Topology Modeling via Cluster Graphs

Balachander Krishnamurthy and Jia Wang

AT&T Labs Research

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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

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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!

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Router graphs

Construction Traceroute-like probing Interface collapsing algorithms

Proc and cons Very fine-grained Expensive

Router graphs are too fine-grained!

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Network-aware clusters

Obtain BGP tables from many places via a script and unify them into on big prefix tableExtract IP addresses from logsPerform longest prefix matching on each IP addressClassify all the IP addresses that have the same longest matched prefix into a cluster (identified by the shared prefix)

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Cluster graphs

Intermediate-level of granularityUndirected graph Node: cluster of routers and hosts Edge: inter-cluster connection

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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

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Super-clusteringGroup clusters into super-clusters based on their originating ASBGP tables: May 2001Web 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

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Busy clusters in super-cluster

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!

AS 1221

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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%

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Cluster path

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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.

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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.

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Comparison of three models

Model AS graph

Cluster graph

Router graph

Granularity Coarse Intermediate

Fine

Construction

Stableness Accuracy

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Conclusion

Examine Internet topology models Cluster graphCompare three modelsCluster 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.