1. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 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. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 2 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

3. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 3 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 Bursty Traffic

4. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 4 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

5. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 5 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, P packet (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 Bursty Traffic

6. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 6 Under the M/G/1 assumption: How does this affect the statistics of signal dependent noises (FWM, inband crosstalk,…) Modelling Bursty Traffic

7. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 7 FWM is due to Kerr nonlinearity Generation of a fourth signal: f 1 +f 2 ‑ f 3 =f 4 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)

8. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 8 You can calculate the value of the FWM-induced distortion if you have the values of the bits being transmitted in all channels (B p ) and their phases (θ p ) Four Wave Mixing (FWM)

9. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 9 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 Inband Crosstalk

10. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 10 You can calculate the value of the inband crosstalk field if you have the values of the bits being transmitted in all channels (B p ) and their phases (θ p ) Inband Crosstalk

11. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 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 (B p ) and their phases (θ p )

12. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 12 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?

13. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 13 Calculation of the PDF of a random variable Y which depends on random variables z 1,…z N through Y=f(z 1,…,z N ) In the first iteration, standard MC is performed On each iteration i, the estimated PDF of Y is stored in the variables P i k A sample of Y is calculated by randomly selecting z i using the Metropolis algorithm Multicanonical Sampling

14. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 14 At the end of the iteration the values of P k i are updated according to the MCMC recurrence relations P k i are normalized such that their sum with respect to k is equal to unity The process is repeated until the PDF reaches sufficiently low values Multicanonical Sampling

15. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 15 System Parameters SymbolQuantityValues  nonlinear coefficient2.4 (Watt×km) -1 cspeed of light in vacuum3×10 8 m/sec λWavelength1.55μm Dfiber chromatic dispersion coefficient 2 ps/km/nm Δfchannel spacing50GHz αThe fiber loss coefficient0.2 dB/km Ltotal fiber length80 km L eff effective length21.169 km Rreceiver responsivity1.28 A/W Nnumber of channels16 Mnumber of interferers10 c02c02 # of photoelectrons in the signal at the receiver 100

16. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 16 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. Are the noises Gaussian?

17. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 17 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 Calculation of the FWM PDF

18. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 18 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 Inband Crosstalk PDF

19. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 19 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 Packet Error Rates

20. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 20 Channel Traffic Load Distribution

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

22. COMMUNICATION SYSTEMS, NETWORKS AND DIGITAL SIGNAL PROCESSING 19-21 July, 2006 22 Thank you! Email: thkam@di.uoa.gr