Performance Estimation of Bursty Wavelength Division Multiplexing Networks

1. Performance Estimation of Bursty Wavelength Division Multiplexing Networks I. Neokosmidis, T. Kamalakis and T. Sphicopoulos University of Athens Department of Informatics and Telecommunications Email: thkam@di.uoa.gr

2. Introduction 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?

3. Bursty Traffic IP over WDM • exponential 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

4. Bursty Traffic • The label of the packets is the wavelength on which they are transmitted • MPS 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

5. 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

6. Modelling Bursty Traffic Under the M/G/1 assumption: How does this affect the statistics of signal dependent noises (FWM, inband crosstalk,…)

7. Four Wave Mixing (FWM) • 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!

8. Four Wave Mixing (FWM) 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)

9. Inband Crosstalk • 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

10. Inband Crosstalk 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)

11. 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)

12. How to model? • Standard Monte Carlo • requires an excessive number of samples (~10/EP) • MultiCanonical Monte Carlo • increases the occurrence of samples in the tail regionsof the PDF (faster) • it can easily be implemented in anygeneral-purpose programming language

13. Multicanonical Sampling • 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 Pik • A sample of Y is calculated by randomly selecting zi using the Metropolis algorithm

14. Multicanonical Sampling • At the end of the iteration the values of Pki are updated according to the MCMC recurrence relations • Pkiare normalized such that their sum with respect to k is equal to unity • The process is repeated until the PDF reaches sufficiently low values

15. System Parameters

16. Are the noises Gaussian? • 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.

17. Calculation of the FWM PDF • 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

18. Inband Crosstalk 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

19. Packet Error Rates • 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 (PERkBER) • 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

20. Channel Traffic Load Distribution

21. Conclusions • 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

22. Thank you! Email: thkam@di.uoa.gr