Performance Estimation of Bursty Wavelength Division Multiplexing Networks

1COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006

Performance Estimation of Performance Estimation of Bursty Wavelength Division Bursty Wavelength Division Multiplexing NetworksMultiplexing Networks

I. Neokosmidis, T. Kamalakis and T. SphicopoulosUniversity of Athens

Department of Informatics and TelecommunicationsEmail: [email protected]


People tend to calculate the performance of an WDM network assuming worst case scenarios:

Optical Sources always on (no bustiness) Phase difference between signals is zero (max

interference)Etc…

What happens in more “average” cases?

Introduction


IP over WDMexponential growth of IP traffic (almost doubles

every six months)WDM is a promising technology (high capacity)

Why IP directly over WDM?Lack of optical random access memories

(RAMs) required for all-optical packet switching

Need for infrastructures / schemes in order to “route” IP packets without optical buffering

Multiprotocol Lambda Switching

Bursty Traffic


The label of the packets is the wavelength on which they are transmitted

MPS network forwards and labels the IP packets according to their FEC

Each wavelength can be modeled as an M/G/1 system (short-range dependence)

The burstiness of each wavelength is characterized by the traffic load ρ

Bursty Traffic


Inside a silent period (between two packets), the power of the source can be assumed zero

Silent periods can be considered as series of “0”s Within a packet, the “1”s and the “0”s appear

with equal likelihood The probability, Ppacket(t), that at any given time t,

a packet is being transmitted equals ρ The traffic load ρ essentially determines the

statistics of the bits

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

t1 t2 t3 t4

T

OFFp0=1-ρ/2

ONp1=ρ/2

t1+t2+t3+t4=ρT

Bursty Traffic


Under the M/G/1 assumption:

0 bit "0" is transmitted 1 / 2p P

1 bit "1" is transmitted / 2p P

How does this affect the statistics of signal dependent noises (FWM, inband crosstalk,…)

Modelling Bursty Traffic


FWM is due to Kerr nonlinearity Generation of a fourth signal: f1+f2‑f3=f4

FWM is very useful in wavelength conversion In a WDM system, some of the products may

coincide with the wavelength channels This causes nonlinear crosstalk between the

WDM channels FWM-induced distortion is therefore signal

dependent!

Four Wave Mixing (FWM)


pqr

npqrpqr

rqpm nqnp

dBBBI cos

3

1

22

sin3

1cos

3

1

nrpqr

pqrpqr

rqp

nrpqr

pqrpqr

rqps nqnp

dBBB

nqnp

dBBBI

You can calculate the value of the FWM-induced distortion if you have the values of the bits being transmitted in all

channels (Bp) and their phases (θp)

Four Wave Mixing (FWM)


It is due to filtering imperfections at optical cross‑connects

It is at the same wavelength as the signal

It cannot be removed using additional filtering

Node 4

Node 1 Node 3

Node 2

2x2Switch

λ1

λ1

λ1 λ1

Inband Crosstalk


M

k

M

n

jkn

T

nkeDdttAS0 00

2)(

2

1

T

nknnkk

kn dttgtgcBcB

D )()(2

*

You can calculate the value of the inband crosstalk field if you have the values of the bits being transmitted in all channels

(Bp) and their phases (θp)

Inband Crosstalk


Similarities…

In both cases you can calculate the value of the noise field if you have the values of the bits being transmitted in all

channels (Bp) and their phases (θp)

F()

z1

z2

z2N

Y

RVs with known PDF

RVs whose PDF we want to compute


Standard Monte Carlo requires an excessive number of samples

(~10/EP)

MultiCanonical Monte Carlo increases the occurrence of samples in the

tail regions of the PDF (faster) it can easily be implemented in any general-

purpose programming language

How to model?


Calculation of the PDF of a random variable Y which depends on random variables z1,…zN through Y=f(z1,…,zN)

In the first iteration, standard MC is performed

On each iteration i, the estimated PDF of Y is stored in the variables Pi

k

A sample of Y is calculated by randomly selecting zi using the Metropolis algorithm

Multicanonical Sampling


At the end of the iteration the values of Pki

are updated according to the MCMC recurrence relations

Pki are normalized such that their sum with

respect to k is equal to unityThe process is repeated until the PDF

reaches sufficiently low values

Multicanonical Sampling


System Parameters

Symbol Quantity Values

nonlinear coefficient 2.4 (Watt×km)-1

c speed of light in vacuum 3×108 m/sec

λ Wavelength 1.55μm

D fiber chromatic dispersion coefficient

2 ps/km/nm

Δf channel spacing 50GHz

α The fiber loss coefficient 0.2 dB/km

L total fiber length 80 km

Leff effective length 21.169 km

R receiver responsivity 1.28 A/W

N number of channels 16

M number of interferers 10

c02 # of photoelectrons in the signal

at the receiver100


For the case of the crosstalk noise, the Gaussian model does not provide an accurate estimate of the BER especially for small values of the traffic load

The error is much more pronounced in the case of FWM noise.

