incentive-compatible inter-domain routing

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1 Incentive- Compatible Inter-Domain Routing Joan Feigenbaum Yale University http://www.cs.yale.edu/homes/jf/ Colloquium at Cornell University; October 2005 Joint work with Michael Schapira and Vijay Ramachandran

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Incentive-Compatible Inter-Domain Routing. Joan Feigenbaum Yale University http://www.cs.yale.edu/homes/jf/ Colloquium at Cornell University; October 2005 Joint work with Michael Schapira and Vijay Ramachandran. UUNET. AT&T. Comcast. Qwest. Inter-Domain Routing. - PowerPoint PPT Presentation

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Page 1: Incentive-Compatible Inter-Domain Routing

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Incentive-CompatibleInter-Domain Routing

Joan FeigenbaumYale Universityhttp://www.cs.yale.edu/homes/jf/

Colloquium at Cornell University; October 2005

Joint work with Michael Schapiraand Vijay Ramachandran

Page 2: Incentive-Compatible Inter-Domain Routing

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Inter-Domain Routing

Establish routes between autonomous systems (ASes).

Currently done with the Border Gateway Protocol (BGP).

AT&T

Qwest

Comcast

UUNET

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Why is Inter-Domain Routing Hard?

• Route choices are based on local policies.

• Autonomy: Policies are uncoordinated.

• Expressiveness: Policies are complex.

AT&T

Qwest

Comcast

UUNET

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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BGP-Route Processing

• Each AS has a routing table with routes to other nodes:

Entire paths are stored (to prevent loops).

Dest. AS Path

AS3 AS5 AS1AS1

AS7 AS2AS2AS2 AS3 AS2

.

.

.

• The computation of a single node is an infinite sequence of stages:

Receive routes from neighbors

UpdateTable

Choose“Best” Route

Send updatesto neighbors

Page 5: Incentive-Compatible Inter-Domain Routing

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Path-Vector Protocol Design

• Pros:– Route choices depend on neighbors’ choices.

=> enforces consistency– Best-route choices are made locally.

=> allows autonomy, expressiveness, …– Routes are loop free and can change with topology,

without any node’s knowing the whole network.

• Cons:– Policy-induced routing anomalies

=> Routes may not be stable.

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Example of Instability: Oscillation

1 2

d

3

Nodes oscillateforever between

1d, 2d, 3dand

12d, 23d, 31d

Prefer routes

through 2

Prefer routes through 3

Prefer routes

through 1

Page 7: Incentive-Compatible Inter-Domain Routing

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Protocol Convergence

• A balance of local and global constraints on policies can assure robust convergence.[Gao, Rexford, Griffin, Wilfong, Shepherd, Sobrinho,

Jaggard, Ramachandran, Feamster, Johari, Balakrishnan, … ]

• These results are concerned only with convergence to unique solutions.

• Recently, private information, optimization, and incentive-compatibility have also been studied in inter-domain routing.

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Economic Mechanism Design

Approach to designing systems for self-interested agents

Truthful mechanisms: Regardless of what other agents do, each agent i maximizes her utility by revealing her true private information.

Agent 1

Agent n

Mechanism

p1

pn

tn

t1a1

an

O

Private information Strategies

Payments

Output

Page 9: Incentive-Compatible Inter-Domain Routing

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Welfare-Maximizing Routing

AS 1

AS n

Mechanism

p1

pn

vn(.)

v1(.)

a1

an

Private information:Route valuations Strategies

• Maximize sum of nodes’ valuations = ∑i vi(Ri) .

• A confluent routing tree and payments are computed in parallel for each destination.

• Source nodes are paid for their contribution to the routing tree.

• We want a BGP-style algorithm that computes routes and payments.

RoutesR1,…,Rn

Page 10: Incentive-Compatible Inter-Domain Routing

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Classes of Routing Policies

• Lowest-Cost Paths (LCP)Nodes’ private information is its own per-packet transit cost.Transit nodes are paid to carry transit traffic and reveal true costs.

• General Policy RoutingNodes’ private information is an unrestricted per-route valuation.

• Next-Hop RoutingNodes’ private information is a per-route valuation.Route valuations depend only on a route’s next hop.

• Subjective-Cost RoutingNodes’ private information is its perceived cost for every other AS.Cost of a route is the sum of source’s perceived transit costs.

• Forbidden-Set RoutingNodes’ private information is a set of ASes through which allocated routes are not allowed.

Page 11: Incentive-Compatible Inter-Domain Routing

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Known Results: Welfare Maximizationand Inter-Domain 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

Page 12: Incentive-Compatible Inter-Domain Routing

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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 atruthful mechanism and a goodBGP-style algorithm?

