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

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 (n 2 measurement) 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(n 2 ) 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. Our Approach Select a basis set of k paths that fully describe O(n 2 ) paths (k «O(n 2 )) Monitor the loss rates of k paths, and infer the loss rates of all other paths Applicable for any additive metrics, like latency End hosts Overlay Network Operation Center topology measurements

6. Modeling of Path Space Path loss rate p, link loss rate l A D C B 1 2 3 p1p1

7. Putting All Paths Together Totally r = O(n 2 ) paths, s links, s «r A D C B 1 2 3 p1p1 … =

8. Sample Path Matrix x 1 - x 2 unknown => cannot compute x 1, x 2 Set of vectors form null space To separate identifiable vs. unidentifiable components: x = x G + x N A D C B 1 2 3 b1b1 b2b2 b3b3 (1,-1,0) x2x2 x1x1 x3x3 (1,1,0) path/row space (measured) null space (unmeasured)

9. Intuition through Topology Virtualization Virtual links: Minimal path segments whose loss rates uniquely identified Can fully describe all paths x G is composed of virtual links A D C B 1 2 3 b1b1 b2b2 b3b3 (1,-1,0) x2x2 x1x1 x3x3 (1,1,0) path/row space (measured) null space (unmeasured) 1 2 Virtualization Virtual links All E2E paths are in path space, i.e., Gx N = 0

10. More Examples Real links (solid) and all of the overlay paths (dotted) traversing them Virtualization Virtual links 1 23 1’2’ Rank(G)=2 1 2 1 2 3 1’ 2’ 4 Rank(G)=3 3’ 4’ 1 2 3

11. Algorithms Select k = rank(G) linearly independent paths to monitor –Use QR decomposition –Leverage sparse matrix: time O(rk 2 ) and memory O(k 2 ) E.g., 10 minutes for n = 350 (r = 61075) and k = 2958 Compute the loss rates of other paths –Time O(k 2 ) and memory O(k 2 ) … = … =

12. How many measurements saved ? k « O(n 2 ) ? 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(n 2 ) –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. Areas and Domains # of hosts US (40).edu33.org3.net2.gov1.us1 Interna- tional (11) Europe (6) France1 Sweden1 Denmark1 Germany1 UK2 Asia (2) Taiwan1 Hong Kong1 Canada2 Australia1 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(n 2 ) 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. Problem Formulation Given an overlay of n end hosts and O(n 2 ) 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(n 2 ) paths (k «O(n 2 )) –Monitor the loss rates of k paths, and infer the loss rates of all other paths –Applicable for any additive metrics, like latency End hosts Overlay Network Operation Center topology measurements

18. Modeling of Path Space Path loss rate p, link loss rate l Put all r = O(n 2 ) paths together Totally s links A D C B 1 2 3 p1p1

19. Sample Path Matrix x 1 - x 2 unknown => cannot compute x 1, x 2 Set of vectors form null space To separate identifiable vs. unidentifiable components: x = x G + x N All E2E paths are in path space, i.e., Gx N = 0 A D C B 1 2 3 b1b1 b2b2 b3b3 (1,-1,0) x2x2 x1x1 x3x3 (1,1,0) path/row space (measured) null space (unmeasured)

20. More Examples Real links (solid) and all of the overlay paths (dotted) traversing them Virtualization Virtual links 1 23 1’2’ Rank(G)=2 1 2 1 2 3 1’ 2’ 4 Rank(G)=3 3’ 4’ 1 2 3

21. 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) BRITE 20K-node hierarchical topology Mercator 284K-node real router topology

22. Algorithms Select k = rank(G) linearly independent paths to monitor –Use rank revealing decomposition –Leverage sparse matrix: time O(rk 2 ) and memory O(k 2 ) E.g., 10 minutes for n = 350 (r = 61075) and k = 2958 Compute the loss rates of other paths –Time O(k 2 ) and memory O(k 2 ) … =

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(k 2 ) time (O(n 2 k 2 ) 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. Areas and Domains # of hosts US (40).edu33.org3.net2.gov1.us1 Interna- tional (11) Europe (6) France1 Sweden1 Denmark1 Germany1 UK2 Asia (2) Taiwan1 Hong Kong1 Canada2 Australia1 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. 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 loss rate [0, 0.05) lossy path [0.05, 1.0] (4.1%) [0.05, 0.1)[0.1, 0.3)[0.3, 0.5)[0.5, 1.0)1.0 %95.9%15.2%31.0%23.9%4.3%25.6% PlanetLab Experiment Results

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. X UC Berkeley UC San Diego Stanford HP Labs Adaptive Overlay Streaming Media 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(n 2 ) 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