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 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 Interdomain Routing Protocol..... 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 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=(R 1,...,R N )  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 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 BGP..... AS 1 Preference AS N Preference Routing Tree

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 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?

Thank you!

Backup Slides

Social Choice Rules (SCR) A set of players V = { 1,...,N } A set of outcomes  = { T 1, …,T M } Player i has its preference R i over   a complete, transitive binary relation Preference profile R = (R 1, …,R N )  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=(R 1,...,R N )  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) O S (M,g,R) = { a  A |  m  S(M,g,R), s.t. g(m) = a } Implementation: predicted outcomes satisfy criteria O S (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  2 nd result does not hold on a special domain which may be of interest in routing context (counter- example, dictatorship)