Incentive-Compatible Interdomain Routing

1
Incentive-CompatibleInterdomain Routing
Joan FeigenbaumYale UniversityVijay
RamachandranStevens Institute of
TechnologyMichael SchapiraThe Hebrew University
2
Interdomain Routing

• Establish routes between autonomous systems
  (ASes).
• Currently done with the Border Gateway Protocol
  (BGP).

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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
ATT
Comcast
Qwest
Avoid routes through ATT ifat all possible.
My link to UUNET is forbackup purposes only.
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Welfare-Maximizing Routing
Private informationRoute 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., ?i vi(Ri) and
• VCG payments (nodes are paid for their
  contribution to the routing tree)
• using a BGP-compatible (distributed) algorithm.

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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 ? k vi(Td) hk()
• where hk is a function that does not depend on
  ks 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).

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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 dont 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

ChooseBestRoute
UpdateRouting Table
Receive routes from neighbors
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 gt1 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 otherstransit traffic, often to
  shortcut a longer route.)

peer
providers
peer
customers
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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 gt BGP always converges
  GR01

Preference Constraints
Scoping Constraints
. . . .
R1
j
k1
provider
. . . . . .
. . . .
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 or ik2R2 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.

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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
  pki(Td) vi(Td) vi(Td-k) for transit k
  0 otherwise.

AS 1
AS 2
AS 2
Best k-avoiding next hops
Destination
AS 4
AS 5
Optimal AS path
AS 2
d
Y
Y
Bit vector from update
AS 1
AS 3
AS 5
Alternate AS path
d
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
Relation 2 Preference
R1
Q1
vi(Q1) gt vi(Q2)
. . .
. . .
d
i
i
d
. . .
R2
Q2
R1 R2
Q1 Q2

• 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 gt robust BGP convergence
  GSW02, GJR03

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Example of a Dispute Cycle
v(12d) 10 v(1d) 5
v(23d) 10 v(2d) 5
1
2
1d
2d
3d
d
31d
12d
23d
3
v(31d) 10 v(3d) 5
Dispute Cycle
Subpath Preference
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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) gt vi((i,k)R2)
R2
IF vk(R1) gt vk(R2)
(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
  gt local optimality.
• Theorem B Local optimality gt If k is not on
  the path from i to d, then payment component pki
  (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 asYale
  University Technical ReportYALEU/DCS/TR-1342
• http//www.cs.yale.edu/publications/techreports/
  tr1342.pdf