Network Topology Properties

1
Network Topology --- Properties

• Prof. Gao
• ECE697A Fall 2003
• Advanced Computer Networks

2
Outline

• How does network topology look like?
• Random Graph?
• Properties of Network Topology
• Degree distribution
• Power law
• Structure
• Hierarchical Structure

3
Network Topology

• On Router Level
• Topology Graph (V, E)
• Each node denotes a router
• Edge is the physical link between two routers
• On AS level
• Topology Graph (V, E)
• Each node denotes an AS
• Edge is AS pair which have a BGP session between
  them

4
Two Levels of Internet Topology--- measured in
May,2001

• Router-level 170589 nodes and 215795 edges
• AS-level 10941 nodes and 22593 edges

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Why Topology Is Important?

• Design Efficient Protocols
• Create Accurate Model for Simulation
• Derive Estimates for Topological Parameters
• Study Fault Tolerance and Anti-Attack Properties

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Power-Law, Zipf, Pareto

• Power-Law (probability distribution function)
• PX x  x-(k1) x-a
• Pareto (cumulative distribution function)
• PX gt x  x-k
• Zipf ( size vs. rank )
• y  r-b
• They are different ways of looking at the same
  thing

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Internet Instances

• Three Snapshots of Internet

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Power Law Properties (degree vs. rank)

• Power Law 1 (rank exponent)
• The degree, dv , of a node v, is proportional to
  the rank of the node, rv, to the power of a
  constant, R
• dv ? rvR

9
Rank Plots

• Log-Log scale graph
• X axis is rank, Y axis is degree

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Power Law Properties (frequency vs. degree)

• Power Law 2 (Out-Degree exponent)
• The frequency, fd, of an out-degree, d, is
  proportional to the out-degree to the power of a
  constant, O
• fd ? dO

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Outdegree Plots

• Log-log scale graph
• X axis is degree, Y axis is frequency

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Power Law Properties(eigenvalues)

• Power Law 3
• The eigenvalues, ?i, of a graph are proportional
  to the order, i, to the power of a constant, ?
• ?i ? i?
• Eigenvalues of a graph are the eigenvalues for
  the adjacency matrix of this graph

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Eigenvalue plots

• Log-log scale graph
• X axis is the order of eigenvalue
• Y axis is the eigenvalue

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What Causes Power Law?

• The rich gets richer
• The poor gets poorer
• Power law is everywhere
• Frequency of characters in English text
• Income distribution
• Popularity of Web site

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Connectivity does not Mean Reachability

• Now we know properties of connectivity
• But connectivity DOES NOTreachability!
• Commercial agreement
• Routing policy
• An annotated topology.

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Route Propagation Policy

• Constrained by contractual commercial agreements
  between administrative domains

Regional ISP B
Regional ISP A
University C
e.g., An AS does not provide transit services
between its providers
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AS Commercial Relationships

• Provider-customer
• customer pays its provider for transit services
• Peer-peer
• exchange traffic between customers
• no exchange of money
• Sibling-sibling
• have mutual transit agreement
• merging ISPs, Internet connection backup
• However, AS relationships are not public!

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AS Relationship Graph
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Route Propagation Rule

• An AS or a set of ASes with sibling relationship
  does not provide transit services between any two
  of its providers and peers
• BGP routing table entries have certain patterns

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Routing Table Entry
704
702
701
1849
1
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Routing Table Entry Patterns
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Heuristic Algorithms

• Infer provider-customer and sibling-sibling
• basic
• refined
• Infer peer-peer
• final

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Basic Algorithms

• Heuristics
• Top provider has largest degree
• Based on patterns on BGP routing table entries
• Consecutive AS pairs on the left of top provider
  are customer-to-provider or sibling-sibling edges
• Consecutive AS pairs on the right of top provider
  are provider-to-customer or sibling-sibling edges

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Initialize Consecutive AS Pair Relationship
uj
uj1
u2
un-1
Maximum degree AS
u1
un
25
uj
uj1
u2
un-1
u1
un
26
ub
ua
uc
uj
uj1
ud
u2
un-1
u1
un
27
ub
ua
uc
ud
u2
u1
28
ub
ua
Assign relationship to AS pairs
uc
uj
uj1
ud
u2
un-1
Sibling-siblingu1,u2 1
u1
un
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Refined Algorithm

• Bogus Routing Entries
• Each routing table entry votes on AS
  relationships
• Ignore sibling-to-sibling relationship concluded
  by only one entry

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Inferring Peer-Peer Relationships

• Peer-peer edge is between top provider and one of
  its neighbors only
• Heuristics
• peer-to-peer edge is between top provider and its
  higher degree neighbor
• degrees of two peers do not differ significantly
• lt R times

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Final Algorithm
uj
uj1
uj-1
un-2
degreeuj-1 lt degreeuj1
u2
un-1
u1
un
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Final Algorithm
uj
uj1
uj-1
un-2
degreeuj / degreeuj1 lt R and degreeuj /
degreeuj1 gt 1/R
u2
un-1
u1
un
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Experimental Verification

• Routing table from Route Views
• Connected to 22 ISPs at 24 locations
• Daily routing table dump
• Routing table from 3 days
• 1999/9/27, 2000/1/2, 2000/3/9
• 1 million routing entries

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Inference Results
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Verification of Inferred Relationships by ATT
Comparing inference results from Basic and
Final(R ) with ATT internal information
8
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Verification of Inferred Relationships by ATT
Comparing inference results from Refined and
Final(R ) with ATT internal information
8
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Verification of Inferred Relationships by ATT
Comparing inference results from Basic and
Final(R60) with ATT internal information
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WHOIS Lookup Service

• Supplies name and address of company that owns an
  AS
• AS pair might have sibling-sibling relation if
• belong to the same company or two merging
  companies
• belong to two small companies located closeby

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Verification by WHOIS lookup Service

• Confirm 101 of 186 inferred sibling-sibling
  relationships (gt 50)
• Some unconfirmed sibling-sibling relationships
  might be due to
• WHOIS service is not up to date
• Not enough information
• Bogus Routes
• Router configuration typo 7018 3561 7057 7075
  7057
• Misconfiguration of small ISPs1239 11116 701
  7018
• ...

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Summary

• AS relationships are inherent aspect of Internet
  architecture
• Our heuristic algorithm is based on routing entry
  pattern derived from policy rules
• Verification
• ATT (99)
• Whois services (gt50)

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More Algorithms

• Inference from multiple vantage points
• Lakshminarayanan Subramanian, Sharad Agarwal,
  Jennifer Rexford, and Randy H. Katz,
  "Characterizing the Internet hierarchy from
  multiple vantage points," in Proc. IEEE INFOCOM,
  June 2002
• Inference with minimum conflict
• Giuseppe Di Battista, Maurizio Patrignani,
  Maurizio Pizzonia, Computing the Types of the
  Relationships between Autonomous Systems, INFOCOM
  2003

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Internet Architecture

• Hierarchical structure
• Backbone
• Edge network

AS1
AS2
AS3
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Hierarchical Topology

• Based on AS relationship
• Tiers
• Provider/Customer

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Hierarchical Topology

• The number of ASes in different tiers on 2001/05,
  there are 11038 ASes
• Tier 1 22 (0.20)
• Tier 2 5228 (47.37)
• Tier 3 4193 (37.99)
• Tier 4 1396 (12.64)
• Tier 5 174 (1.67)
• Tier 6 19 (0.17)
• Tier 7 6 (0.05)

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Summary

• Properties of Internet Topology
• Power Law Relationship
• Annotated Topology
• Hierarchical Structure
• Next topic, how to generate Internet topology