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

01238

11

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

10 A

Multiplicative Model Realization

Iteration/scale

01238

11

Time Series Comparison of Models

time unit

24 ms

12 ms

6 ms

Berkeley data Multiplicative model Additive model

Histogram Comparison of Modelstime 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

)],0[

(min],0[number queue T

TACTB iii

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]

)( st)( rt

• 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

100Mbps-1 packets, 134.1

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 SLACRice and ChicagoRice 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

Efficiency Accuracy

pathchirp pathload pathChirp10-90%

pathloadAvg.min-max

30Mbps 0.35MB 3.9MB 19-29Mbps 16-31Mbps

50Mbps 0.75MB 5.6MB 39-48Mbps 39-52Mbps

70Mbps 0.6MB 8.6MB 54-63Mbps 63-74Mbps

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