Incentive-Compatible Interdomain Routing

1. Incentive-CompatibleInterdomain Routing Joan FeigenbaumYale UniversityVijay RamachandranStevens Institute of TechnologyMichael SchapiraThe Hebrew University

2. Verizon AT&T Comcast Qwest Interdomain Routing Establish routes between autonomous systems (ASes). Currently done with the Border Gateway Protocol (BGP).

3. Why is Interdomain Routing Hard? • Route choices are based on local policies. • Autonomy: Policies are uncoordinated. • Expressiveness: Policies are complex. Always chooseshortest paths. Load-balance myoutgoing traffic. Verizon AT&T Comcast Qwest Avoid routes through AT&T ifat all possible. My link to UUNET is forbackup purposes only.

4. Welfare-Maximizing Routing Private information:Route valuations Strategies Mechanism a1 v1(.) p1 AS 1 RoutesR1,…,Rn an vn(.) pn AS n • For each destination (independently / in parallel), compute: • A confluent routing tree that maximizes the sum of nodes’ valuations for that destination, i.e., ∑ivi(Ri) ; and • VCG payments (nodes are paid for their contribution to the routing tree) • … using a BGP-compatible (distributed) algorithm.

5. VCG Payments Td is the optimal routing tree to destination d. Td-k is the optimal tree to d if node k is removed. • The VCG payment to node k is of the form pk = ∑ikvi(Td) – hk(•) where hk is a function that does not depend on k’s valuation. • If hk({vi}) = ∑i ≠ kvi(Td-k), then the payment to each node is pk(Td) = ∑i ≠ k [vi(Td) – vi(Td-k)].

6. Payment Components • The total payment to node k can be broken down into payment components:pk(Td) = ∑i ≠ kpki(Td). • Each payment component depends only on the valuations at some node i: pki(Td) = vi(Td) – vi(Td-k). • Compute these in a distributed manner. • Problem: We don’t want to run an algorithm for every Td-k (not efficient).

7. Routing-Protocol Desiderata • Does not assume a priori knowledge of the network topology • Distributed • Autonomy-preserving • Dynamic (responds to network changes) • Space- and communication-efficient • Complies with Internet next-hop forwarding

8. BGP Route Processing • The computation of a single node repeats the following: Choose“Best”Route UpdateRouting Table Send updatesto neighbors Receive routes from neighbors • Paths go through neighbors’ choices, which enforces consistency. • Decisions are made locally, which preserves autonomy. • Uncoordinated policies can induce protocol oscillations. (Much recent work addresses BGP convergence.) • Recently, private information, optimization, and incentive-compatibility have also been studied.

9. Known Results: Welfare Maximizationand Interdomain Routing

10. Question • These are mostly negative results. • Is there a realistic and useful class of routing policies (i.e., something broaderthan LCPs) for which we can get anincentive-compatible, BGP-compatible algorithm to compute routes and payments?

11. Gao-Rexford Framework (1) Neighboring pairs of ASes have one of: • a customer-provider relationship(One node is purchasing connectivity fromthe other node.) • a peering relationship(Nodes have offered to carry each other’stransit traffic, often to shortcut a longer route.) peer providers peer customers

12. Gao-Rexford Framework (2) • Global constraint: no customer-provider cycles • Local preference and scoping constraints, which are consistent with Internet economics: • Gao-Rexford conditions => BGP always converges [GR01] Preference Constraints Scoping Constraints . . . . R1 j provider k1 . . . . . . . . . . d . . . . i peer d i R2 . . . . . . m k2 k customer • If k1 and k2 are both customers, peers, or providers of i, then either ik1R1 orik2R2 can be more valued at i. • If one is a customer, prefer the route through it. If not, prefer the peer route. • Export customer routes to all neighbors and export all routes to customers. • Export peer and provider routes to all customers only.

13. Efficient Payment Computation • Next-hop valuations: The valuation of a route depends only on its next hop. • Theorem: If Gao-Rexford conditions hold and ASes have next-hop policies, then routes and payments can be computed with “good” space efficiency. * (We only run “BGP” once.)

14. Next-Hop Payment Computation • Send augmented BGP update message whenever best route or availability of ak-avoiding route changes: • When an update message is received: • Store path and bits in routing table. • Scan bits to update best k-avoiding next hop. AS Path ki-avoiding path known?

15. Next-Hop Routing Table • Store usable routes, availability of k-avoiding routes from neighbors (for all stored routes), and best k-avoiding next hops (for current most preferred route). • Payment components are derived from next hops:pki(Td) = vi(Td) – vi(Td-k) for transit k ; = 0 otherwise. Best k-avoiding next hops AS 2 AS 2 AS 1 Destination Optimal AS path AS 4 AS 5 AS 2 d Y Y Bit vector from update Alternate AS path AS 3 AS 5 AS 1 d Y Y Bit vector from update

16. Towards a General Theory • Gao-Rexford + Next-Hop valuations are a special case. • We identify a broad sufficient condition for valuations that permit BGP-compatible, incentive-compatible computation of routes and VCG payments.

17. Dispute Cycles Relation 1: Subpath Relation 2: Preference Q1 R1 vi(Q1) > vi(Q2) . . . . . . d i i d . . . R2 Q2 Q1Q2 R1R2 • Valuations do not induce a dispute cycle iff there is no cycle formed by the above relations on all permitted paths in the network. • No dispute cycle => robust BGP convergence [GSW02, GJR03]

18. Example of a Dispute Cycle v(12d) = 10 v(1d) = 5 v(23d) = 10 v(2d) = 5 2 1 1d 2d 3d d 31d 12d 23d 3 v(31d) = 10 v(3d) = 5 Dispute Cycle Subpath Preference

19. Policy Consistency Valuations are policy consistentiff, for all routes R1 and R2(whose extensions arenot rejected), R1 . . . . k i d . . . THEN vi((i,k)R1) > vi((i,k)R2) R2 IF vk(R1) > vk(R2) (analogous toisotonicity [Sob.03])

20. Optimality • Theorem: If the valuation functions are policy consistent and do not induce a dispute cycle, then BGP converges to theglobally optimal routing tree.

21. Efficiently Computing Payments • Local optimality: In a globally optimal routing tree, every node gets its most valued route. • Theorem A: No dispute cycle + policy consistency => local optimality. • Theorem B: Local optimality => If k is not on the path from i to d, then payment component pki (Td) = 0.

22. Conclusions • Gao-Rexford + Next-Hop valuations are a reasonable class of policies that admit incentive-compatible, BGP-compatible computation of routes and VCG payments. • Only a constant-factor increase in BGP routing-table size is required. • Dispute-cycle-free and policy-consistent valuations generalize this result.

23. Future Work • Approximability of the interdomain-routing problem? • Without restrictions on policies, no good approximation ratio is achievable [FSS04]. • Remove bank? • Optimal communication complexity?

24. Technical Report Full version of this paper is available asYale University Technical ReportYALEU/DCS/TR-1342 http://www.cs.yale.edu/publications/techreports/tr1342.pdf