1. Topology Generation Suat Mercan

2. 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. 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. 5 Topology Characterization Average degree Degree distribution Clustering Coreness Shortest path distance Betweenness

6. 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 7 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. 8

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 9

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

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 11

12. 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 12 v u d(u,v)

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 13

14. 14 Generator Examples

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

16. 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. 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. 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. 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. 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. 21 Thank You!