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
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
Outline
Motivation
A social choice model for interdomain routing
Implications of the model
Summary & future work
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
A social choice model for interdomain routing
Implications of the model
Summary & future work
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)
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