Searching for stability in interdomain routing
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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

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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?


Searching for stability in interdomain routing

Thank you

Questions?


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