Download Topology generators

Topology Generation
Suat Mercan
Outline
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Motivation
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Topology Characterization
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Levels of Topology
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Modeling Techniques
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Types of Topology Generators
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Motivation for Internet Topology
Research
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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
Topological Characteristics of
Internet
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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
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Average degree
Degree distribution
Clustering
Coreness
Shortest path distance
Betweenness
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Topology Research Challenges
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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
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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
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Topology Modeling
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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
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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
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Topology generators are important for simulations
There is no single, comprehensive generator
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Types of Generators
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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
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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
u
d(u,v)
v
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Transit-stub model
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Router level model
Transit domains
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Stub domains
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placed in 2-d space
populated with routers
connected to each other
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
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Produces topologies based on several different models.
Flat random graphs
N-Level model
Transit-Stub model
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BRITE
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Router level and AS level
Capture the properties
power law relationship
 network evolution
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Key Ideas
Preferential connectivity of a new node to existing nodes
 Incremental growth of the network
 Connection locality
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Input
Size of plane (to assign the node)
 Number of links added per new node
 Preferential connectivity
 Incremental growth
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BRITE
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Method
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Step 1: Generate small
backbone, with nodes placed:
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randomly or
concentrated (skewed)
Step 2: Add nodes one at a
time (incremental growth)
Step 3: New node has constant
# of edges connected using:
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preferential connectivity and/or
locality
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INET
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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
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Method
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Step 1. Build spanning tree over
nodes with degree larger than 1,
using preferential connectivity.
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Step 2
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randomly select node u not in
tree
join u to existing node v with
probability d(v)/d(w)
Connect degree 1 nodes using
preferential connectivity
Step 3
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Add remaining edges using
preferential connectivity
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Evaluation
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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!
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