Incentive-Compatible Inter-Domain Routing

1
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

2
Inter-Domain Routing

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

3
Why is Inter-Domain Routing Hard?

• Route choices are based on local policies.
• Autonomy Policies are uncoordinated.
• Expressiveness Policies are complex.

Always chooseshortest paths.
Load-balance myoutgoing traffic.
Avoid routes through ATT ifat all possible.
My link to UUNET is forbackup purposes only.
4
BGP-Route Processing

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

Dest.
AS Path
AS3
AS5
AS1
AS1
AS7
AS2
AS2
AS2
AS3
AS2
.
.
.
Entire paths are stored (to prevent loops).

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

Receive routes from neighbors
ChooseBest Route
Send updatesto neighbors
UpdateTable
5
Path-Vector Protocol Design

• Pros
• Route choices depend on neighbors choices. gt
  enforces consistency
• Best-route choices are made locally. gt allows
  autonomy, expressiveness,
• Routes are loop free and can change with
  topology, without any nodes knowing the whole
  network.
• Cons
• Policy-induced routing anomalies gt Routes may
  not be stable.

6
Example of Instability Oscillation
Prefer routes through 3
Nodes oscillateforever between 1d, 2d,
3d and 12d, 23d, 31d
2
1
Prefer routes through 2
d
Prefer routes through 1
3
7
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.

8
Economic Mechanism Design

• Approach to designing systems for self-interested
  agents

Private information
Strategies
Mechanism
t1
a1
Agent 1
p1
Output
O
tn
an
pn
Agent n
Payments
Truthful mechanisms Regardless of what other
agents do, each agent i maximizes her utility
by revealing her true private information.
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Welfare-Maximizing Routing
Private informationRoute valuations
Strategies
Mechanism
a1
v1(.)
p1
AS 1
RoutesR1,,Rn
an
vn(.)
pn
AS n

• 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.

10
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 routes next hop.
• Subjective-Cost RoutingNodes private
  information is its perceived cost for every other
  AS.Cost of a route is the sum of sources
  perceived transit costs.
• Forbidden-Set RoutingNodes private information
  is a set of ASes through which allocated routes
  are not allowed.

11
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 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 atruthful mechanism and a
  goodBGP-style algorithm?

13
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 ks valuation.

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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 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 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 n1 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
  gt node optimality.
• Theorem B Node optimality gt If k is not on
  the path from i to d, then payment component pki
  (Td) 0.

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Lowest-Cost Paths (LCP)
LCP and Path Prices
LCP cost
Dest.
Cost

AS3
AS5
AS1
c(i,1)
AS1
c1

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

Update routes and payments
Advertise modified routes and payments
Receive routes and payments from neighbors
Final state Node i has accurate values.
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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
j
Key observations

• Min-cost k-avoiding path
• passes through one of is neighbors

k
a

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

i
b
d
cb ci
Using this, we can show that prices can be
computed with local dynamic programming, with
nodes exchanging only costs and payments.
22
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 no dispute GR01,GGR01

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.
• 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
v(245d) 100v(235d) 50v(236d) 50 21
unavail.
v(135d) 100v(136d) 100v(1245d) 50123,
17unavail.
cust./prov.
peer
v(35d) 100v(36d) 50v(3245d) 3031
unavail.
1
3
2
4
v(45d) 100v(4235d) 50
5
6
v(6d) 100v(635d) 50v(63245d) 50
v(5d) 100v(536d) 20v(54236d) 8
v(7245d) 100v(7235d) 100v(7236d)
100v(71245d) 50v(7135d) 50
7
d
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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
  pki(Td) vi(Td) vi(Td-k) for transit k
  0 otherwise.

Best k-avoiding next hops
AS 1
AS 2
AS 2
Destination
AS 2
AS 4
AS 5
Optimal AS path
d
Y
Y
Bit vector from update
Alternate AS path
AS 1
AS 3
AS 5
d
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
Hard(BGP may not converge)
No assumptions
Non-optimal(BGP will converge, butthe solution
may be arbitrarilyfar from optimal.)
No dispute cycle
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.)