Document

A Survey on Physical Network
Topology Estimation
October 21, 2005
Chikayama-Taura Lab.
Tatsuya Shirai
2005/10/21
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Background
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Progress of parallel processing
technologies
Costs of parallel processing
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Cost of computation
Cost of communication
Clusters, Grid Environments
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Cost of communication becomes bigger
with larger scale
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Allocation Policy
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Needs to closely allocate hosts frequently
communicating with each other
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With multiple clusters, allocate within clusters
In single cluster, allocate to use the same
switches
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Difficulty of estimate the cost
of communication

Shared link
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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
1
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3
100Mbps
4
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Desired Functions
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Ideally,
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Present network information to users
Configure allocation automatically
Needs to analyze network topology
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Other applications

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Network trouble shooting
Discovery of bottlenecks
Research on routing protocol
Simplification of local network
etc…
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Agenda
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Background
Network Topology
End-to-End Measurement
Researches
Conclusion
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Agenda

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Background
Network Topology
End-to-End Measurement
Researches
Conclusion
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Network Topology
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A structure of a network
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node
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host
router
switch, hub
link
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IP Layer Topology
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Structure of network
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node
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host
router
switch, hub
Link
Difficulty in collecting
information of LAN
structure
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Protocol-Based Algorithms
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Protocol
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
[Richard et al, ‘04]
, etc.
Hardware-dependent
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SNMP [Yuri et al, ’01] ,
Customized Protocol
Some hubs or switches doesn’t support
required protocols.
Deterministic estimation
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End-to-End Measurement
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Metric

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Hardware independent
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Packet loss rates [Bestavros et al, ‘02]
Delays [Coates et al, ‘01]
Always possible to measure topologies of
hosts who can communicate with root
Probabilistic
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Classification
IP layer
Protocol
based
End-to-End
Measurement
Nodes
Hosts,
routers
Hosts,
routers,
switches
Hosts,
routers,
switches,
hubs, …
Hardware
dependency
dependent
dependent
independent
Estimation
Deterministic Deterministic Probabilistic
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Agenda



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Background
Network Topology
End-to-End Measurement
Researches
Conclusion
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End-to-End Measurement
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Assume topologies are Tree-structured
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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
unused
non-branching
branching
actual topology
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estimated topology
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End-to-End Measurement

Assume topologies are Tree-structured


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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
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With a small variance, estimation is
deterministic
With a large variance, estimation is
probabilistic
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Use statistics
Search the topology that fits the most with
measurement
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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
Procedures consist of 2 steps
1. Measurement
2. Estimation
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Agenda

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Background
Network Topology
End-to-End Measurement
Researches
Conclusion
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Researches
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Maximum Likelihood Network Topology
Identification from edge-based unicast
measurements [Coates et al. ’01 SIGMETRICS]
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
Metric : Delay
Estimation: Maximum Likelihood Estimation
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Measurement –Sandwich Probe –
1
Measure delay of a link
shared 2 hosts (e.g. 2 and 4) d
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

2
3
4
d+⊿d
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Measurement

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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 = μ1+d
X32 = μ1+μ2+d
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d
μ1
μ2
2
3
4
X32
X42
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Estimation
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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


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The value of “fitting”
1
μ1
Set particular topology and
delay as a parameter
Likelihood = Π f(Xij)
3
2
X32= μ1+μ2
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μ1
4
X42= μ1
μ1
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Search Space of MLE
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
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Give many possible topologies to search
for MLE
Too wide to compute all topologies
Premise
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Similar topologies have similar likelihoods
⇒ Markov Chain Monte Carlo (MCMC)
(e.g. Hill Climbing)
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Similar Topologies –Step–
Birth step
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Insert a node
1
2
3
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Death step
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1
4
2
3
Delete a node
1
4
2
3
1
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
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Experimental Setup
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Measurement
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The root host and ten other hosts
2
Sent 8600 probes (O(n ))
For 8 minutes
MLE
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For 30-120 seconds
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The estimated
topology using
traceroute
The estimated
topology using
Coates’ method
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Agenda
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Background
Network Topology
End-to-End Measurement
Researches
Conclusion
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Conclusion
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Conclusion
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I Indicated importance of topology
estimation and introduced one methods
with End-to-End measurement
Future Works
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Topology Estimation within LAN of many
nodes
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