1. ISSCS 2009, Iasi, Romania1 Forecasting WiMAX BS Traffic by Statistical Processing in the Wavelet Domain Cristina Stolojescu 1, Alina Cușnir 2, Sorin Moga 3, Alexandru Isar 1 1 Politehnica University, Timisoara, Romania, 2 Alcatel-Lucent, Timisoara, Romania, 3 Telecom Bretagne, Brest, France.

2. ISSCS 2009, Iasi, Romania2 Goal predict where and when BS upgrading must take place in a WiMAX network statistical data processing in the wavelets domain

3. ISSCS 2009, Iasi, Romania3 Papagiannaki & alls, 2003 Wire network 1.5 years of data with 15 minutes granularity

4. ISSCS 2009, Iasi, Romania4 Potential of generalization Pros & cons Accurate forecasting Stationary network High volume of data required

5. ISSCS 2009, Iasi, Romania5 Proposed Method Wireless network containing 64 BSs, 11 weeks of data with 15 minutes granularity.

6. ISSCS 2009, Iasi, Romania6 Initial Observations The weekly traffic for a BS (arbitrarily selected). The corresponding power spectral density. Analyzing the first week of the considered period for all the 64 BSs we have found a periodicity of 24 hours in 77% of cases.

7. ISSCS 2009, Iasi, Romania7 MRA d 3 and d 4 – variability.c 6 – long term trend

8. ISSCS 2009, Iasi, Romania8 ANOVA

9. ISSCS 2009, Iasi, Romania9 Validation

10. ISSCS 2009, Iasi, Romania10 Parameters Extraction

11. ISSCS 2009, Iasi, Romania11 ARIMA MODELING

12. ISSCS 2009, Iasi, Romania12 Long Term Trend Estimation Applying the Box-Jenkins methodology for the first difference of the time series c 6 in our example we have obtained an ARIMA(011) model for the overall tendency:

13. ISSCS 2009, Iasi, Romania13 Where and when an upgrading must take place ?

14. ISSCS 2009, Iasi, Romania14 Saturation Risk BS μ [Mb/w] BS μ [Mb/w] BS μ [Mb/w] 61173.8249143.5657131.63 63169.2759135.7051126.21 62150.233133.3554115.12 48147.9058132.154106.55 56105.35

15. ISSCS 2009, Iasi, Romania15 Conclusions The proposed methodology is capable to isolate the overall long term trend and to identify those components that significantly contribute to its variability. Predictions based on approximations of those components provide accurate estimates with a minimal computational overhead.

16. ISSCS 2009, Iasi, Romania16 Metcalfe’s Law “The value of any communication network grows as the square of the number of users of the network” Andrew J. Viterbi, Four Laws of Nature and Society: The Governing Principles of Digital Wireless Communication Networks, in: H. Vincent POOR, Gregory W. WORNELL, Wireless Communications-Signal Processing Perspectives, Prentice Hall, 1998