incentive-compatible inter-domain routing
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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 PresentationTRANSCRIPT
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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
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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
3
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
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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
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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
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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
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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.
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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
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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?
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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.
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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]
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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 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
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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.
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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 => 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
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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
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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?
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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.)