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Searching for Stability in Interdomain Routing. Rahul Sami (University of Michigan) Michael Schapira (Yale/UC Berkeley) Aviv Zohar (Hebrew University). Border Gateway Protocol (BGP). Akamai. Yahoo!. AT&T. Comcast. Path-vector routing Routing between Autonomous Systems

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searching for stability in interdomain routing

Searching for Stability in Interdomain Routing

Rahul Sami (University of Michigan)

Michael Schapira (Yale/UC Berkeley)

Aviv Zohar (Hebrew University)

border gateway protocol bgp
Border Gateway Protocol (BGP)

Akamai

Yahoo!

AT&T

Comcast

  • Path-vector routing
  • Routing between Autonomous Systems
    • ASes can apply routing policies
convergence oscillation
Convergence/Oscillation

Uncoordinated policies can lead to persistent global route oscillations

  • [Varadhan, Govindan, Estrin]
  • [Griffin, Wilfong], [Griffin, Shepherd, Wilfong]
    • Several sufficient conditions for stable convergence [GR01, GGR01,GJR03,FJB05,..]
    • open question: can a network have two stable solutions, but no oscillation?
our results
Our Results

Two stable solutions imply potential BGP oscillations

our results1
Our Results
  • Two stable solutions imply potential BGP oscillations
  • If preferences satisfy Gao-Rexford constraints
    • Convergence of n AS network could require Ω(n) timein the wost case
    • with α-level hierarchy, BGP converges after at most 2α+2 “phases”
bgp model routes and preferences
BGP model: Routes and Preferences

route

dest

Prefer AS27

Prefer shorter

AS1

AS3;AS1

AS1

AS27;AS3;AS1

AS1

AS8; AS4;AS1

AS2

AS4;AS2

  • Atomic AS/ representative router
  • Router state:
    • Available routes to each destination
    • Route preference rules
    • Currently selected route
  • Abstract away export filters, MEDs, etc.
bgp model dynamics
BGP model: Dynamics

(for any one destination)

j

  • Each AS i actions:
    • select best route from available routes
    • advertise current route to neighbor j
  • Evolution governed by sequence of action events
  • Arbitrary (adversarial) timing, with two restrictions:
    • Fair sequence (no starvation)
    • Messages not delayed in transit (though may be dropped/lost)

i

k

state transition graphs
State-Transition Graphs

*

State: profile of all routers’ current routes and beliefs about their available routes

Transition: change following route selection or advertisement

state transition graphs1
State-Transition Graphs

*

* Zero state

State: profile of all routers’ current routes and beliefs about their available routes

Transition: change following route selection or advertisement

state transition graphs2
State-Transition Graphs

*

* Zero state

Stable state(s)

State: profile of all routers’ current routes and beliefs about their available routes

Transition: change following route selection or advertisement

main proof sketch regions
Main Proof sketch: Regions

*

  • Stable states: blue, red, …
  • Nonstable states:
    • blue if all paths lead to blue stable state
    • red if all paths lead to red stable state
    • purple otherwise
proof sketch confluence
Proof Sketch: Confluence

p

a

b

b

a

?

a,b : different actions

a

  • Key lemma: from any purple state p, there is a (fair) path to another purple state
  • Proof:
    • If all paths to red states, p would be red
    • cannot have paths to both blue and red state:
    • => must have path to some purple state p’
main result summary
Main result: Summary

If there are 2 or more stable states, zero state is purple

From every purple state, fair path to another purple state

Finite number of states=> must cycle sometime

=> BGP can oscillate on this instance!

convergence time
Convergence Time
  • Gao-Rexford conditions
    • Assume: longest cust-prov chain length is α
  • Asynchronous model
    • “Phase”: each router triggered at least once
  • Result: reach stable solution in at most 2α+2 phases
discussion future work
Discussion & Future Work

Main result applies to [GSW] and other models

Average case instead of worst-case?

Compositional theory for safe policies?

slide16

Thank you

Questions?

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