Interdomain Routing as Social Choice

1
Interdomain Routing as Social Choice

• Ronny R. Dakdouk, Semih Salihoglu, Hao
  Wang, Haiyong Xie, Yang Richard Yang
• Yale University
• IBC06

2
Outline

• Motivation
• A social choice model for interdomain routing
• Implications of the model
• Summary future work

3
Motivation

• Importance of Interdomain Routing
• Stability
• excessive churn can cause router crash
• Efficiency
• routes influence latency, loss rate, network
  congestion, etc.
• Why policy-based routing?
• Domain autonomy Autonomous System (AS)
• Traffic engineering objectives latency, cost,
  etc.

4
BGP

• The de facto interdomain routing protocol of the
  current Internet
• Support policy-based, path-vector routing
• Path propagated from destination
• Import export policy
• BGP decision process selects path to use
• Local preference value
• AS path length
• and so on

5
Policy Interactions Could Lead to Oscillations

• The BAD GADGET example
• - 0 is the destination
• - the route selection policy of each AS is to
  prefer its counter clock-wise neighbor

Policy interaction causes routing instability !
6
Previous Studies

• Policy Disputes (Dispute Wheels) may cause
  instability Griffien et al. 99
• Economic/Business considerations may lead to
  stability Gao Rexford 00
• Design incentive-compatible mechanisms
  Feigenbaum et al. 02
• Interdomain Routing for Traffic Engineering Wang
  et al. 05

7
Whats Missing

• Efficiency (Pareto optimality)
• Previous studies focus on BGP-like protocols
• Increasing concern about extension of BGP or
  replacement (next-generation protocol)
• Need a systematic methodology
• Identify desired properties
• Feasibility Implementation
• Implementation in strategic settings
• Autonomous System may execute the protocol
  strategically so long as the strategic actions do
  not violate the protocol specification!

8
Our approach - A Black Box View of Interdomain
Routing

• An interdomain routing system defines a mapping
  (a social choice rule)
• A protocol implements this mapping
• Social choice rule Implementation

AS 1 Preference
Interdomain Routing Protocol
AS 1 Route
.....
.....
AS N Preference
AS N Route
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In this Talk

• A social choice model for interdomain routing
• Implications of the model
• Some results from literature
• A case study of BGP from the social choice
  perspective

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Outline

• Motivation
• A social choice model for interdomain routing
• Implications of the model
• Summary future work

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A Social Choice Model for Interdomain Routing

• Whats the set of players?
• This is easy, the ASes are the players
• Whats the set common of outcomes?
• Difficulty
• AS cares about its own egress route, possibly
  some others routes, but not most others routes
• The theory requires a common set of outcomes
• Solution
• Use routing trees or sink trees as the unifying
  set of outcomes

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Routing Trees (Sink Trees)

• Each AS i 1, 2, 3 has a route to the
  destination (AS 0)
• T(i) AS is route to AS 0
• Consistency requirement
• If T(i) (i, j) P, then T(j) P

A routing tree
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Realizable Routing Trees

• Not all topologically consistent routing trees
  are realizable
• Import/Export policies
• The common set of outcomes is the set of
  realizable routing trees

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Local Routing Policies as Preference Relations

• Why does this work?
• Example The preference of AS i depends on its
  own egress route only, say, r1 gt r2
• The equivalent preference AS i is indifferent to
  all outcomes in which it has the same egress
  route
• E.g If T1(i) r1, T2(i) r2, T3(i) r2, then
• T1 gti T2 i T3

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Local Routing Policies as Preference Relations
(cont)

• Not just a match of theory
• Can express more general local policies
• Policies that depend not only on egress routes of
  the AS itself, but also incoming traffic patterns
• AS 1 prefers its customer 3 to send traffic
  through it, so T1 gt1 T2

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Preference Domains

• All possible combinations of preferences of
  individual ASes
• Traditional preference domains
• Unrestricted domain
• Unrestricted domain of strict preferences
• Two special domains in interdomain routing
• The domain of unrestricted route preference
• The domain of strict route preference

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Preference Domains (cont)

• The domain of unrestricted route preference
• Requires If T1(i) T2(i), then T1 i T2
• Intuition An AS cares only about egress routes
• The domain of strict route preference
• Requires If T1(i) T2(i), then T1 i T2
• Also requires if T1(i) ? T2(i) then T1 ?i T2
• Intuition An AS further strictly differentiates
  between different routes

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Interdomain Social Choice Rule (SCR)

• An interdomain SCR is a correspondence
• F R(R1,...,RN) ? P ? F(R) ? A
• F incorporates the criteria of which routing
  tree(s) are deemed optimal F(R)

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An example
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Some Desirable Properties of Interdomain Routing
SCR

• Non-emptiness
• All destinations are always reachable
• Uniqueness
• No oscillations possible
• Unanimity
• (Strong) Pareto optimality
• Efficient routing decision
• Non-dictatorship
• Retain AS autonomy

