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An Algebraic Approach to Practical and Scalable Overlay Network Monitoring

An Algebraic Approach to Practical and Scalable Overlay Network Monitoring. Yan Chen . David Bindel, Hanhee Song, and Randy H. Katz. University of California at Berkeley. Northwestern University. ACM SIGCOMM 2004. Motivation.

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An Algebraic Approach to Practical and Scalable Overlay Network Monitoring

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  1. An Algebraic Approach to Practical and Scalable Overlay Network Monitoring Yan Chen David Bindel, Hanhee Song, and Randy H. Katz University of California at Berkeley Northwestern University ACM SIGCOMM 2004

  2. Motivation • Infrastructure ossification led to thrust of overlay and P2P applications • Such applications flexible on paths and targets, thus can benefit from E2E distance monitoring • Overlay routing/location • VPN management/provisioning • Service redirection/placement … • Requirements for E2E monitoring system • Scalable & efficient: small amount of probing traffic • Accurate: capture congestion/failures • Adaptive: nodes join/leave, topology changes • Robust: tolerate measurement errors • Balanced measurement load

  3. Related Work • General metrics: RON (n2measurement) • Latency estimation • Link-level-measurement: min set cover (Ozmultu et al), similar approach for giving bounds of other metrics (Tang & McKinley) • Clustering-based: IDMaps, Internet Isobar, etc. • Coordinate-based: GNP, Virtual Landmarks, Vivaldi, etc. • Network tomography • Focusing on inferring the characteristics of physical links rather than E2E paths • Limited measurements -> under-constrained system, unidentifiable links

  4. Problem Formulation Given an overlay of n end hosts and O(n2) paths, how to select a minimal subset of paths to monitor so that the loss rates/latency of all other paths can be inferred. Assumptions: • Topology measurable • Can only measure the E2E path, not the link

  5. Outlines • An algebraic approach framework • Algorithms for a fixed set of overlay nodes • Scalability analysis • Adaptive dynamic algorithms • Measurement load balancing • Handling topology measurement errors • Simulations and Internet experiments

  6. Overlay Network Operation Center End hosts topology measurements Our Approach Select a basis set of k paths that fully describe O(n2) paths (k «O(n2)) • Monitor the loss rates of k paths, and infer the loss rates of all other paths • Applicable for any additive metrics, like latency

  7. A p1 1 3 Modeling of Path Space D C 2 B Path loss rate p, link loss rate l

  8. Putting All Paths Together Totally r = O(n2) paths, s links, s <<r = …

  9. A b2 1 3 b1 D b3 C 2 B Virtualization 2 1 Virtual links Sample Path Matrix • x1 - x2unknown => cannot compute x1, x2 • To separate identifiable vs. unidentifiable components: x = xG + xN • All E2E paths (G) are orthogonal to xN, i.e., GxN = 0

  10. 1 1’ 2’ 2 1 2 3 Rank(G)=2 2’ 1’ 1 1 3’ 2 2 4 3 3 4’ Rank(G)=3 Intuition through Topology Virtualization Virtual links: minimal path segments whose loss rates uniquely identified • Can fully describe all paths • xG composed of virtual links Virtualization Real links (solid) and all of the overlay paths (dotted) traversing them Virtual links

  11. = Algorithms • Select k = rank(G) linearly independent paths to monitor (one time) • Use QR decomposition • Leverage sparse matrix: time O(rk2) and memory O(k2) • E.g., 79 seconds for n = 300 (r = 44850) and k = 2541 • Compute the loss rates of other paths (continuously) • Time O(k2) and memory O(k2) = … …

  12. Outlines • An algebraic approach framework • Algorithms for fixed set of overlay nodes • Scalability analysis • Adaptive dynamic algorithms • Measurement load balancing • Handling topology measurement errors • simulations and Internet experiments

  13. How many measurements saved ? k « O(n2) ? For a power-law Internet topology • When the majority of end hosts are on the overlay • When a small portion of end hosts are on overlay • If Internet a pure hierarchical structure (tree): k = O(n) • If Internet no hierarchy at all (worst case, clique): k = O(n2) • Internet has moderate hierarchical structure [TGJ+02] k = O(n) (with proof) For reasonably large n, (e.g., 100), k = O(nlogn)