Page 13: Incentive-Compatible Inter-Domain Routing

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General Approach

• Find a class of policies for which BGP converges to an optimal tree T (i.e., onethat maximizes the sum of the valuations of all source nodes).

• Use VCG payment formula to ensure truthfulness, i.e., payment to node k is

pk = ∑i k vi(T) – hk(•)

where hk is a function that does notdepend on node k’s valuation.

Page 14: Incentive-Compatible Inter-Domain Routing

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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 convergence [GSW02, GJR03]

Page 15: Incentive-Compatible Inter-Domain Routing

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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

Page 16: Incentive-Compatible Inter-Domain Routing

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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])

Page 17: Incentive-Compatible Inter-Domain Routing

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Optimality and Payment Formula

• Theorem: If the valuation functions are policy consistent and do not induce a dispute cycle, then BGP computesoptimal routes.

• Payment to node k:

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 avoiding node k.

– This is the VCG formula, with hk({vi}) = ∑i ≠ k vi(Td-k).

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Computing Routes and Payments

• The “algorithm”:

Run n+1 parallel instances of BGPon G, G-1, G-2, …, G-n.

• Result: optimal trees Td, Td-1, …, Td

-n

• For all i, k, node i can compute a component of the payment to k:

pki(Td) = vi(Td) – vi(Td

-k).

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

pk(Td) = ∑i ≠ k pki(Td).

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Efficiently Computing Payments?

• Node optimality: In a globally optimal routing tree, every node gets its most valued (locally optimal) route.

• Theorem A: No dispute cycle + policy consistency => node optimality.

• Theorem B: Node optimality =>If k is not on the path from i to d, thenpayment component pk

i (Td) = 0.

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Lowest-Cost Paths (LCP)

AS3 AS5

c(i,1) AS1 c1

Dest. Cost LCP and Path Prices LCP cost

AS1

• Initially, all payments are set to .• Then, each node runs the following computation:

Final state: Node i has accurate values.pkij

p3 i1 p5

i1

Receive routes and payments from neighbors

Update routes and payments

Advertise modified routesand payments

Page 21: Incentive-Compatible Inter-Domain Routing

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Computing LCP Payments [FPSS02]

= ck + Cost of min-cost k-avoiding path from i to j – Cost of LCP from i to j

pkij

a

bdi

k

jKey observations:

• Min-cost k-avoiding path passes through one of i’s neighbors

• Payment can be related to costs and payments at adjacent nodes, e.g.,

= + cb + cipk

ij pkbj

pkij

Using this, we can show that prices can be computedwith local dynamic programming, with nodes exchanging only costs and payments.

Page 22: Incentive-Compatible Inter-Domain Routing

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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

Page 23: Incentive-Compatible Inter-Domain Routing

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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 => no dispute [GR01,GGR01]

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

Page 24: Incentive-Compatible Inter-Domain Routing

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Efficient Payment Computation

• Next-hop valuations: The valuation of a route depends only on its next hop.

• Observation: Next-hop valuations are policy consistent.

• Theorem: If Gao-Rexford conditions hold and ASes have next-hop policies, then the payment-computation algorithm has the same space-efficiency as in the LCP case.

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Example of Gao-Rexford + Next Hop

peercust./prov.

7 d

1 2 3

4

5 6

v(7245d) = 100v(7235d) = 100v(7236d) = 100v(71245d) = 50v(7135d) = 50

v(135d) = 100v(136d) = 100v(1245d) = 50[123…, 17…unavail.]

v(245d) = 100v(235d) = 50v(236d) = 50[21… unavail.]

v(45d) = 100v(4235d) = 50

v(5d) = 100v(536d) = 20v(54236d) = 8

v(35d) = 100v(36d) = 50v(3245d) = 30[31… unavail.]

v(6d) = 100v(635d) = 50v(63245d) = 50

Page 26: Incentive-Compatible Inter-Domain Routing

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Next-Hop Routing Table for AS7

• Store usable routes, availability of k-avoiding routes from neighbors (for all), and bestk-avoiding next hops (for preferred).

• 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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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?

Page 28: Incentive-Compatible Inter-Domain Routing

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Summary of Sufficient Conditions

No assumptions Hard(BGP may not converge)

No dispute cycle Non-optimal(BGP will converge, butthe solution may be arbitrarilyfar from optimal.)

No dispute cycleand policy consistency

Optimal convergence(but payment computation mightbe highly space-consuming)

No dispute cycle andnext-hop or lowest-cost valuations(special cases ofpolicy consistency)

Optimal convergenceand good BGP-style algorithm(Requires O(1) additional spaceper transit node.)