

(5)

links)on TEs e(accumulat

(4)

TEs) ocapacity tlink (convert

(3)

capacity)link ocapacity tpath (convert

(2) ),( R

on)satisfacti (demand

(1) )( Minimize

EercG

EeafG

EecMz

EefMz

Nnlt

EetMz

Eezx

Ddox

aCrClC

se

se

Re

se

se

Ae

se

Rse

se

Ase

sn

Ae

se

se

TEse

Lp

se

sp

sod

Jp

sp

Nn Ee

se

Ase

Rsn

TE

n

e

od

Robust model

(16)

TEs) tolinkson DS3s ofn (conversio

(15)

flows)link toflowspath ofn (conversio

(14) -

s)constraint (demand

(13)

)constraint(budget

(12) ,),(

(11) ,),(

pieces)function regret ofion (accumulat

(10) P Minimize

e

4

1

4

1

Ss

4

1s

EetMz

Eezx

EezzRx

BudgetaCrClCE

SsDdozz

SsDdozz

zczc

TEe

eLp

p

odsodssod

Jp

sp

Eee

Ae

R

Nnn

TE

kodskods

kodskods

Dod kodsk

okodsk

uk

e

od

Robust model (cont.)

(24)

fibers)on (bounds

(23) 4,...1,,),( 4

R0

(22) 4,...1,,),( 4

R0

pieces) individualon (bounds

(21)

(20)

regens) and amplifiers tochannels andfiber ofn (conversio

(19)

(18)

channels) and fibers tolinkson DS3s ofn (conversio

max

max

Eecf

kSsDdoz

kSsDdoz

EercG

EeafG

EecMz

EefMz

ee

odsk

odsk

eeRe

eeAe

eR

e

eA

e

Mean-Value model

(24)-(15) (13), sconstraint and

),(

Subject to

Minimize

),(

bygiven be scenarios demand theofmean Let the

DdoRx

E

DdoRPR

odJp

p

Ss

sodsod

od

Stochastic Programming Model

(24)-(13) sconstraint

Subject to

min

ityinfeasibilfor cost penalty thebe Let

),(

Ss Ddoodsodss zzdPE

d

Worst Case Model

(24)-(13) sconstraint

Subject to

max Minimize),(

Ss Ddo

odsodsSs

zzdE

Regional US network – DA problem

European multinational network – KL problem

Test problems overview

Source Total Nodes 67 Total Links 107 Total Demand Pairs 200 Number of Paths/Demand 4 Total Demand Scenarios 5

Source Total Nodes 18 Total Links 35 Total Demand Pairs 100 Number of Paths/Demand 4 Total Demand Scenarios 5

2960

2437

21

3119

2327 34

4 50

18 17 49

404865

3

14

69

66

9 22 6821

11 1643

10

635626

5125 53

5 2861

33

45 47 42

4135

59

5412

58

44

55 8

64

713

62

38

39 57

52

67

3632

3046

6

20

DA Test Problem 16

11 12

3

15

4

6

16

1

10

9

2

8

13

14 18

7

17

5

Legend

1 Brussels

2 Copenhagen

3 Paris

4 Berlin

5 Athens

6 Dublin

7 Rome

8 Luxembourg

9 Amsterdam

10 Oslo

11 Lisbon

12 Madrid

13 Stockholm

14 Zurich

15 London

16 Zagreb

17 Prague

18 Vienna

European Problem17

DA – method comparison

Scenario Prob. TEs Rs As CPU Seconds Equipment Cost 1 0.15 24,996 3962 563 0.5 1,848,000,000 2 0.20 39,456 6502 864 0.5 2,925,000,000 3 0.30 51,882 8074 1101 0.5 3,791,000,000 4 0.20 65,086 10,122 1355 0.6 4,742,000,000 5 0.15 76,848 12,447 1584 0.5 5,630,000,000

Expected Value

— 51,749 8,208 1096 — 3,792,000,000

DA – results

Budget Method TEs Rs As

Equipment Cost

CPU Seconds

Unrouted Demand

Scaled Regret

Mean Value 51,800 8117 1081 3,780,000,000 0.7 15.5% 1.40 Stoch. Prog. 44,373 7446 918 3,273,000,000 1.8 20.4% 1.82 5,630,000,000 Worst Case 39,098 5495 757 2,773,000,000 4.6 27.2% 3.75 Robust Opt. 63,122 10,813 1425 4,734,000,000 2.7 5.2% 1.00 Mean Value 51,800 8117 1081 3,780,000,000 0.2 15.5% 1.11 Stoch. Prog. 44,373 7446 918 3,273,000,000 0.6 20.4% 1.44 3,787,000,000 Worst Case 39,098 5495 757 2,773,000,000 2.1 27.2% 2.95 Robust Opt. 52,159 8108 1061 3,787,000,000 4.5 12.6% 1.00

