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

The Internet Congestion key problem

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

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

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

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

Multiscale Tree Structure time unit 4 ms 2 ms 1 ms

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

Additive Model Sample Realization Iteration/scale

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

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

Multiplicative Model Realization Iteration/scale

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

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

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

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

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

From Links to Paths Inferring path properties useful for many applications

pathChirp Efficient Available Bandwidth Estimation

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

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

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

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

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

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

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

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

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

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

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

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

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

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