scaling properties of the internet graph
DESCRIPTION
Scaling Properties of the Internet Graph. Aditya Akella With Shuchi Chawla, Arvind Kannan and Srinivasan Seshan PODC 2003. Internet Evolution. AS-level graph. AS interconnects: varied capacities. Internet Evolution. Say, network doubles in size. Internet Evolution. - PowerPoint PPT PresentationTRANSCRIPT
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Scaling Properties of the Internet GraphAditya Akella
With Shuchi Chawla, Arvind Kannan and Srinivasan Seshan
PODC 2003
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Internet Evolution
AS interconnects: varied capacities
AS-level graph
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Internet Evolution Say, network
doubles in size
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Internet Evolution
Moore’s-law like scaling sufficient?
If so, good scaling!
Double all capacities?
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Internet Evolution Plain doubling
not enough?
Moore’s-law like scaling insufficient?
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Internet Evolution
Congested hot-spots
If so, poor scaling!!
Plain doubling not enough?
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Key Questions
How does the worst congestion grow? O(n)? O(n2)?
How much of this is due to… Power-law structure?
Other distributions Routing algorithm?
BGP-Policy routing Traffic demand matrix?
What can be done? Redesign the network? Change routing?
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Outline
Analysis Overview
Results from simulation
Discussion of results, network design
Conclusion
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Outline
Analysis OverviewOutline key observations
Results from simulation
Discussion of results, network design
Conclusion
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Analysis
To understand scaling properties of power-law graphs Sanity check the (more realistic) simulation results
Simple evolutionary model Preferential Connectivity
Known to yield power-law graphs Unit traffic between all node-pairs
Routed along the shortest path
How does maximum congestion depend on n, the number of vertices? Congestion on an edge == number of shortest path routes using the
edge
Analysis mainly for intuition; simulation results have the final say.
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Key Observations (I) e* -- edge between the top two degree nodes s1 and s2.
Observation 1: A significant fraction of single-source shortest path trees (n) trees) in the graph contain e*.
S1
S2
e*
S1
S2
e*
e* occurs in both trees
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Key Observations (II)
Observation 2: In at least a constant fraction of the (n) shortest path trees, s1 and s2 retain at least a constant fraction of their degrees.
S1
S2
e*
4/4
4/5S1
S2
e*
5/5
3/4
S1 ,S2 retain most of their degrees
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Key Observations (III)
Observation 3: The degrees of s1 and s2 are (n1/).
And
In each tree that e* belongs to, congestion on
e* min{degtree(s1), degtree(s2)}.
S1
S2
e*
So…
Congestion(e*) 3
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Key Result
Theorem: The expected maximum edge congestion is (n1+1/) (shortest path routing, any-2-any).
(n1.8) or worse for the Internet. Bad Scaling!
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Outline
Analysis Overview
Results from simulation
Discussion of results, network design
Conclusion
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Outline
Analysis Overview
Results from simulationMethodologyA few plots
Discussion of results, network design
Conclusion
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Methodology: Outline
TopologyPower-law
Real AS-level topologies Inet-3.0 generated synthetic
Exponential Inet-3.0 generated; density same as similar-
sized Inet power-law graphs
Tree-like Grown from the preferential connectivity model
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Methodology: Outline
Routing algorithmShortest-pathBGP routing
Policy-based, valley-free Synthetic graphs: heuristically classify edges
before imposing policy routing
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Methodology: Outline
Traffic matrixUniform demands: Any-2-any
Between all pairs
Non-uniform: Clout model Between “leaves” or “stubs” Popularity: average degree of the neighbors Stub identification
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Methodology: Outline
Topology X Routing X Traffic matrix
We seek Max edge congestion as a function of n
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Shortest-Path Routing (Any-2-any)
Exponential >> Power law graphs > Power-law trees
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Policy Routing (Any-2-Any)
Poor scaling just like shortest path, but…
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Policy Routing vs. Shortest PathAny-2-Any
Synthetic Graphs
Real Graphs
Policy routing is never worse!
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The Clout Model
Scaling is even worse
Same true for policy… But policy routing is better again!
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Outline
Analysis overview
Results from simulation
Discussion of results, network design
Conclusion
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Discussion
Scaling according to Moore’s law insufficientCongested hot-spots in the “core”
May have to alter routing or the macroscopic structureRouting: Diffuse demand in a centralized
mannerStructure: Add additional edges to the graph
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Adding Parallel Links
Intuition: Congestion higher on edges with higher avg degree
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Adding Parallel Links
#parallel links is dependant on degrees of nodes at the ends of the edge
Candidate functionsMinimum, Maximum, Sum and Product of
degrees Shortest path routing, any-2-any New edge congestion = edge
congestion/#parallel links
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Parallel Links
Even min yields (n) scaling!Desirable extent of AS-AS peering
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Conclusion
Congestion scales poorly in Internet-like graphs
Policy-routing does not worsen the congestion
Alleviation possible via simple, straight-forward mechanisms