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Tomography-based Overlay Network Monitoring

Tomography-based Overlay Network Monitoring

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Tomography-based Overlay Network Monitoring

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  1. Tomography-based Overlay Network Monitoring Yan Chen, David Bindel, and Randy H. Katz UC Berkeley

  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 • Incrementally deployable • Easy to use

  3. Existing Work • General Metrics: RON (n2measurement) • Latency Estimation • Clustering-based: IDMaps, Internet Isobar, etc. • Coordinate-based: GNP, ICS, Virtual Landmarks • 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. 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

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

  7. A p1 1 3 Putting All Paths Together D C 2 B Totally r = O(n2) paths, s links, s «r = …

  8. 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

  9. 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

  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 More Examples 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 • Use QR 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) = … …

  12. 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) (extensive linear regression tests on both synthetic and real topologies)

  13. Practical Issues • Topology measurement errors tolerance • Measurement load balancing on end hosts • Randomized algorithm • Adaptive to topology changes • Add/remove end hosts and routing changes • Efficient algorithms for incrementally update of selected paths

  14. 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

  15. Conclusions • A tomography-based overlay network monitoring system • Given n end hosts, characterize O(n2) paths with a basis set of O(n logn) paths • Selectively monitor the basis set for their loss rates, then infer the loss rates of all other paths • Both simulation and PlanetLab experiments show promising results

  16. Backup Slides

  17. Overlay Network Operation Center End hosts topology measurements 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. • Key idea: based on topology, 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

  18. 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

  19. 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

  20. 1 1’ 2’ 2 1 2 3 Rank(G)=2 2’ 1’ 1 1 3’ 2 2 4 3 3 4’ Rank(G)=3 More Examples Virtualization Real links (solid) and all of the overlay paths (dotted) traversing them Virtual links

  21. 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(n logn)

  22. 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)

  23. 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

  24. 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

  25. 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 The essential info described by p : • Add/remove end hosts , Routing changes • Topology relatively stable in order of a day => incremental detection

  26. 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

  27. Experiments on Planet Lab • 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 • Simultaneous topology measurement • Traceroute • Experiments: 6/24 – 6/27 • 100 experiments in peak hours

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

  29. 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

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

  31. 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

  32. 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

  33. Topology/Dynamics Issues • Out of 13 sets of pair-wise traceroute … • On average 248 out of 2550 paths have no or incomplete routing information • No router aliases resolved Conclusion: robust against topology measurement errors • Simulation on adding/removing end hosts and routing changes also give good results

  34. 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

  35. 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

  36. Adaptive Streaming Media Architecture

  37. 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