Topology Modeling via Cluster Graphs Balachander Krishnamurthy and

Topology Modeling via Cluster Graphs Balachander Krishnamurthy and Jia Wang AT&T Labs Research 11/1/2001 Topology Modeling via Cluster Graphs

Internet Topology graphs Understand Internet topology Traffic patterns n Protocol design n Performance evaluation n Two levels of granularity Inter-domain level – AS graphs n Router level – router graphs n 11/1/2001 Topology Modeling via Cluster Graphs 2

AS graphs Construction: n n n AS-Path-based: BGP routing tables or update messages Traceroute-based Synthetic: power laws Pros and cons n n Coarse-grained Easy to generate Incomplete Connectivity reachability AS graphs are too coarse-grained! 11/1/2001 Topology Modeling via Cluster Graphs 3

Router graphs Construction Traceroute-like probing n Interface collapsing algorithms n Proc and cons Very fine-grained n Expensive n Router graphs are too fine-grained! 11/1/2001 Topology Modeling via Cluster Graphs 4

Network-aware clusters Obtain BGP tables from many places via a script and unify them into on big prefix table Extract IP addresses from logs Perform longest prefix matching on each IP address Classify all the IP addresses that have the same longest matched prefix into a cluster (identified by the shared prefix) 11/1/2001 Topology Modeling via Cluster Graphs 5

Cluster graphs Intermediate-level of granularity Undirected graph Node: cluster of routers and hosts n Edge: inter-cluster connection n 11/1/2001 Topology Modeling via Cluster Graphs 6

Cluster graphs Construction n Hierarchical graphs Traceroute-based graphs Synthetic graphs 11/1/2001 • Based Extendon Traceroute ASsome graph to sampled observed by IPs modeling in characteristics, interesting the clusters size/weight e. g. , power of • AS laws Construct a cluster path • Use for each cluster-AS sampledmapping IP • extracted Merge cluster from paths BGP tables into a cluster graph Topology Modeling via Cluster Graphs 7

Super-clustering Group clusters into super-clusters based on their originating AS BGP tables: May 2001 Web log: a large portal site in March 2001 n # # # n # of super-clusters with size >1: 436 n Avg size of super-clusters: 2. 4 n n 11/1/2001 of of of requests: 104 M unique IPs: 7. 6 M clusters: 15, 789 busy clusters (70% of the total): 3, 000 super-clusters: 1, 250 Topology Modeling via Cluster Graphs 8

Busy clusters in super-cluster AS 1221 Cluster prefix Common name suffix 139. 130. 0. 0/16 wnise. com 139. 134. 0. 0/16 tmns. net. au 192. 148. 160. 0/24 telstra. com. au 203. 32. 0. 0/14 ocs. com. au 203. 36. 0. 0/16 tricksoft. com. au 203. 38. 0. 0/16 panorama. net. au 203. 0. 0. 0/10 geelong. netlink. com. au 203. 0. 0. 0/12 iaccess. com. au ASes are too coarse-grained! 11/1/2001 Topology Modeling via Cluster Graphs 9

Cluster graph Top 99 busy clusters # unique IPs: 1. 2 M n Sample 99 IPs (1 from each cluster) n Traceroute to 99 sampled IPs Ignore probes returning ‘*’: 17% n Ignore unreachable probes(!N, !H, !P, !X): 0. 3% n 11/1/2001 Topology Modeling via Cluster Graphs 10

Cluster path 11/1/2001 Topology Modeling via Cluster Graphs 11

Cluster graph vs AS graph Observations Cluster graph has 34% more nodes and 15% more edges than AS graph. n The average node degree in cluster graph is 15% less than that in AS graph. n Correlation between cluster hop counts and end-to-end hop counts is stronger than that of AS hop counts. n 11/1/2001 Topology Modeling via Cluster Graphs 12

Cluster graph vs router graph Observations Constructing cluster graph needs much less traceroutes than router graph (99 vs thousands). n More traceroutes show that cluster graph is more stable than router graph. n 11/1/2001 Topology Modeling via Cluster Graphs 13

Comparison of three models Model Granularity AS graph Cluster graph Router graph Coarse Intermediate Fine Construction Stableness Accuracy 11/1/2001 Topology Modeling via Cluster Graphs 14

Conclusion Examine Internet topology models Cluster graph Compare three models Cluster graphs are less complicated and more stable than router graphs. Cluster graph can be obtained as easy as AS graphs while providing more fine-grained information that capture the Internet topology. 11/1/2001 Topology Modeling via Cluster Graphs 15