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Incentive-Compatible Interdomain Routing. Joan Feigenbaum Yale University Vijay Ramachandran Stevens Institute of Technology Michael Schapira The Hebrew University. Verizon. AT&T. Comcast. Qwest. Interdomain Routing. Establish routes between autonomous systems (ASes).

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incentive compatible interdomain routing

Incentive-CompatibleInterdomain Routing

Joan FeigenbaumYale UniversityVijay RamachandranStevens Institute of TechnologyMichael SchapiraThe Hebrew University

interdomain routing

Verizon

AT&T

Comcast

Qwest

Interdomain Routing

Establish routes between autonomous systems (ASes).

Currently done with the Border Gateway Protocol (BGP).

why is interdomain routing hard
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.

welfare maximizing routing
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.
vcg payments
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)].

payment components
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).
routing protocol desiderata
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
bgp route processing
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.
question
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?
gao rexford framework 1
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

gao rexford framework 2
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.
efficient payment computation
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.)

next hop payment computation
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?

next hop routing table
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

towards a general theory
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.
dispute cycles
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]
example of a dispute cycle
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

policy consistency
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])

optimality
Optimality
  • Theorem: If the valuation functions are policy consistent and do not induce a dispute cycle, then BGP converges to theglobally optimal routing tree.
efficiently computing payments
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.
conclusions
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.
future work
Future Work
  • Approximability of the interdomain-routing problem?
    • Without restrictions on policies, no good approximation ratio is achievable [FSS04].
  • Remove bank?
  • Optimal communication complexity?
technical report
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