1. Multiplicative Wavelet Traffic Model and pathChirp: Efficient Available Bandwidth Estimation Vinay Ribeiro

2. The Internet Congestion key problem

3. Network Traffic Modeling Traffic = packet arrival process on a link Traffic is bursty Bursts can cause buffer overflows Need accurate traffic models for –Simulation, estimation, prediction, control

4. Multiscale Aggregation Analysis of Traffic time unit 4 ms 2 ms 1 ms

5. Failure of Classical Models time unit 600 ms 60 ms 6 ms Internet Traffic Classical Traffic Model Internet traffic is self-similar: looks similar at different time scales

6. Why Self-similarity is Important Self-similarity leads to larger queues Classical models are overly optimistic

7. Multiscale Tree Structure time unit 4 ms 2 ms 1 ms

8. Additive Traffic Model Generate additive innovations, W Match variance at each level in tree Fast O(N) algorithm Coarse-to-fine multiscale synthesis

9. Additive Model Sample Realization Iteration/scale 0 1 2 3 8 11

10. Limitations of Additive Models Addition  Gaussian process Gaussian, takes negative values Gaussian not spiky Goal: model that gives positive and spiky data

11. Multiplicative Traffic Model Generate independent positive multiplicative innovations, Fast O(N) synthesis algorithm Coarse-to-fine multiscale synthesis

12. Multiplicative Model Realization Iteration/scale 0 1 2 3 8 11

13. Time Series Comparison of Models time unit 24 ms 12 ms 6 ms Berkeley data Multiplicative model Additive model

14. Histogram Comparison of Models time unit 24 ms 12 ms 6 ms Berkeley data Multiplicative model Additive model

15. Queuing Experiments Study queue overflow probability P(Q>b)

16. Queuing Results Plot log P(Q>b) vs. b Additive model underestimates losses (congestion) Berkeley traffic Multiplicative model Additive model

17. Advantages of Multiplicative Model Synthesized traffic –Positive –Spiky –Self-similar Algorithm –Fast O(N) synthesis Queuing –Outperforms additive model Uses –Simulation, estimation, congestion control, prediction

18. From Links to Paths Inferring path properties useful for many applications

19. pathChirp Efficient Available Bandwidth Estimation

20. Available Bandwidth Unused capacity along path Available bandwidth: Goal: estimate available bandwidth from probe packet transfer delays Delay=speed of light propagation + queuing delay

21. Applications Network monitoring Server selection Route selection (e.g. BGP) SLA verification Congestion control

22. Available Bandwidth Probing Tool Requirements Fast estimate within few RTTs Unobtrusive introduce light probing load Accurate No topology information (e.g. link speeds) Robust to multiple congested links No topology information (e.g. link speeds) Robust to multiple congested links

23. Principle of Self-Induced Congestion Advantages –No topology information required –Robust to multiple bottlenecks TCP-Vegas uses self-induced congestion principle Probing rate < available bw  no delay increase Probing rate > available bw  delay increases

24. Trains of Packet-Pairs (TOPP) [Melander et al] Vary sender packet-pair spacing Compute avg. receiver packet-pair spacing Constrained regression based estimate Shortcoming: packet-pairs do not capture temporal queuing behavior useful for available bandwidth estimation Packet-pairs Packet train

25. Pathload [Jain & Dovrolis] Constant bit rate (CBR) packet trains Vary rate of successive trains Converge to available bandwidth Shortcoming Efficiency: only one data rate per train

26. Chirp Packet Trains Exponentially decrease packet spacing within packet train Wide range of probing rates Efficient: few packets

27. CBR Cross-Traffic Scenario Point of onset of increase in queuing delay gives available bandwidth

28. Bursty Cross-Traffic Scenario Goal: exploit information in queuing delay signature Use principle of self-induced congestion

29. pathChirp Tool UDP probe packets No clock synchronization required, only uses relative queuing delay within a chirp duration Computation at receiver Context switching detection User specified average probing rate open source distribution at spin.rice.edu

30. Internet Experiments 3 common hops between SLAC  Rice and Chicago  Rice paths Estimates fall in proportion to introduced Poisson traffic

31. Comparison with TOPP 30% utilization Equal avg. probing rates for pathChirp and TOPP Result: pathChirp outperforms TOPP 70% utilization

32. Comparison with Pathload 100Mbps links pathChirp uses 10 times fewer bytes for comparable accuracy Available bandwidth EfficiencyAccuracy pathchirppathloadpathChirp 10-90% pathload Avg.min-max 30Mbps0.35MB3.9MB19-29Mbps16-31Mbps 50Mbps0.75MB5.6MB39-48Mbps39-52Mbps 70Mbps0.6MB8.6MB54-63Mbps63-74Mbps

33. Summary Multiplicative wavelet model for traffic –Positive and spiky data –Outperforms additive Gaussian models –Freeware code: dsp.rice.edu pathChirp –Special chirp packet trains –Efficient available bandwidth estimation –Freeware code: spin.rice.edu