  14. BRITE 20K-node hierarchical topology Mercator 284K-node real router topology Linear Regression Tests of the Hypothesis • BRITE Router-level Topologies • Barbarasi-Albert, Waxman, Hierarchical models • Mercator Real Topology • Most have the best fit with O(n) except the hierarchical ones fit best with O(nlogn)

  15. Outlines • An algebraic approach framework • Algorithms for fixed set of overlay nodes • Scalability analysis • Adaptive dynamic algorithms • Measurement load balancing • Handling topology measurement errors • Simulations and Internet experiments

  16. Topology Changes • Basic building block: add/remove one path • Incremental changes: O(k2) time (O(n2k2) for re-scan) • Add path: check linear dependency with old basis set, • Delete path p : hard when • Intuitively, two steps • Add/remove end hosts , Routing changes • Routing relatively stable in order of a day => incremental detection

  17. A b2 Virtualization 1 3 b1 D 2 1 Virtual links b3 C 2 B Topology Change Example

  18. Other Practical Issues • Measurement load balancing • Randomly reorder the paths in G before scanning them for selection of • Has no effect on the loss rate estimation accuracy • Topology measurement errors tolerance • Care about path loss rates than any interior links • Router aliases => Let it be: assign similar loss rates to the same links • Path (segments) without topology info => add virtual links to bypass

  19. Outlines • An algebraic approach framework • Algorithms for fixed set of overlay nodes • Scalability analysis • Adaptive dynamic algorithms • Measurement load balancing • Handling topology measurement errors • Simulations and Internet experiments

  20. Evaluation • Extensive Simulations • See paper • Experiments on PlanetLab • 51 hosts, each from different organizations • 51 × 50 = 2,550 paths • Simultaneous loss rate measurement • 300 trials, 300 msec each • In each trial, send a 40-byte UDP pkt to every other host • Topology measurement (traceroute) • 100 experiments in peak hours of North America

  21. PlanetLab Experiment Results • Loss rate distribution • On average k = 872 out of 2550 • Metrics • Absolute error |p – p’ |: • Average 0.0027 for all paths, 0.0058 for lossy paths • Relative error [BDPT02] • Average 1.1 for all paths, and 1.7 for lossy paths

  22. More Experiment Results • Running time • Setup (path selection): 0.75 seconds • Update (for all 2550 paths): 0.16 seconds • More results on topology change adaptation: see paper • Robustness • Out of 14 sets of pair-wise traceroute … • On average 245 out of 2550 paths have no or incomplete routing information • No router aliases resolved Conclusion: robust against topology measurement errors

  23. Results for Measurement Load Balancing • Simulation on an overlay of 300 end hosts, average load 8.5 • With balancing: Gaussian-like load distribution • Without: heavily skewed, with the max almost 20 times the average

  24. Conclusions • A tomography-based overlay network monitoring system • Given n end hosts, characterize O(n2) paths with a basis set of O(nlogn) paths • Selectively monitor the basis set for their loss rates, then infer the loss rates of all other paths • Adaptive to topology changes • Balanced measurement load • Topology measurement error tolerance • Both simulation and PlanetLab experiments show promising results • Built an adaptive overlay streaming media system on top of it

  25. Backup Slides

  26. Other Practical Issues • Topology measurement errors tolerance • Care about path loss rates than any interior links • Poor router alias resolution => assign similar loss rates to the same links • Unidentifiable routers => add virtual links to bypass • Measurement load balancing on end hosts • Randomly order the paths for scan and selection of

  27. A p1 1 3 Modeling of Path Space D C 2 B Path loss rate p, link loss rate l Put all r = O(n2) paths together Totally s links

  28. x2 A b2 (1,1,0) 1 3 b1 (1,-1,0) path/row space (measured) D null space (unmeasured) b3 C 2 x1 B x3 Sample Path Matrix • x1 - x2unknown => cannot compute x1, x2 • Set of vectors form null space • To separate identifiable vs. unidentifiable components: x = xG + xN • All E2E paths are in path space, i.e., GxN = 0

  29. x2 (1,1,0) (1,-1,0) path/row space (measured) null space (unmeasured) x1 A b2 x3 Virtualization 1 3 b1 D 2 1 Virtual links b3 C 2 B Intuition through Topology Virtualization Virtual links: • Minimal path segments whose loss rates uniquely identified • Can fully describe all paths • xG is composed of virtual links All E2E paths are in path space, i.e., GxN = 0

