CMPE 588 MODELLING OF INTERNET

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CMPE 588 MODELLING OF INTERNET

• TOWARDS MODELLING THE INTERNET TOPOLGY
• -
• THE INTERACTIVE GROWTH MODEL
• by
• Shi Zhou, Raul J. Modragon
• -
• Ahmet OLGUN

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OUTLINE

• INTRODUCTION
• RICH-CLUB PHENOMENON
• DEGREE-BASED INTERNET TOPOLOGY GENERATORS
• Inet-3.0 Model
• Barabasi-Albert (BA) Model
• Generalized Linear Preference (GLP) Model
• INTERACTIVE GROWTH (IG) MODEL
• MODEL VALIDATION
• Degree Distribution
• Low-range degree distribution
• High-range degree distribution
• Maximum degree
• Rich-club Phenomenon
• Rich-club connectivity
• Node-node link distribution
• CONCLUSIONS

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INTRODUCTION

• Aim Modelling Internet Topology
• The Internet topology at the AS graph has
• Power-law degree distribution (Faloutsos)
• Tier structure (Subramanian)
• Internet power-law topology generators
• Degree-based
• Structure-based (Tangmunarunkit found degree
  distributions produced by these generators are
  not power-laws)
• Interactive Growth (IG) model based on joint
  growth of new nodes and new links is introduced

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INTRODUCTION (cntd)

• power-law degree distribution
• The fraction of nodes with degree d 1/db for
  some constant b gt 0
• tier structure (layers)
• AS graph

Router
AS
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INTRODUCTION (cntd)

• AS graph is compared against
• IG Model (proposed)
• three degree-based models
• Inet-3.0 model
• BA Scale-free model
• GLP model
• It has been shown that IG model favors other
• Closely resembles degree distribution of AS graph
• Matches the hierarchical structure

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RICH-CLUB PHENOMENON

• Rich nodes
• Power-law technologies have small number of nodes
  having large number of links.
• AS graph shows this phenomenon
• Rich nodes are well connected to each other
• Rich nodes are connected preferentially to the
  other rich nodes.
• It s measured in the
• Original-maps of the AS graph (BGP Routing tables
  by University of Oregon Route Views Project)
• Extended-maps of the AS graph (BGP Routing tables
  Looking Glass (LG) data Internet Routing
  Registry data)

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RICH-CLUB PHENOMENON (cntd)

• Comparison of original-maps extended-maps
• Both have similiar number of nodes
• Extended-maps have 40 more links than the
  original-maps
• Research Outcome
• Majority of missing links in the original-maps
  are connecting rich nodes of the extended-map
• Therefore extended-maps show rich-club phenomenon
  stronger than the original-maps
• Why rich-club phenomenon is relevant?

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RICH-CLUB PHENOMENON (cntd)

• Connectivity between rich nodes can be crucial
  for network properties (routing effieciency,
  redundancy, robustness, ...)
• Alternative routing paths
• Super traffic hub
• It is simple way to differentiate tier structures
  between power-law topologies

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DEGREE-BASEDINTERNET TOPOLOGY GENERATORS

• Inet-3.0 model
• Barabasi-Albert (BA) model
• Generalized Linear Preference Model

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Inet-3.0 model

• Designed to match the measurements of the
  original-maps of the AS graph
• of links generated depends on
• Total of nodes
• Percentage of nodes with degree 1
• Typically generates 26 less links than
  extended-AS graph

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Barabasi-Albert (BA) model

• Power-law degree distribution can arise from two
  mechanisms
• Growth (addition of new nodes)
• preferential attachment (new nodes are
  preferentially attached to nodes that are already
  well connected)
• Probability of attachment
• Using mean-field theory it is estimated that BA
  model generates networks with degree distribution
  P(k) k-3

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Generalized Linear Preference (GLP) model

• A modification of the BA model.
• Evolution of AS graph mostly due to two reasons
• The addition of new nodes
• The addition of new links between existing nodes
• It starts with m0 nodes connected through m0-1
  links

