Interdomain Routing as Social Choice

1. Interdomain Routing as Social Choice Ronny R. Dakdouk, Semih Salihoglu, Hao Wang, Haiyong Xie, Yang Richard Yang Yale University IBC’06

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

3. 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.

4. 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…

5. 2 1 0 2 0 2 4 0 3 2 0 3 0 1 3 0 1 0 3 3 1 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 !

6. 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]

7. 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!

8. 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

9. 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

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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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)

19. An example

20. 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

21. 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

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

23. 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

24. 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

25. Reverse engineering BGP • Non-emptiness: X • Uniqueness: X • Unanimity:  • Strong Pareto Optimality:  only on strict route preference domain • Non-dictatorship: X

26. BGP in strategic settings

27. 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)

28. 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

29. 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

30. 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?

31. Thank you!

32. Backup Slides

33. 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”

34. 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

35. 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

36. 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?

37. 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)

38. 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

39. 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

40. 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

41. 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)