Long-Term Forecasting of Internet Backbone Traffic

1. Long-Term Forecasting of Internet Backbone Traffic Dina Papagiannaki with Nina Taft, Zhi-Li Zhang, Christophe Diot

2. Why is it important? • Current best practices for IP traffic forecasting rely on marketing predictions • Backbone links large fraction of network operator’s investment • They have large provisioning cycles (between 6 and 18 months). • Current practices can be greatly enhanced using historical network measurements

3. Where/When in the backbone? • Goal: Where and When links have to be upgraded/added in the core of an IP backbone network • Where? • Measure traffic aggregate between adjacent PoPs • When? • We provide the forecast for current trends • Operators decide “when” based on SLAs, current provisioning practices, etc.

4. SNMP Topology Model Reduction (ANOVA) Wavelet Multiresolution Analysis 1 signal 7 signals Traffic Aggregates 2 signals Individual Forecasts (ARIMA) Weekly time series PoP pair forecast Methodology Roadmap

5. Sprint IP topology

6. Observation 1: Periodicities at 12 and 24 hour cycle

7. Observation 2: Long-Term Trend and Spikes

8. SNMP Topology Model Reduction (ANOVA) Wavelet Multiresolution Analysis 1 signal 7 signals Traffic Aggregates 2 signals Individual Forecasts (ARIMA) Weekly time series PoP pair forecast Methodology Roadmap

9. Wavelet Multiresolution Analysis (MRA) • Decompose into trend plus details at different time scales (time scale as power of 2). • Finest time scale = 90 minutes • Coarsest time scale = 96 hours • à-trous wavelet transform until 6th timescale (2^6*1.5 hours=96 hours) using B3 spline filter.

10. Wavelet Decomposition Approximations Details

11. SNMP Topology Model Reduction (ANOVA) Wavelet Multiresolution Analysis 1 signal 7 signals Traffic Aggregates 2 signals Individual Forecasts (ARIMA) Weekly time series PoP pair forecast Methodology Roadmap

12. Reducing the model • Overall trend accounts for 95%-97% of total energy • The maximum amount of energy in the details is located at the 3rd timescale (i.e. 12 hours)

13. Analysis of Variance • Accounts for 80-94% of total variance • Time series can be easily further compacted into weekly time series

14. SNMP Topology Model Reduction (ANOVA) Wavelet Multiresolution Analysis 1 signal 7 signals Traffic Aggregates 2 signals Individual Forecasts (ARIMA) Weekly time series PoP pair forecast Methodology Roadmap

15. Forecasting weekly components l(j) and dt3(j) • Autoregressive Integrated Moving Average models • Box-Cox methodology for fitting • Evaluation based on standard fitting indices • Traffic forecast derived through the model

16. Evaluation of Forecasts

17. Benefits • Highly accurate forecasts. • Minimal computational complexity. • The technique focuses on the aspects of the traffic that need to be modeled for the purpose of capacity planning. • The time series analyzed are significantly smaller than the initial ones. • Direct application of Box-Cox methodology leads to highly inaccurate forecasts on initial data.

18. Future Work • Forecasting IP traffic matrices • As individual OD pairs? • Or perhaps principal components? • Are eigenvectors “stable” across time? • Issue: what do we do about sampling?

19. Questions? Thank you!