DSTIS 2009 - VIII International Conference on Decision Support for

Telecommunications and Information Society - Coimbra, September 4-7, 2009

Impact of Tra�c Randomness on

Restoration Coe�cient in Optical

Transport Networks

Claunir Pavan, Rui Manuel Morais, Armando Nolasco Pinto

c⃝2005, it - instituto de telecomunicações

Motivation

∙ The dimensioning of optical networks consists in determining the quantitiesof resources necessary to transport a given tra�c.

∙ Commercial tools are available to help us on the dimensioning task.

However, designers depend on a variety of inputs.

∙ Computational e�ort grows rapidly with network size and complexity. For

large networks the time required may be prohibitive.

∙ We aim to develop a method for quickly quantifying network elements

and CapEx with incomplete information.

Introduction

∙ Restoration coe�cient is

the ratio between working and

spare capacity.

∙ ⟨kr⟩= ψminW o

∙ We focus on survivable networks.

∙ Shared mesh restoration

mechanism.

∙ Single link failures.

1

2

4

3

5

1

2

4

3

5

1-3,2-32-4

1-4,3-54-5

1-2,1-32-5

1-4,1-52-5

2-4,3-43-5

1

2

4

3

5

1-32-3

1-5,2-53-5,4-5

1-4,1-52-4,2-5

1-2,1-32-4,2-5

3-43-5

1

2

4

3

5

1-2,2-42-3,2-5

2-5,3-54-5

1-2,1-31-41-5

1

2

4

3

5

1-3,2-33-4,3-5

4-5

1-2,1-32-4,2-53-4,3-5

1-5,2-53-5

1-4,2-43-4

1

2

4

3

5

1-3,2-33-5

1-5,2-53-5,4-5

1-4,2-44-5

1-2,1-32-4,2-53-5

3-4

1

2

4

3

5

1-2,2-32-4,2-5

3-54-5

1-3,1-42-3,2-41-5

2-51-3,2-33-4,3-5

1

2

4

3

53-54-5

1-4,2-4

1-5,2-5

1-3,2-31-2,1-32-4,2-5

3-4,3-5

a) b)

c) d) e)

f) g) h)

6 4

4 6

4

4

1-2,1-32-4,2-53-4,3-5

Calculating Restoration Capacity

∙ The time consuming for this task grows rapidly.

200

250

300

350

400T

ime

(m

inu

tes)

Working capacity

Restoration capacity

0

50

100

150

200 300 500 700 1400

Tim

e (

min

ute

s)

Number of demandsNumber of demands

∙ How to calculate ⟨kr⟩ without extensive simulation?

Calculating Restoration Capacity

∙ In [1] the author published a semi-empirical expression to estimate ⟨kr⟩.

∙ The expression is function of the mean nodal degree.

∙ Indeed, we verify that ⟨kr⟩ depends also on the number of nodes.

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 10 20 30 40 50 60 70 80 90 100 110

Re

sto

rati

on

co

eff

icie

nt

Number of nodes

⟨δ⟩≈ 2.5 ⟨δ⟩≈ 3.5 ⟨δ⟩≈ 4.5

[1] S. K. Korotky, "Network Global Expectation Model," J. Lightw. Technol. 2004.

Our Approach

∙ We proposed an approximation based on statistical methods.

∙ We developed a model to generate realistic transport network

topologies2.

∙ Wrote a software tool to generate a meaningful data set.

∙ Obtained ⟨kr⟩ from more than 50 thousand transport networks.

∙ Made linear and non-linear regressions.

[2] C. Pavan et al., "Generating Realistic Survivable Transport Network Topologies,"submitted to IEEE/OSA J. Opt. Commun. Netw., 2009.

The Proposed Approximation

∙ From the least square method we obtained a variety of curve �t equations.

∙ Using ⟨δ ⟩ as dependent variable we obtained:

⟨kr⟩= bo+b1

⟨δ ⟩(1)

∙ From (1) and using N as dependent variable we found:

∙ b0 = 1.01−0.21ln(N) and b1 = 0.45N0.32.

∙ And �nally:

∙ ⟨kr⟩= 1.01−0.21ln(N)+ 0.45N0.32

⟨δ ⟩ .

Impact of Tra�c and Randomness on ⟨kr⟩∙ Simulations were conducted over a variety of networks and tra�c.

1

1.1

1.2

1.3

1 2 3 4 5

Re

sto

rati

on

Co

eff

icie

nt

Simulations over RNP topology

Uniform

0 - 4

0 - 10

0 - 20

0 - 50

0.7

0.8

0.9

1

1 2 3 4 5

Re

sto

rati

on

co

eff

icie

nt

Simulations over EON topology

Uniform

0 - 4

0 - 10

0 - 20

0 - 50

0.7

0.8

0.9

1

1 2 3 4 5

Re

sto

rati

on

co

eff

icie

nt

Simulations over OMNICOM topology

Uniform

0 - 4

0 - 10

0 - 20

0 - 50

0.7

0.8

0.9

1

1 2 3 4 5

Re

sto

rati

on

co

eff

icie

nt

Simulations over USA100 topology

Uniform

0 - 4

0 - 10

0 - 20

0 - 50

Impact of Tra�c and Randomness on ⟨kr⟩∙ For networks with N > 20 the maximum di�erence was less than 5%.

