A Survey on Physical Network Topology Estimation


1
A Survey on Physical Network Topology Estimation

• October 21 2005
• Chikayama-Taura Lab.
• Tatsuya Shirai

2
Background

• Progress of parallel processing technologies
• Costs of parallel processing
• Cost of computation
• Cost of communication
• Clusters Grid Environments
• Cost of communication becomes bigger with larger
  scale

3
Allocation Policy

• Needs to closely allocate hosts frequently
  communicating with each other
• With multiple clusters allocate within clusters
• In single cluster allocate to use the same
  switches

4
Difficulty of estimate the cost of communication

• Shared link
• Each hosts can solely communicate at 100Mbps
• But all hosts can communicate at less than 50Mbps
  at a time
• All hosts need to work together to know this
  relation

100Mbps
5
Desired Functions

• Ideally
• Present network information to users
• Configure allocation automatically
• Needs to analyze network topology

6
Other applications

• Network trouble shooting
• Discovery of bottlenecks
• Research on routing protocol
• Simplification of local network
• etc

7
Agenda

• Background
• Network Topology
• End-to-End Measurement
• Researches
• Conclusion

8
Agenda

• Background
• Network Topology
• End-to-End Measurement
• Researches
• Conclusion

9
Network Topology

• A structure of a network
• node
• host
• router
• switch hub
• link

10
IP Layer Topology

• Structure of network
• node
• host
• router
• switch hub
• Link
• Difficulty in collecting information of LAN
  structure

11
Protocol-Based Algorithms

• Protocol
• SNMP Yuri et al 01
• Customized Protocol Richard et al 04 etc.
• Hardware-dependent
• Some hubs or switches doesnt support required
  protocols.
• Deterministic estimation

12
End-to-End Measurement

• Metric
• Packet loss rates Bestavros et al 02
• Delays Coates et al 01
• Hardware independent
• Always possible to measure topologies of hosts
  who can communicate with root
• Probabilistic

13
Classification
14
Agenda

• Background
• Network Topology
• End-to-End Measurement
• Researches
• Conclusion

15
End-to-End Measurement

• Assume topologies are Tree-structured
• Only one route exists between two hosts.
• Does not be changed while measuring
• Estimate branches of routes connecting hosts

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Estimated topology using End-to-End Measurement
actual topology
estimated topology
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End-to-End Measurement

• Assume topologies are Tree-structured
• Only one route exists between two hosts.
• Does not be changed while measuring
• Estimate branches of routes connecting hosts
• Variance in the measurements

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Variance of measurements

• With a small variance estimation is
  deterministic
• With a large variance estimation is
  probabilistic
• Use statistics
• Search the topology that fits the most with
  measurement

19
End-to-End Measurement

• Assume topologies are Tree-structured
• Only one route exists between two hosts.
• Does not be changed while measuring
• Estimate branches of routes connecting hosts
• Variance in the measurements
• Procedures consist of 2 steps
• 1. Measurement
• 2. Estimation

20
Agenda

• Background
• Network Topology
• End-to-End Measurement
• Researches
• Conclusion

21
Researches

• Maximum Likelihood Network Topology
  Identification from edge-based unicast
  measurements Coates et al. 01 SIGMETRICS
• Metric Delay
• Estimation Maximum Likelihood Estimation

22
Measurement Sandwich Probe
1

• Measure delay of a link shared 2 hosts (e.g. 2
  and 4)
• 1. Send a small packet to 4
• 2. After constant time send a large packet to 2
• 3. Without break send a small packet to 4 again

d
3
4
2
dd
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Measurement
1

• The arrival of the second packet is delayed
  because the large packet is slower
• Assume that all branched nodes are not store
  forward
• Can measure delay (or bandwidth) of shared link
• X42 µ1d
• X32 µ1µ2d

d
µ1
µ2
3
4
2
X42
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Estimation

• Assume delay of each shared link obeys Gaussian
  f(x)
• Search the topology best fitting the measurements
• Maximum Likelihood Estimation (MLE)

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Likelihood

• The value of fitting
• Set particular topology and delay as a parameter
• Likelihood f(Xij)

µ1
X32 µ1µ2
X42 µ1
µ1
µ1
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Search Space of MLE

• Give many possible topologies to search for MLE
• Too wide to compute all topologies
• Premise
• Similar topologies have similar likelihoods
• Markov Chain Monte Carlo (MCMC)
• (e.g. Hill Climbing)

27
Similar Topologies Step

• Birth step
• Insert a node

• Death step
• Delete a node

1
1
1
1
2
3
4
2
3
4
2
3
4
2
3
4
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Procedure of MLE

• 1. Give a topology at random
• 2. Make a small modification
• 3. If the new topology has greater likelihood
  adopt new topology
• 4. If a likelihood is at local maximum
• return to procedure 1
• 5. Otherwise goto2
• Can get a great likelihood topology in feasible
  time

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Experiment

• Experimental Setup
• The root host and ten other hosts
• Measurement
• Sent 8600 probes (O(n ))
• For 8 minutes
• MLE
• For 30-120 seconds

2
30
The estimated topology using traceroute
The estimated topology using Coates method
31
Agenda

• Background
• Network Topology
• End-to-End Measurement
• Researches
• Conclusion

32
Conclusion

• Conclusion
• I Indicated importance of topology estimation and
  introduced one methods with End-to-End
  measurement
• Future Works
• Topology Estimation within LAN of many nodes

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Information of Network

• Network Tomography
• Topology (construction of Network)
• Bandwidth Packet loss rate Shared link
• Analysis of the topology is the first step to
  estimating characteristics of a network

34
Researches

• Maximum Likelihood Network Topology
  Identification from edge-based unicast
  measurements Coates et al. 01 SIGMETRICS
• Metric Delay
• Estimation Maximum Likelihood Estimation
• Multicast Topology Inference from End-to-End
  Measurements Duffield et al. 02 IEEE Trans
• Metric Packet loss
• Estimation Maximum Likelihood Estimation

35
Coates Method

• Policy
• Measure delay of links shared by each pair of
  hosts
• Compute likelihood of many topologies and link
  delay
• Pick up the topology with the maximum likelihood

36

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Sandwitch Probing
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Shared Link
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Similar Topologies Step

• Methods to update topologies
• Birth step
• Death step
• µ-step

µa
µe
µc
µd
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Death step

• Delete a node (reverse of Birth step)

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µ-step

• Change a delay value of a link

µa
µa
µb
µb
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Birth step

• Insert a node

43
Death step

• Delete a node (reverse of Birth step)

44
µ-step

• Change a delay value of a link

µa
µa
µb
µb
45
d
dd
46
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The actual topology
The estimated topology