On The Marginal Utility of Network Topology Measurements

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On The Marginal Utility of Network Topology
Measurements

• John Byers
• with
• Paul Barford (now at Wisconsin),
• Azer Bestavros, and Mark Crovella

2
Measurement Philosophy

• Current Dogma When conducting a wide-area
  measurement study more is better.
• More measurements
• More measurement sites
• True, but taking more measurements and deploying
  more infrastructure is expensive!
• Our focus How much better is more?
• Even harder When can we stop measuring?
• Not much work on this topic in our community.

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Problem InstanceDiscovering Internet Topology

• Typical goal discover the router-level Internet
  graph
• Typical approach merge lists of known nodes and
  edges
• Traceroute reports the IP path from A to B
• i.e., how IP paths are overlaid on the router
  graph

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Traceroute studies

• Yield overlays of projections from Ss to Ds
• Sources active, expensive
• Destinations passive, cheap

D
D
D
D
D
S
S
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Motivating Questions

• How should we use traceroute and what can it
  discover?
• Physical topology (nodes, links)?
• IP routing topology?
• Whats a good way to organize a
  collection-of-traceroutes study?
• Many sources?
• Many destinations?
• How much is enough?

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Theoretical Inroads

• Take a graph G (V, E) and a routing algorithm
  R.
• Choose j sources and k destinations at random.
• Consider the subgraph G (V, E) induced by
  routes from R between all (S, D) pairs.
• How do expected values of V and E scale as
  a function of j and k ?
• Chuang-Sirbu scaling law is special case for j
  1.
• Marginal utility of adding k1 st source or
  destination is expected contribution to V or
  E.

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What might we expect?

• Two extremal cases
• Clique each new (S, D) discovers a new path
• Star each new S or D discovers only a small
  neighborhood

D
D
D
D
D
D
D
D
D
D
Clique
Star
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Skitter to the Rescue

• Two datasets from CAIDA
• Small dataset May 2000
• 8 sources, 1277 destinations, 20K paths
• Sources in New Zealand, Japan, Singapore, San
  Jose (2), Ottawa, London, Washington
• All sources traced to all destinations
• Large dataset October 2000, 30 times bigger
• 12 sources, 313709 destinations, 600K paths
• No destination common to all sources, or vice
  versa

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Interface Disambiguation

• Traceroutes report only on interfaces used
• Routers often have multiple interfaces
• But merging traceroutes requires matching routers
• Solution probe each interface from some site X
• Routers are supposed to respond on the interface
  used for routing to X
• Results in set of (probe interface, response
  interface) pairs
• Each connected component is taken to be a router

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Classifying Nodes

• Core, border, stub, leaf
• Solely from traceroute information

Leaf
Border
Core
Stub
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Classification depends on msmts
Core
Stub
Border
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Limitations and Caveats

• Interface disambiguation
• 13 of interfaces never responded
• Node classification
• Identifying a border node requires two paths to
  it
• Representativeness
• Datasets are small, may not be representative
• Skitter sources not selected at random
• Unknown coverage of true network
• Diminishing returns may not signify good coverage

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Diminishing Returns (Small Dataset)
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Diminishing Returns (Large Dataset)
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Diminishing returns by Classification (Small
Dataset)
Core
Stub
Border
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What Does This Suggest?
D
D
S
D
D
S
D
D
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Adding Destinations Nodes
Slope is about 3
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Adding Destinations Links
Slope is about 4
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Add Sources or Destinations?
Isolines represent constant node discovery,
varying Ss or Ds
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Node Degree Distribution
1 Source
8 Sources
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Node Degree Distribution Tail
8 Sources
1 Source
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Degree distribution convergence RMSE
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Information Theory Plug

• Can compare marginal utility of different
  processes.

Link Discovery
Node Discovery
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Related Work

• Pansiot Grad 98
• First multi-traceroute study
• Similar methodology, incl. interface
  disambiguation
• Chuang Sirbu 98Phillips, Shenker
  Tangmunarunkit 99
• single-source case, found sublinear growth of
  multicast tree with added destinations
• Govindan Tangmunarunkit 00
• Extensive node discovery, overcoming limitations
  of traceroute
• Broido Claffy 01
• Larger datasets more detailed look at graph
  structure

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Conclusions

• Rigorous quantification of marginal utility of
  additional measurements.
• To discover all physical nodes, traceroute is
  inefficient
• Diminishing returns many Ss and Ds needed
• Trading off Ss and Ds
• Adding destinations seems more cost-effective
• To discover how typical routes pass through
  network, traceroute is informative
• Routing core and feeders
• Much of routing core is visible from few Ss
  (given enough Ds)