Topology Generation

1. Topology Generation Suat Mercan

2. Outline • Motivation • Topology Characterization • Levels of Topology • Modeling Techniques • Types of Topology Generators

3. 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

4. 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

5. Topology Characterization • Average degree • Degree distribution • Clustering • Coreness • Shortest path distance • Betweenness

6. 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

7. Levels of Topology 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

8. 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.

9. 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

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

11. 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

12. Waxman model u d(u,v) v • 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

13. 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

14. Generator Examples

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

16. 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

17. 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

18. 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

19. 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

20. 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

21. Thank You!