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Incentive-CompatibleInterdomain Routing

Joan FeigenbaumYale University

Vijay RamachandranStevens Institute of Technology

Michael SchapiraThe Hebrew University

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Interdomain Routing

Establish routes between autonomous systems (ASes).

Currently done with the Border Gateway Protocol (BGP).

AT&T

Qwest

Comcast

Verizon

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Why is Interdomain Routing Hard?

• Route choices are based on local policies.

• Autonomy: Policies are uncoordinated.

• Expressiveness: Policies are complex.

AT&T

Qwest

Comcast

Verizon

My link to UUNET is forbackup purposes only.

Load-balance myoutgoing traffic.

Always chooseshortest paths.

Avoid routes through AT&T ifat all possible.

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Welfare-Maximizing Routing

AS 1

AS n

Mechanism

p1

pn

vn(.)

v1(.)

a1

an

Private information:Route valuations Strategies

For each destination (independently / in parallel), compute:

• A confluent routing tree that maximizes the sum of nodes’ valuations for that destination, i.e., ∑i vi(Ri) ; and

• VCG payments (nodes are paid for their contribution to the routing tree)

… using a BGP-compatible (distributed) algorithm.

RoutesR1,…,Rn

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VCG Payments

• The VCG payment to node k is of the form

pk = ∑i k vi(Td) – hk(•)

where hk is a function that does not depend on k’s valuation.

• If hk({vi}) = ∑i ≠ k vi(Td-k),

then the payment to each node is

pk(Td) = ∑i ≠ k [vi(Td) – vi(Td-k)].

Td is the optimal routing tree to destination d.Td

-k is the optimal tree to d if node k is removed.

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Payment Components

• The total payment to node k can be broken down into payment components:

pk(Td) = ∑i ≠ k pki(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).

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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

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BGP Route Processing

• The computation of a single node repeats the following:

Receive routes from neighbors

UpdateRouting Table

Choose“Best”Route

Send updatesto 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.

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Known Results: Welfare Maximizationand Interdomain Routing

Routing-Policy Class

Good CentralizedAlgorithm?

Good DistributedAlgorithm?

LCP*

General Policy (and hard to approximate)

(and hard to approximate)

Next Hop

Subjective Cost (incl. some special cases)

(approx. is easy if >1 tree)

Forbidden Set

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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?

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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.)

peerproviders

customers

peer

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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

. . . . . .

. . . . . .i

dR1

R2

k2

k1

• If k1 and k2 are both customers, peers, or providers of i, then either ik1R1 or ik2R2 can be more valued at i.

• If one is a customer, prefer the route through it. If not, prefer the peer route.

Scoping Constraints

d

k

i

j

• Export customer routes to all neighbors and export all routes to customers.

• Export peer and provider routes to all customers only.

m

. . . .. . . .

. . . .peer

customer

provider

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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.)

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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 k1 AS k2 … AS ki

Y/N Y/N … Y/N

AS Path

ki-avoiding path known?

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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: pk

i(Td) = vi(Td) – vi(Td-k) for transit k ;

= 0 otherwise.

Destination

dAS 2 AS 4 AS 5 Optimal AS path

Y Y Bit vector from update

AS 1 AS 2 AS 2 Best k-avoiding next hops

dAS 1 AS 3 AS 5 Alternate AS path

Y Y Bit vector from update

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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.

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Dispute Cycles

Relation 1: Subpath

. . .

R1

R2

R1 R2

Relation 2: Preference

. . .

. . .

Q1

Q2

vi(Q1) > vi(Q2)

Q1 Q2

dd

ii

• 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]

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Example of a Dispute Cycle

1 2

d

3

v(12d) = 10v(1d) = 5

v(23d) = 10v(2d) = 5

v(31d) = 10v(3d) = 5

1d 2d 3d

31d 12d 23d

Dispute Cycle

SubpathPreference

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Policy Consistency

. . .

. . . .

d

k i

IFvk(R1) > vk(R2)

R2

R1

THENvi((i,k)R1) > vi((i,k)R2)

Valuations are policy consistentiff, for all routes R1 and R2

(whose extensions arenot rejected),

(analogous toisotonicity [Sob.03])

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Optimality

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

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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, thenpayment component pk

i (Td) = 0.

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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.

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Future Work

• Approximability of the interdomain-routing problem?– Without restrictions on policies, no good

approximation ratio is achievable [FSS04].

• Remove bank?

• Optimal communication complexity?

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Technical Report

Full version of this paper is available as

Yale University Technical ReportYALEU/DCS/TR-1342

http://www.cs.yale.edu/publications/techreports/tr1342.pdf