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

Motivation

A social choice model for interdomain routing

Implications of the model

Summary & future work

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.

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

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

2

0

31

2 1 02 0

1 3 01 0

3 2 03 0

4

3

Policy interaction causes routing instability !

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

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

An interdomain routing system defines a mapping (a social choice rule)

A protocol implements this mappingSocial choice rule + Implementation

Interdomain Routing P

rotocol

..... .....

AS 1 Preference

AS N Preference

AS 1 Route

AS N Route

In this Talk


Implications of the model Some results from literature A case study of BGP from the social choice

perspective

Outline

Motivation




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)

Each AS i = 1, 2, 3 has a route to the destination (AS 0)T(i) = AS i’s route to AS 0Consistency requirement:

If T(i) = (i, j) P, then T(j) = PA routing tree

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

Why does this work? Example: The preference of AS i depends o

n its own egress route only, say, r1 > r2 The equivalent preference: AS i is indiffere

nt to all outcomes in which it has the same egress route

E.g: If T1(i) = r1, T2(i) = r2, T3(i) = r2, thenT1 >i T2 =i T3

Local Routing Policies as Preference Relations (cont’)

Not just a match of theoryCan 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

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’)

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)

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

Some Desirable Properties of Interdomain Routing SCRNon-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

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 im

plementation of an interdomain SCR

Outline

Motivation




Some Results from Literature

On the unrestricted domain No non-empty SCR that is non-dictatorial, stra

tegy-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 Na

sh-implementable No strong-Pareto optimal and non-empty SCR

that is Nash-implementable

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

BGP

..... .....

AS 1 Preference

AS N Preference

Routing Tree

Reverse engineering BGP

Non-emptiness: XUniqueness: XUnanimity: Strong Pareto Optimality: only on

strict route preference domainNon-dictatorship: X

BGP in strategic settings

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

BGP is (theoretically) Nash implementable (actually, also strong implementable)

But, only in a very simple game formThe problem: the simple game form may

not be followed by the ASes

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?

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?

Thank you!

Backup Slides

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 relationPreference profile R = (R1,…,RN)

R completely specifies the “world state”

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)

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

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 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 o

utcome based on action/message profile (e.g, majority wins)

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 Implementation

The predicted outcome(s)OS(M,g,R) = { a A | m S(M,g,R), s.t. g(m) = a

}Implementation: predicted outcomes sat

isfy criteriaOS(M,g,R) = F(R), for all R P

Protocol as Implementation - Feasibility

Dominant Strategy implementationGibbard’s non-dominance theorem:

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

Some Results from Literature

On the unrestricted route preference domain) “Almost no” non-empty and strong Pareto opti

mal 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)

interdomain routing as social choice

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