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Generalized Linear Preference (GLP) model (cntd)

• At each time step
• With probability p m lt m0 new links are added
  between m pairs of nodes chosen from existing
  nodes
• With probability 1-p a new node is added and
  connected to m existing nodes

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Generalized Linear Preference (GLP) model (cntd)

• Probability to choose node i is,
• Constant parameter can be adjusted such that
  nodes have a stronger preference of high degree
  nodes than BA model
• It matches AS graph (original-maps) in terms of
  two characteristics of small-world networks
• Characteristic path length
• Clustering coefficient

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Interactive Growth (IG) model

• Also reflects two main operations
• Addition of new nodes
• Addition of new links
• So, what is difference?
• Growth of links and nodes are interdependent in
  IG model
• At each time step a new node is connected to
  existing nodes (host nodes), and new links will
  connect the host nodes to other existing nodes
  (peer nodes)
• By the way, IG model uses same linear preference
  as BA model when choosing existing nodes to
  connect.

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Interactive Growth (IG) model (cntd)
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Interactive Growth (IG) model (cntd)

• What about actual internet?
• New nodes bring new traffic load to its host
  nodes
• Results?
• Increase of traffic volume
• Change of traffic pattern around host nodes
• In order to balance network traffic and optimize
  network performance addition of new links between
  hosts and peers is triggered.

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Interactive Growth (IG) model (cntd)

• This joint growth of new nodes and new links is
  called INTERACTIVE GROWTH
• Impacts of INTERACTIVE GROWTH
• Rich nodes of IG model is better inter-connected
  than BA model
• Rich nodes of IG model have higher degrees than
  those of BA model

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Interactive Growth (IG) model (cntd)

• Time-evolution of node degree in both the BA and
  IG obeys a power-law
• Barabase predicted theta of BA is 0.5, authors
  calculated IGs 0.6
• What is reason?
• During interactive growth host nodes connect to
  peer nodes as well

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MODEL VALIDATION
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DEGREE DISTRIBUTION

• Degree distribution P(k) is the percentage of
  nodes with degree k
• Degree distribution of AS graph deviates from a
  strict power law.
• So, it is studied in three levels
• Low-range (klt3)
• High range (1000 richest nodes)
• Maximum degree
• NOTEP(1)ltP(2) in AS graph. Only IG shows this
• WHY P(1) P(2) IS IMPORTANT???
• 70 of AS graph!!!

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DEGREE DISTRIBUTION(cntd)
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RICH CLUB PHENOMENON

• RICH CLUB CONNECTIVITY
• INTER-CONNECTION BETWEEN RICH NODES
• INTERESTING NOTE GLPs gt AS
• NODE-NODE LINK DISTRIBUTION
• L(Ri,Rj) number of links connecting nodes with
  rank ri to nodes with rj. Ranks are normalized by
  total number of nodes and ri lt rj

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RICH CLUB PHENOMENON(cntd)
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RICH CLUB PHENOMENON(cntd)
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CONCLUSIONS

• Inet-3.0 is not a dynamic model
• The BA model generates a strict power-law degree
  distribution which is very from AS graph gt
  network structure is different, because ...
• ALL NEW LINKS CONNECT WITH NEW NODES. Due to
  PREFERENTIAL ATTACHMENT, AS NETWORK GROWS THE
  PROBABILITY FOR A NEW NODE TO BECOME RICH NODE
  DECREASES...
• SO, rich nodes are NOT well connected
• GLP model does not reproduce details of degree
  distribution of AS graph.
• NOTE rich club phenomenon obtained is
  significantly stronger than AS graph

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CONCLUSIONS (cntd)

• IG model compares favorable with others
• Simple and dynamic
• Resemles degree distribution of AS graph
• Matches hierarchical structure of AS graph
• POSSIBLE IMPROVEMENTS
• Including BANDWITH and DELAY as model parameters

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• THANKS
• Q A