  30. Algorithms = … • Select k = rank(G) linearly independent paths to monitor • Use rank revealing decomposition • Leverage sparse matrix: time O(rk2) and memory O(k2) • E.g., 10 minutes for n = 350 (r = 61075) and k = 2958 • Compute the loss rates of other paths • Time O(k2) and memory O(k2)

  31. Practical Issues • Topology measurement errors tolerance • Care about path loss rates than any interior links • Poor router alias resolution => assign similar loss rates to the same links • Unidentifiable routers => add virtual links to bypass • Measurement load balancing on end hosts • Randomly order the paths for scan and selection of • Topology Changes • Efficient algorithms for incrementally update of for adding/removing end hosts & routing changes

  32. More Experiment Results • Measurement load balancing Putting load values of each node in 10 equally spaced bins • Running time • Setup (path selection): 0.75 seconds • Update (for all 2550 paths): 0.16 seconds • More results on topology change adaptation: see paper With load balancing Without load balancing

  33. Work in Progress • Provide it as a continuous service on PlanetLab • Network diagnostics: Which links or path segments are down • Iterative methods for better speed and scalability

  34. Evaluation • Simulation • Topology • BRITE: Barabasi-Albert, Waxman, hierarchical: 1K – 20K nodes • Real topology from Mercator: 284K nodes • Fraction of end hosts on the overlay: 1 - 10% • Loss rate distribution (90% links are good) • Good link: 0-1% loss rate; bad link: 5-10% loss rates • Good link: 0-1% loss rate; bad link: 1-100% loss rates • Loss model: • Bernouli: independent drop of packet • Gilbert: busty drop of packet • Path loss rate simulated via transmission of 10K pkts • Experiments on PlanetLab

  35. Evaluation • Extensive Simulations • Experiments on PlanetLab • 51 hosts, each from different organizations • 51 × 50 = 2,550 paths • On average k = 872 • Results Highlight • Avg real loss rate: 0.023 • Absolute error mean: 0.0027 90% < 0.014 • Relative error mean: 1.1 90% < 2.0 • On average 248 out of 2550 paths have no or incomplete routing information • No router aliases resolved

  36. Sensitivity Test of Sending Frequency • Big jump for # of lossy paths when the sending rate is over 12.8 Mbps

  37. PlanetLab Experiment Results • Loss rate distribution • Metrics • Absolute error |p – p’ |: • Average 0.0027 for all paths, 0.0058 for lossy paths • Relative error [BDPT02] • Lossy path inference: coverage and false positive ratio • On average k = 872 out of 2550

  38. Accuracy Results for One Experiment • 95% of absolute error < 0.0014 • 95% of relative error < 2.1

  39. Accuracy Results for All Experiments • For each experiment, get its 95% absolute & relative errors • Most have absolute error < 0.0135 and relative error < 2.0

  40. Lossy Path Inference Accuracy • 90 out of 100 runs have coverage over 85% and false positive less than 10% • Many caused by the 5% threshold boundary effects

  41. Performance Improvement with Overlay • With single-node relay • Loss rate improvement • Among 10,980 lossy paths: • 5,705 paths (52.0%) have loss rate reduced by 0.05 or more • 3,084 paths (28.1%) change from lossy to non-lossy • Throughput improvement • Estimated with • 60,320 paths (24%) with non-zero loss rate, throughput computable • Among them, 32,939 (54.6%) paths have throughput improved, 13,734 (22.8%) paths have throughput doubled or more • Implications: use overlay path to bypass congestion or failures

  42. Adaptive Overlay Streaming Media Stanford UC San Diego UC Berkeley X HP Labs • Implemented with Winamp client and SHOUTcast server • Congestion introduced with a Packet Shaper • Skip-free playback: server buffering and rewinding • Total adaptation time < 4 seconds

  43. Adaptive Streaming Media Architecture

  44. Conclusions • A tomography-based overlay network monitoring system • Given n end hosts, characterize O(n2) paths with a basis set of O(nlogn) paths • Selectively monitor O(nlogn) paths to compute the loss rates of the basis set, then infer the loss rates of all other paths • Both simulation and real Internet experiments promising • Built adaptive overlay streaming media system on top of monitoring services • Bypass congestion/failures for smooth playback within seconds

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