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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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