The Gaussian approximation cannot predict the maximum power that the system can tolerate. 0,2 0,4 0,6 0,8 1,0

4

6

8

10

12

14

16

18

20

4

6

8

10

12

14

16

18

20

SXR

(dB)

Pin (

dBm

)

Traffic load

BER=10-9

FWM-MCMC FWM-Gaussian approximation Crosstalk-MCMC Crosstalk-Gaussian approximation

(b)

0,2 0,4 0,6 0,8 1,010-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

BE

R

Traffic load

FWM Pin=8dBm

MCMC Gaussian approximation

In-band crosstalk SXR=12dB MCMC Gaussian approximation

(a)

Are the noises Gaussian?


As the traffic becomes heavier, the average power at each wavelength is increased

An increment of the traffic load leads to a broadening of the PDFs

-30 -20 -10 0 10 20 3010

-14

10-12

10-10

10-8

10-6

10-4

10-2

1

pdf

Im

= 0.2 = 0.4 = 0.6 = 0.8 = 1

(a)

0 100 200 300 40010-12

10-10

10-8

10-6

10-4

10-2

1

pdf

Is

= 0.2 = 0.4 = 0.6 = 0.8 = 1

(b)

Calculation of the FWM PDF


The pdf of the decision variable is strongly dependent on the value of ρ

As the traffic becomes lighter, smaller BER values are obtained for the same SXR

For light traffic, more nodes can be concatenated in the network

There is a strong dependence between the system performance and the SXR

0 50 100 150 200 250 30010-12

10-10

10-8

10-6

10-4

10-2

1

bs=1

pdf (

phot

oele

ctro

ns-1

)

S (photoelectrons)

= 0.2 = 0.4 = 0.6 = 0.8 = 1

bs=0

(a)

10 11 12 13 14 15 1610-12

10-10

10-8

10-6

10-4

10-2

1

BE

R

SXR (dB)

= 0.2 = 0.4 = 0.6 = 0.8 = 1

(b)

Inband Crosstalk PDF


The performance of the higher layers can be quantified in terms of the packet error rate

PER=1‑(1‑BER)k k=256bytes=2048bits (short

packets) and k=1500bytes=12000bits (long packets)

The PER has almost the same behaviour as the BER (PERkBER)

The PER is higher for longer packets (segmentation)

Erroneous receptions could cause packet retransmissions and/or loss of quality of service

Inaccuracy of the Gaussian model, especially in the case of FWM noise

0,2 0,4 0,6 0,8 1,010-14

10-12

10-10

10-8

10-6

10-4

10-2

1

PE

R

Traffic load

FWM, Pin=8dBm

MCMC, Short Packets MCMC, Long Packets Gaussian, Short Packets Gaussian, Long Packets

(b)

0,2 0,4 0,6 0,8 1,010-14

10-12

10-10

10-8

10-6

10-4

10-2

1

PE

R

Traffic load

In-band crosstalk SXR=12dB MCMC, Short Packets MCMC, Long Packets Gaussian, Short Packets Gaussian, Long Packets

(a)

Packet Error Rates


Channel Traffic Load Distribution

0 2 4 6 8 10 12 14 16 1810-16

10-14

10-12

10-10

10-8

10-6

BE

R

Channel Number

FWM, Pin=7.6dBm

=0.6 mean()=0.6

(c)

0 2 4 6 8 10 12 14 16 180,0

0,2

0,4

0,6

0,8

1,0

1,2

Traf

fic lo

ad

Channels (a)


The MCMC method is used to study the statistical behavior of FWM and inband crosstalk taking into account the impact of traffic burstiness in an IP over MPλS‑based WDM network

The MCMC method is proved to be more efficient (faster) and accurate

The performance of such systems is very sensitive to the traffic load

The Gaussian approximation does not yield accurate results

Careful traffic engineering can improve the system performance in terms of the BER

Conclusions


Thank you!

Email: [email protected]

Performance Estimation of Bursty Wavelength Division Multiplexing Networks

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