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Protocol as Implementation

• No central authority for interdomain routing
• ASes execute routing protocols
• Protocol specifies syntax and semantics of
  messages
• May also specify some actions that should be
  taken for some events
• Still leaves room for policy-specific actions lt-
  strategic behavior here!
• Therefore, a protocol can be modeled as
  implementation of an interdomain SCR

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Outline

• Motivation
• A social choice model for interdomain routing
• Implications of the model
• Summary future work

23
Some Results from Literature

• On the unrestricted domain
• No non-empty SCR that is non-dictatorial,
  strategy-proof, and has at least three possible
  routing trees at outcomes Gibbards
  non-dominance theorem
• On the unrestricted route preference domain
• No non-constant, single-valued SCR that is
  Nash-implementable
• No strong-Pareto optimal and non-empty SCR that
  is Nash-implementable

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A Case Study of BGP

• Assumption 1 ASes follow the greedy BGP route
  selection strategy
• Assumption 2 if T1(i) T2(i) then either T1(i)
  or T2(i) can be chosen

AS 1 Preference
Routing Tree
BGP
.....
.....
AS N Preference
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Reverse engineering BGP

• Non-emptiness X
• Uniqueness X
• Unanimity ?
• Strong Pareto Optimality ? only on strict route
  preference domain
• Non-dictatorship X

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BGP in strategic settings
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BGP is manipulable!

• If AS 1 and 3 follow the default BGP strategy,
  then AS 2 has a better strategy
• If (3,0) is available, selects (2, 3, 0)
• Otherwise, if (1, 0) is available, selects (2, 1,
  0)
• Otherwise, selects (2, 0)
• The idea AS 2 does not easily give AS 3 the
  chance of exploiting itself!
• Comparison of strategies for AS 2 (AS 1, 3 follow
  default BGP strategy)
• Greedy strategy depend on timing, either (2, 1,
  0) or (2, 3, 0)
• The strategy above always (2, 3, 0)

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Possibility of fixing BGP

• BGP is (theoretically) Nash implementable
  (actually, also strong implementable)
• But, only in a very simple game form
• The problem the simple game form may not be
  followed by the ASes

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Summary

• Viewed as a black-box, interdomain routing is an
  SCR implementation
• Strategic implementation impose stringent
  constraints on SCRs
• The greedy BGP strategy has its merit, but is
  manipulable

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Whats next?

• Design of next-generation protocol (the goal!)
• Stability, optimality, incentive-compatible
• Scalability
• Scalability may serve as an aide (complexity may
  limit viable manipulation of the protocol)
• What is a reasonable preference domain to
  consider?
• A specialized theory of social choice
  implementation for routing?

31

• Thank you!

32

• Backup Slides

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Social Choice Rules (SCR)

• A set of players V 1,...,N
• A set of outcomes ? T1,,TM
• Player i has its preference Ri over ?
• a complete, transitive binary relation
• Preference profile R (R1,,RN)
• R completely specifies the world state

34
Preference Domains

• Preference domain P a non-empty set of
  potential preference profiles
• Why a domain? The preference profile that will
  show up is not known in advance
• Some example domains
• Unrestricted domain
• Unrestricted domain of strict preferences

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Social Choice Rule (SCR)

• An SCR is a correspondence
• F R(R1,...,RN) ? P ? F(R) ? A
• F incorporates the criteria of which outcomes are
  deemed optimal F(R)
• Some example criteria
• Pareto Optimal (weak/strong/indifference)
• (Non-)Dictatorship
• Unanimity

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SCR Implementation

• The designer of a SCR has his/her criteria of
  what outcomes should emerge given players
  preferences
• But, the designer does not know R
• Question What can the designer do to ensure his
  criteria get satisfied?

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SCR Implementation

• Implementation rules to elicit designers
  desired outcome(s)
• Game Form (M,g)
• M Available action/message for players (e.g,
  cast ballots)
• g Rules (outcome function) to decide the outcome
  based on action/message profile (e.g, majority
  wins)

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SCR Implementation

• Given the rules, players will evaluate their
  strategies (e.g, vote ones second favorite may
  be better, if the first is sure to lose)
• Solution Concepts predict players strategic
  behaviors
• Given (M,g,R), prediction is that players will
  play action profiles S ? A

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SCR Implementation

• The predicted outcome(s)
• OS(M,g,R) a ? A ? m ? S(M,g,R), s.t. g(m)
  a
• Implementation predicted outcomes satisfy
  criteria
• OS(M,g,R) F(R), for all R ? P

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Protocol as Implementation - Feasibility

• Dominant Strategy implementation
• Gibbards non-dominance theorem
• No dominant strategy implementation of
  non-dictatorial SCR w/ gt 3 possible outcomes on
  unrestricted domain

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Some Results from Literature

• On the unrestricted route preference domain)
• Almost no non-empty and strong Pareto optimal
  SCR can be Nash implementable
• If we want a unique routing solution (social
  choice function, SCF), then only constant SCF can
  be Nash implementable
• 2nd result does not hold on a special domain
  which may be of interest in routing context
  (counter-example, dictatorship)