0.0

0.2

0.4

0.6

0.8

1.0

0

20

40

60

80

100

120

140

160

uniform 0-5 0-10 0-20 0-50

Re

sto

rati

on

co

eff

icie

nt

Nu

mb

er

of

cha

nn

els

(th

ou

san

ds)

Traffic model

Restoration channels

Working channels

Restoration coefficient

Final Remarks

∙ Tra�c randomness does not impact signi�cantly the restoration coe�cient,

mainly for networks larger than 20 nodes.

∙ Results show that we can estimate the restoration coe�cient with good

accuracy, without complete information about the network.

Contact:

pavan@ua.pt

Backup slides

Application for ⟨kr⟩

∙ Estimation of CapEx in Optical

Networks.

∙ Estimation of the number of

network components.

∙ Number of transponders.∙ Number of ports on EXCs.

IP Router

SDH EXC

WDM Terminal OLA

10 GE Cards

STM-64 PoS Cards

STM-64 Gray Cards

10 G Transponders

Cost Model

∙ Total cost of the network is:

∙ Costs of Transmission + Costs of Bandwidth Management

∙ CT =CT RANS +CBWM

∙ Costs of Transmission (links):

∙ WDM terminals + transponders + ampli�ers

∙ CT RANS = L(2γt0+ ⟨tk⟩γt1+ ⟨a⟩γt2)

∙ Costs of Bandwidth Management (nodes):

∙ IP routers + tributary ports + line ports + EXCs + EXC ports

∙ CBWM = N(γi0+ ⟨PIPT ⟩γi1+ ⟨PIPL⟩γi2+ γe0+ ⟨PkEXC⟩γe1)

Cost Model

∙ Normalized cost for the network components4.

Component Variable Cost

IP/MPLS Router Basic γi0 16.67

10 GE Interface γi1 1.05

STM-64 PoS Interface Card γi2 4.58

SDH/OTN EXC Basic γe0 26.67

STM-64 Gray Interface Card γe1 0.67

WDM Terminal, LH (40 channels) γt0 4.17

WDM Transponder, LH (10 Gbits/s) γt1 1.00

Optical Line Ampli�er, LH (100 km span) γt2 1.92

[4] R. Huelsermann et al., "Cost modeling and evaluation of capital expenditures in opticalmultilayer networks" J. Opt. Netw., 2008.

Cost Model

Variable Expression

Average nodal degree ⟨δ ⟩= 2LN

Average link length ⟨s⟩= 1L ∑

Ll=1 sl

Average OLAs ⟨a⟩= 1L ∑

Ll=1

⌈sl

span

⌉−1

Average tra�c demand ⟨d⟩= 2N ∑

N−1i=1 ∑

Nj=i+1 di j = N−1

Average number of hops ⟨h⟩= 1D ∑

N−1i=1 ∑

Nj=i+1 hi jdi j

Cost Model

Variable Expression

Average number of demands ⟨W o⟩= ⟨d⟩⟨h⟩⟨δ ⟩

Restoration coe�cient ⟨kr⟩= ψ

⟨W o⟩L

Average number of IP Ports PIPT = PIPL = ⟨d⟩

Average number of EXC Ports (surv.) ⟨PkEXC⟩= ⟨d⟩[1+ ⟨h⟩](1+ ⟨kr⟩)

Average number of transponders (surv.) ⟨tk⟩= 2⟨W o⟩(1+ ⟨kr⟩)

Required Approximations

∙ In the lack of topological information, some variables must be estimated.

Variable Expression

Average link length ?

Average number of hops ?

Restoration coe�cient ?

Actual Approximations

Cost Expression

Average link length1 ⟨s⟩ ≈√

A√N−1

Average number of hops1 ⟨h⟩ ≈√

(N−2)(⟨δ ⟩−1)

Restoration coe�cient ⟨kr⟩ ≈ 1.01−0.21ln(N)+ 0.45N0.32

⟨δ ⟩

[1] S. K. Korotky, "Network Global Expectation Model," J. Lightw. Technol. 2004.

Experiments

∙ European Optical Network, with A=11.180.000 km2.

∙ Routing through shortest path strategy.

∙ Restoration through the shared path technique.

Results

∙ Quantities of networkcomponent.

∙ EXC gray ports with

error of 10%.

∙ Transponders with error

of 2%.

∙ OLAs with error of 0%.

1000

1500

2000

Qua

ntiti

es o

f com

pone

nts OPNET

Approximation10%

2%

0

500

OT

N E

XC

s B

asic

OT

N E

XC

Gra

y P

orts

IP R

oute

r

IP R

oute

r G

E

Car

ds

IP R

oute

r P

oS

Car

ds

WD

M T

Ms

Tran

spon

ders

OLA

s

Qua

ntiti

es o

f com

pone

nts

Network componentsOT

N E

XC

s B

asic

OT

N E

XC

Gra

y

Network components

Results

∙ CapEx for BWM with

error of 3.5%.

∙ CapEx for TRANS with

error of 1.5%.

∙ CapEx for TOTAL cost

with error of 2.5%.

4000

5000

6000

7000

Nor

mal

ized

cos

ts

OPNET

Approximation

3.5%

2.5%

0

1000

2000

3000

CBWM CTRANS CTOTAL

Nor

mal

ized

cos

ts

C C C

1.5%

CBWM CTRANS CTOTAL

Network costsCBWM

CTRANS

CTOTAL