Interdomain Routing as Social Choice

Interdomain Routing as Social ChoiceRonny R. Dakdouk, Semih Salihoglu, Hao Wang, Haiyong Xie, Yang Richard

Yang

Yale University

IBC’06

OutlineMotivationA social choice model for interdomain routingImplications of the modelSummary & future work

MotivationImportance 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 InternetSupport 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 StudiesPolicy 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 MissingEfficiency (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 Protocol

..... .....AS 1 Preference

AS N Preference

AS 1 Route

AS N Route

In this Talk

A social choice model for interdomain routingImplications of the model

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


A Social Choice Model for Interdomain RoutingWhat’s the set of players?

This is easy, the ASes are the playersWhat’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) = P

A routing tree

Realizable Routing TreesNot 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 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’)

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 DomainsAll 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 reachableUniqueness

No oscillations possibleUnanimity(Strong) Pareto optimality

Efficient routing decisionNon-dictatorship

Retain AS autonomy

Protocol as ImplementationNo central authority for interdomain routing

ASes execute routing protocolsProtocol 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


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

Assumption 1: ASes follow the greedy BGP route selection strategyAssumption 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 BGPNon-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 BGPBGP 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

SummaryViewed as a black-box, interdomain routing is an SCR + implementationStrategic implementation impose stringent constraints on SCRsThe 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 DomainsPreference 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 ImplementationThe 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 ImplementationImplementation: 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 ImplementationGiven 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 ImplementationThe predicted outcome(s)

OS(M,g,R) = { a A | m S(M,g,R), s.t. g(m) = a }Implementation: predicted outcomes satisfy 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 LiteratureOn 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)

Documents

Interdomain Routing as Social Choice