Topology Generation

Suat Mercan

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Outline Motivation

Topology Characterization

Levels of Topology

Modeling Techniques

Types of Topology Generators

Motivation for Internet Topology Research

Design of better protocols Optimization of protocols Develop network planning Better network design Realistic models for simulation Meaningful simulations Analysis of topological characteristics Performance evaluation

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Topological Characteristics of Internet

Complex network – irregular & dynamically evolving Topology changes due to: VPNs, P2P, mobile nets Different applications reside: e.g. www, e-mail, P2P No central node Built on two domains: transit and stub – there is loose hierarchy e.g. tiered ISPs It has small-world effect and scale-free properties – small-world: identical concept to six degrees of separation – scale-free: there isn’t any characteristic scale to fit

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Topology Characterization

Average degree Degree distribution Clustering Coreness Shortest path distance Betweenness

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Topology Research Challenges

Internet is constantly evolving – peering relationships, adding/deleting links Lack of data from ISPs – due to competiveness, protection against attackers Inference via active and passive measurements Lack of comprehensive topology generators Lack of interdisciplinary collaboration

Levels of Topology

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Link layer topology – characterization of the physical connectivity in a network Network layer topology – IP interface: data is collected via traceroute tool – Router: interfaces aggregated via alias resolution

technique – PoP: routers or interfaces aggregated in same geo.

location – AS: provides info about the connectivity of ASes Overlay topology – canonical example - P2P networks – influenced by peer participation and the underlying

protocol

Topology Modeling

Modeling is essential for internet topology generators Mathematical modelling of the characteristics of the

Internet is a key stage for successful generation of realistic topologies.

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Modeling Techniques

Random graph model - simple, easy, not realistic for internet Waxman model - incorporated location information into random graphs Hierarchical model - captures the hierarchical structure of the internet Power law model – most widely used - captures statistical characteristics of the internet: y=axk

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Topology Generators

Topology generators are important for simulations There is no single, comprehensive generator

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Types of Generators

Random graph generators - Graphs are generated by a random process Preferential attachment generators - Rich gets richer, leading to power law effects Geographical generators - Incorporates geographical constraints

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Waxman model

Router level model Nodes placed at random in

2-d space with maximum Euclidean distance L

Probability of edge (u,v): a*e-d/(bL), where d is

Euclidean distance (u,v), a and b are constants

Models locality

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v

u d(u,v)

Transit-stub model

Router level model Transit domains

placed in 2-d space populated with routers connected to each other

Stub domains placed in 2-d space populated with routers connected to transit

domains Models hierarchy

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Generator Examples

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GT-ITM

Produces topologies based on several different models. Flat random graphs N-Level model Transit-Stub model

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BRITE

Router level and AS level Capture the properties

power law relationship network evolution

Key Ideas Preferential connectivity of a new node to existing nodes Incremental growth of the network Connection locality

Input Size of plane (to assign the node) Number of links added per new node Preferential connectivity Incremental growth

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BRITE

Method Step 1: Generate small

backbone, with nodes placed: randomly or concentrated (skewed)

Step 2: Add nodes one at a time (incremental growth)

Step 3: New node has constant # of edges connected using:

preferential connectivity and/or locality

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INET

Router level and AS level model Generate degree sequence

Power Law Distribution

Input Total number of nodes Percentage of degree-one nodes Random seeds

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INET

Method Step 1. Build spanning tree over

nodes with degree larger than 1, using preferential connectivity.

randomly select node u not in tree join u to existing node v with

probability d(v)/d(w) Step 2

Connect degree 1 nodes using preferential connectivity

Step 3 Add remaining edges using

preferential connectivity

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Evaluation Representativeness: The generated topologies must be

accurate, based on the input arguments such as hierarchical structure and degree distribution characteristics.

Flexibility: In the absence of a universally accepted model, the generator should include different methods and models.

Extensibility: The tool should allow the user to extend the generator’s capabilities by adding their own new generation models.

Efficiency: The tool should be efficient for generating large topologies while keeping the required statistical characteristics intact. This can make it possible to test real world scenarios

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Thank You!