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Network Tomography Using Passive End-to-End Measurements

Network Tomography Using Passive End-to-End Measurements. Lili Qiu Joint work with Venkata N. Padmanabhan and Helen J. Wang Microsoft Research DIMACS’2002. Overview. Goal: Determine internal network characteristics using passive, end-to-end measurements

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Network Tomography Using Passive End-to-End Measurements

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  1. Network Tomography Using Passive End-to-End Measurements Lili Qiu Joint work with Venkata N. Padmanabhan and Helen J. Wang Microsoft Research DIMACS’2002

  2. Overview • Goal: Determine internal network characteristics using passive, end-to-end measurements • find trouble spots in the network (e.g., AT&T-Sprint peering point) • Metrics of interest • Link loss rate our focus • Raw bandwidth • Available bandwidth • Traffic rate … • Why interesting • Server selection • Resolve the trouble spots Web Server AT&T Sprint MCI UUNET Earthlink Why so slow? AOL Qwest

  3. Topological Metrics Topological metrics are poor predictors of packet loss rate All links are not equal  need to identify the lossy links

  4. S A B Previous Work • Active probing to infer link loss rate • multicast probes • striped unicast probes • Pros & cons • accurate since individual loss events identified • expensive because of extra probe traffic S A B

  5. Problem Formulation • Goal • Identify lossy links rather than determine exact loss rate • Passive observation of existing traffic • Active probing to discover network topology can be done infrequently in the background server (1-l1)*(1-l2)*(1-l4) = (1-p1) (1-l1)*(1-l2)*(1-l5) = (1-p2) … (1-l1)*(1-l3)*(1-l8) = (1-p5) Under-constrained system of equations l1 l3 l2 l4 l5 l6 l7 l8 clients p1 p2 p3 p4 p5

  6. #1: Random Sampling • Randomly sample the solution space • Repeat this several times • Draw conclusions based on overall statistics • How to do random sampling? • determine loss rate bound for each link using best downstream client • iterate over all links: • pick loss rate at random within bounds • update bounds for other links • Problem: little tolerance for estimation error server l1 l3 l2 l4 l5 l6 l7 l8 p1 p2 p3 p4 p5 clients

  7. #2: Linear Optimization Goals • Parsimonious explanation • Robust to error in client loss rate estimate Li = log(1/(1-li)), Pj = log(1/(1-pj)) minimize Li + |Sj| L1+L2+L4 + S1 = P1 L1+L2+L5 + S2 = P2 … L1+L3+L8 + S5 = P5 Can be turned into a linear program server l1 l3 l2 l4 l5 l6 l7 l8 p1 p2 p3 p4 p5 clients

  8. # 3: Gibbs Sampling • D • observed packet transmission and loss at the clients •  • ensemble of loss rates of links in the network • Goal • determine the posterior distribution P(|D) • Approach • Use Markov Chain Monte Carlo with Gibbs sampling to obtain samples from P(|D) • Draw conclusions based on the samples

  9. # 3: Gibbs Sampling (Cont.) • Applying Gibbs sampling to network tomography • 1) Initialize link loss rates arbitrarily • 2) For j = 1 : warmup for each link i compute P(li|D, {li’}) where li is loss rate of link i, and {li’} = kI lk • 3) For j = 1 : realSamples for each link i compute P(li|D, {li’}) • Use all the samples obtained at step 3 to approximate P(|D)

  10. Performance Evaluation • Simulation experiments • Trace-driven validation

  11. Simulation Experiments • Advantage: no uncertainty about link loss rate! • Methodology • Topologies used: • randomly-generated: 20 - 3000 nodes, max degree = 5-50 • real topology obtained by tracing paths to microsoft.com clients • randomly-generated packet loss events at each link • A fraction f of the links are good, and the rest are “bad” • LM1: good links: 0 – 1%, bad links: 5 – 10% • LM2: good links: 0 – 1%, bad links: 1 – 100% • Goodness metrics: • Coverage: # correctly inferred lossy links • False positive: # incorrectly inferred lossy links

  12. Random Topologies

  13. Trace-driven Validation • Validation approach • Divide client traces into two: tomography and validation • Tomography data set => loss inference • Validation set => check if clients downstream of the inferred lossy links experience high loss • Experimental setup • Real topologies and loss traces collected from traceroute and tcpdump at microsoft.com during Dec. 20, 2000 and Jan. 11, 2002 • Results • False positive rate is between 5 – 30% • Likely candidates for lossy links: • links crossing an inter-AS boundary • links having a large delay (e.g. transcontinental links) • links that terminate at clients

  14. Summary • Passive network tomography is feasible • Tradeoff between computational cost and accuracy • Gibbs sampling is accurate but expensive to run • Random sampling is quickest but with high false positive • Random sampling may still be useful in practice when the number of lossy links is small • Acknowledgements: • MSR: Dimitris Achlioptas, Christian Borgs, Jennifer Chayes, David Heckerman, Chris Meek, David Wilson • ITG/GNS: Rob Emanuel, Scott Hogan

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