2005/10/21 1

A Survey on Physical Network Topology Estimation

October 21, 2005Chikayama-Taura Lab.

Tatsuya Shirai

2005/10/21 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

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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

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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

1

2

3

4100Mbps

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Desired Functions

Ideally, Present network information to users Configure allocation automatically

Needs to analyze network topology

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Other applications

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

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Agenda

Background Network Topology End-to-End Measurement Researches Conclusion

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Agenda

Background Network Topology End-to-End Measurement Researches Conclusion

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Network Topology

A structure of a network node

host router switch, hub

link

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IP Layer Topology Structure of network

node host router switch, hub

Link Difficulty in collecting

information of LAN structure

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Protocol-Based Algorithms

Protocol SNMP [Yuri et al, ’01] ,

Customized Protocol [Richard et al, ‘04] , etc.

Hardware-dependent Some hubs or switches doesn’t

support required protocols. Deterministic estimation

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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

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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

Background Network Topology End-to-End Measurement Researches Conclusion

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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

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Estimated topology using End-to-End Measurement

non-branching

unused

branching

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

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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. Measurement2. Estimation

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Agenda

Background Network Topology End-to-End Measurement Researches Conclusion

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Researches

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

Estimation

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Measurement –Sandwich Probe –

Measure delay of a link shared 2 hosts (e.g. 2 and 4)

1. Send a small packet to 42. After constant time, send

a large packet to 23. Without break, send a

small packet to 4 again

1

2 3 4

d

d+⊿d

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Measurement

X42X32

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

μ1

μ2

1

2 3 4

d

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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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Likelihood1

2 3 4

The value of “fitting”

Set particular topology and delay as a parameter

Likelihood = Π f(Xij)

μ1

μ1

X32= μ1+μ2

μ1

X42= 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)

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Similar Topologies –Step–

Birth step Insert a node

1

2 3 4

1

2 3 4

1

2 3 4

1

2 3 4

Death step Delete a node

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Procedure of MLE

1. Give a topology at random2. Make a small modification3. If the new topology has greater

likelihood, adopt new topology4. If a likelihood is at local maximum,

return to procedure 15. Otherwise goto2 Can get a great likelihood topology in

feasible time

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2

Experiment

Experimental Setup The root host and ten other hosts

Measurement Sent 8600 probes (O(n )) For 8 minutes

MLE For 30-120 seconds

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The estimated topology using

traceroute

The estimated topology

using Coates’ method

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Agenda

Background Network Topology End-to-End Measurement Researches Conclusion

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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