Mean Value — — — No Feasible

Solution 0.3 100% —

Stoch. Prog. 25,583 3696 515 1,832,000,000 3.9 42.3% 1.15 1,848,000,000 Worst Case 27,180 2960 505 1,848,000,000 6.6 42.3% 1.51 Robust Opt. 25,856 3575 539 1,848,000,000 5.6 43.3% 1.00

KL – individual scenarios

Scenario Prob. TEs Rs As CPU Seconds Equipment Cost 1 0.15 12,767 7275 638 0.3 1,539,356,770 2 0.20 17,493 11,691 958 0.3 2,288,919,583 3 0.30 24,020 15,783 1178 0.3 3,052,619,167 4 0.20 29,295 19,196 1455 0.2 3,727,940,417 5 0.15 35,732 23,606 1760 0.3 4,554,614,375

Expected Value

— 23,837 15,545 1196 — 3,033,250,000

KL – method comparison

Budget Method TEs Rs As Equip. Cost CPU

Seconds Unrouted

Demand Scaled Regret

Mean Value 25,124 15,350 1221 3,094,700,000 1.1 15.4% 1.41 Stoch. Prog. 20,264 14,168 996 2,644,620,000 0.6 20.8% 1.94

4,554,610,000 Worst Case 17,977 11,812 872 2,279,830,000 1.1 27.8% 4.05 Robust Opt. 27,520 21,348 1614 3,890,840,000 1.0 5.6% 1.00 Mean Value 23,978 15,382 1198 3,028,460,000 0.5 15.4% 1.11 Stoch. Prog. 20,264 14,168 996 2,644,620,000 0.2 20.8% 1.52

3,032,690,000 Worst Case 17,977 11,812 872 2,279,830,000 0.4 27.9% 3.20 Robust Opt. 23,967 15,548 1181 3,032,690,000 200.0 13.1% 1.00

Mean Value — — — No Feasible

Solution ? 100% —

Stoch. Prog. 12,154 7456 666 1,537,150,000 2.7 42.7% 1.19 1,539,360,000 Worst Case 12,782 7222 645 1,539,360,000 1.9 44.4% 1.71

Robust Opt. 13,562 7172 575 1,539,360,000 5.6 43.3% 1.00

Network Protection

Dedicated Protection – 1 + 1 Protection

P-Cycle Protection – Grover Stamatelakis (restoration speed of bi-directional rings at the cost of shared protection)

Shared Protection – Path Restoration

25

2

6

15

4

3No Protection

TE = 2 A = 11 R = 5 Cost = 6.00

2

2

6

15

4

3P-Cycle

TE = 8 A = 32 R = 20 Cost = 18.00

2

6

15

4

3Dedicated

TE = 6 A = 32 R = 15 Cost = 17.5

2

6

15

4

3Shared

TE = 6 A = 32 R = 15 Cost = 17.50

Example 1 Demand: (1,4) of 192 DS3s (1 )

26

2

6

15

4

3No Protection

TE = 6 A = 20 R = 13 Cost = 11.34

2

2

6

15

4

3P-Cycle

TE = 18 A = 32 R = 43 Cost = 20.34

2

6

15

4

3Dedicated

TE = 18 A = 32 R = 45 Cost = 20.50

2

6

15

4

3Shared

TE = 16 A = 32 R = 39 Cost = 19.92

Example 2 Demands: (1,4) 192 DS3s (1 ), (1,3) 384 DS3s ( 2 )

2

2

2

2

2

22

2

2

2

2

27

2

6

15

4

3No Protection

TE = 34 A = 45 R = 91 Cost = 31.48

2

2

6

15

4

3P-Cycle

TE = 70 A = 88 R = 185 Cost = 62.30

2

6

15

4

3Dedicated

TE = 70 A = 47 R = 181 Cost = 66.48

2

6

15

4

3Shared

TE = 72 A = 88 R = 194 Cost = 63.12

Example 3 Demands: (1,4) of 1 , (1,3) of 2 , (2,5) of 4

2

2

2

44

4

4

22

2

4

4

4

4

6

6

2

2

2

2

22

2 2

2

4

4

4

44

28

Protection Type

(1,4) = 1 (1,4) = 1(1,3) = 2

(1,4) = 1(1,3) = 2(2,5) = 4

None 6.00(working)

11.34(working)

31.48(working)

1+1 17.50 20.50 66.48

P-Cycle 18.00(same

working)

20.34(same

working)

62.30(new

working)

Shared 17.50 19.92 63.12

29