Tomographybased Overlay Network Monitoring

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 (n2 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 -gt 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
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
Modeling of Path Space
A
1
3
D
C
2
B

• Path loss rate p, link loss rate l

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


8
Sample Path Matrix

• x1 - x2 unknown gt cannot compute x1, x2
• Set of vectors
• form null space
• To separate identifiable vs. unidentifiable
  components x xG xN

9
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
More Examples
Virtualization
Real links (solid) and all of the overlay paths
(dotted) traversing them
Virtual links
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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)

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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
  TGJ02

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 lt 0.014
• Relative error mean 1.1 90 lt 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
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
Modeling of Path Space
A
1
3
D
C
2
B

• Path loss rate p, link loss rate l

Put all r O(n2) paths together Totally s links
19
Sample Path Matrix

• x1 - x2 unknown gt 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
More Examples
Virtualization
Real links (solid) and all of the overlay paths
(dotted) traversing them
Virtual links
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)

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
• gt assign similar loss rates to the same links
• Unidentifiable routers
• gt 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
• gt incremental detection

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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

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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 lt 0.0014
• 95 of relative error lt 2.1

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Accuracy Results for All Experiments

• For each experiment, get its 95 absolute
  relative errors
• Most have absolute error lt 0.0135 and relative
  error lt 2.0

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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 lt 4 seconds

36
Adaptive Streaming Media Architecture
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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