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## 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

- 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…

2 0

2

4

0

3 2 0

3 0

1 3 0

1 0

3

3

1

Policy Interactions Could Lead to OscillationsThe 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

- 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 mapping
- Social choice rule + Implementation

AS 1 Preference

Interdomain Routing Protocol

AS 1 Route

.....

.....

AS N Preference

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 0
- Consistency requirement:
- If T(i) = (i, j) P, then T(j) = P

A 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 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 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

- 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)

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

- 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

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, 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 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

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

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 form
- The 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?

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 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 outcome 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 satisfy criteria
- OS(M,g,R) = F(R), for all R P

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 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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