Interdomain routing as social choice
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Interdomain Routing as Social Choice. Ronny R. Dakdouk, Semih Salihoglu, Hao Wang, Haiyong Xie, Yang Richard Yang Yale University IBC ’ 06. Outline. Motivation A social choice model for interdomain routing Implications of the model Summary & future work. Motivation.

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Interdomain Routing as Social Choice

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Interdomain routing as social choice

Interdomain Routing as Social Choice

Ronny R. Dakdouk, Semih Salihoglu, Hao Wang, Haiyong Xie, Yang Richard Yang

Yale University

IBC’06


Outline

Outline

  • Motivation

    A social choice model for interdomain routing

  • Implications of the model

  • Summary & future work


Motivation

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.


Interdomain routing as social choice

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…


Policy interactions could lead to oscillations

2 1 0

2 0

2

4

0

3 2 0

3 0

1 3 0

1 0

3

3

1

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 !


Previous studies

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]


What s missing

What’s 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!


Our approach a black box view of interdomain routing

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


In this talk

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


Outline1

Outline

  • Motivation

    A social choice model for interdomain routing

  • Implications of the model

  • Summary & future work


A social choice model for interdomain routing

A Social Choice Model for Interdomain Routing

  • What’s the set of players?

    • This is easy, the ASes are the players

  • What’s 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


Routing trees sink trees

Routing Trees (Sink Trees)

  • Each AS i = 1, 2, 3 has a route to the destination (AS 0)

  • T(i) = AS i’s route to AS 0

  • Consistency requirement:

  • If T(i) = (i, j) P, then T(j) = P

A routing tree


Realizable routing trees

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


Local routing policies as preference relations

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 > 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 >i T2 =i T3


Local routing policies as preference relations cont

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 >1 T2


Preference domains

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


Preference domains cont

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


Interdomain social choice rule scr

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)


An example

An example


Some desirable properties of interdomain routing scr

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


Protocol as implementation

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 <- strategic behavior here!

  • Therefore, a protocol can be modeled as implementation of an interdomain SCR


Outline2

Outline

  • Motivation

    A social choice model for interdomain routing

  • Implications of the model

  • Summary & future work


Some results from literature

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 [Gibbard’s 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


A case study of bgp

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


Reverse engineering bgp

Reverse engineering BGP

  • Non-emptiness: X

  • Uniqueness: X

  • Unanimity: 

  • Strong Pareto Optimality:  only on strict route preference domain

  • Non-dictatorship: X


Bgp in strategic settings

BGP in strategic settings


Bgp is manipulable

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)


Possibility of fixing bgp

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


Summary

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


What s next

What’s 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?


Interdomain routing as social choice

  • Thank you!


Interdomain routing as social choice

  • Backup Slides


Social choice rules scr

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”


Preference domains1

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


Social choice rule scr

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


Scr implementation

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?


Scr implementation1

SCR Implementation

  • Implementation: rules to elicit designer’s 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)


Scr implementation2

SCR Implementation

  • Given the rules, players will evaluate their strategies (e.g, vote one’s 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


Scr implementation3

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


Protocol as implementation feasibility

Protocol as Implementation - Feasibility

  • Dominant Strategy implementation

  • Gibbard’s non-dominance theorem:

  • No dominant strategy implementation of non-dictatorial SCR w/ >= 3 possible outcomes on unrestricted domain


Some results from literature1

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)


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