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

2. 11/1/2001Topology Modeling via Cluster Graphs2 Internet Topology graphs Understand Internet topology Traffic patterns Protocol design Performance evaluation Two levels of granularity Inter-domain level – AS graphs Router level – router graphs

3. 11/1/2001Topology Modeling via Cluster Graphs3 AS graphs Construction: AS-Path-based: BGP routing tables or update messages Traceroute-based Synthetic: power laws Pros and cons Coarse-grained Easy to generate Incomplete Connectivity reachability AS graphs are too coarse-grained!

4. 11/1/2001Topology Modeling via Cluster Graphs4 Router graphs Construction Traceroute-like probing Interface collapsing algorithms Proc and cons Very fine-grained Expensive Router graphs are too fine-grained!

5. 11/1/2001Topology Modeling via Cluster Graphs5 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)

6. 11/1/2001Topology Modeling via Cluster Graphs6 Cluster graphs Intermediate-level of granularity Undirected graph Node: cluster of routers and hosts Edge: inter-cluster connection

7. 11/1/2001Topology Modeling via Cluster Graphs7 Cluster graphs Construction Hierarchical graphs Traceroute-based graphs Synthetic graphs Extend AS graph by modeling the size/weight of AS Use cluster-AS mapping extracted from BGP tables Traceroute to sampled IPs in interesting clusters Construct a cluster path for each sampled IP Merge cluster paths into a cluster graph Based on some observed characteristics, e.g., power laws

8. 11/1/2001Topology Modeling via Cluster Graphs8 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 # of requests: 104M # of unique IPs: 7.6M # of clusters: 15,789 # of busy clusters (70% of the total): 3,000 # of super-clusters: 1,250 # of super-clusters with size >1: 436 Avg size of super-clusters: 2.4

9. 11/1/2001Topology Modeling via Cluster Graphs9 Busy clusters in super-cluster Cluster prefixCommon name suffix 139.130.0.0/16wnise.com 139.134.0.0/16tmns.net.au 192.148.160.0/24telstra.com.au 203.32.0.0/14ocs.com.au 203.36.0.0/16tricksoft.com.au 203.38.0.0/16panorama.net.au 203.0.0.0/10geelong.netlink.com.au 203.0.0.0/12iaccess.com.au ASes are too coarse-grained! AS 1221

10. 11/1/2001Topology Modeling via Cluster Graphs10 Cluster graph Top 99 busy clusters # unique IPs: 1.2M Sample 99 IPs (1 from each cluster) Traceroute to 99 sampled IPs Ignore probes returning *: 17% Ignore unreachable probes(!N, !H, !P, !X): 0.3%

11. 11/1/2001Topology Modeling via Cluster Graphs11 Cluster path

12. 11/1/2001Topology Modeling via Cluster Graphs12 Cluster graph vs AS graph Observations Cluster graph has 34% more nodes and 15% more edges than AS graph. The average node degree in cluster graph is 15% less than that in AS graph. Correlation between cluster hop counts and end-to-end hop counts is stronger than that of AS hop counts.

13. 11/1/2001Topology Modeling via Cluster Graphs13 Cluster graph vs router graph Observations Constructing cluster graph needs much less traceroutes than router graph (99 vs thousands). More traceroutes show that cluster graph is more stable than router graph.

14. 11/1/2001Topology Modeling via Cluster Graphs14 Comparison of three models ModelAS graphCluster graphRouter graph GranularityCoarseIntermediateFine Construction Stableness Accuracy

15. 11/1/2001Topology Modeling via Cluster Graphs15 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.