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					Incentive-Compatible
Interdomain Routing

Joan Feigenbaum
Yale University

Vijay Ramachandran
Stevens Institute of Technology

Michael Schapira
The Hebrew University
                                  1
          Interdomain Routing

Establish routes between autonomous systems (ASes).

                         Verizon

           AT&T                     Comcast

                       Qwest


Currently done with the Border Gateway Protocol (BGP).

                                                         2
Why is Interdomain Routing Hard?

• Route choices are based on local policies.
• Autonomy: Policies are uncoordinated.
• Expressiveness: Policies are complex.
                                               Always choose
Load-balance my                                shortest paths.
outgoing traffic.              Verizon

                     AT&T                Comcast

                              Qwest
                                                   Avoid routes
    My link to UUNET is for                        through AT&T if
    backup purposes only.                          at all possible.
                                                                      3
     Welfare-Maximizing Routing
Private information:
                                Strategies
Route valuations
      v1(.                        a1
       )            AS 1                       p1
                                                                         Routes
                                                     Mechanism           R1,
                                                                         …,
      vn(.                         an
                                                                         Rn
       )            AS n                      pn

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.
                                                                                  4
                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 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)].
                                                      5
        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).
                                              6
  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
                                              7
         BGP Route Processing
• The computation of a single node repeats the following:
                        Update      Choose
      Receive routes                           Send updates
                        Routing      “Best”
      from neighbors                            to neighbors
                         Table       Route

• 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.
                                                               8
 Known Results: Welfare Maximization
      and Interdomain Routing
Routing-Policy         Good                           Good
    Class           Centralized                    Distributed
                    Algorithm?                     Algorithm?
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                                             
                                                                              9
                Question

• These are mostly negative results.

• Is there a realistic and useful class of
  routing policies (i.e., something broader
  than LCPs) for which we can get an
  incentive-compatible, BGP-compatible
  algorithm to compute routes and
  payments?

                                              10
  Gao-Rexford Framework (1)
Neighboring pairs of ASes have one of:
  – a customer-provider relationship
    (One node is purchasing connectivity from
    the other node.)
  – a peering relationship
    (Nodes have offered to carry each other’s
    transit traffic, often to shortcut a longer route.)
                      peer
                                      providers

                        peer
                                       customers
                                                          11
        Gao-Rexford Framework (2)
• Global constraint: no customer-provider cycles
• Local preference and scoping constraints, which are consistent
  with Internet economics:

    Preference Constraints                         Scoping Constraints
             k1            R                         provider   j              ....
                         ...1..
                             .                d
    i                                                               peer                  d
                            R                             i
                          . . .2. . .                                      m
               k2
                                                    customer    k
    • If k1 and k2 are both customers, peers,
      or providers of i, then either ik1R1 or      • Export customer routes to all neighbors
      ik2R2 can be more valued at i.                 and export all routes to customers.
    • If one is a customer, prefer the route       • Export peer and provider routes to
      through it. If not, prefer the peer route.     all customers only.


• Gao-Rexford conditions => BGP always converges [GR01]
                                                                                               12
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.)
                                            13
  Next-Hop Payment Computation

• Send augmented BGP update message
  whenever best route or availability of a
  k-avoiding route changes:
   AS k1 AS k2    …     AS ki   AS Path

    Y/N Y/N       …     Y/N     ki-avoiding path known?

• When an update message is received:
  – Store path and bits in routing table.
  – Scan bits to update best k-avoiding next hop.

                                                          14
            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).
   Destination   AS 1   AS 2   AS 2    Best k-avoiding next hops
                 AS 2   AS 4   AS 5    Optimal AS path
        d
                         Y      Y      Bit vector from update

                 AS 1   AS 3   AS 5    Alternate AS path
       d
                         Y      Y      Bit vector from update


• Payment components are derived from next hops:
    pki(Td) = vi(Td) – vi(Td-k) for transit k ;
            = 0 otherwise.
                                                                   15
    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.


                                                 16
                       Dispute Cycles
 Relation 1: Subpath                Relation 2: Preference
              R1                                     Q1
                                                             vi(Q1) > 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 => robust BGP convergence [GSW02, GJR03]
                                                                               17
      Example of a Dispute Cycle
v(12d) = 10                  v(23d) = 10
v(1d) = 5                    v(2d) = 5
          1              2


                                       1d        2d            3d
                     d


                                      31d       12d            23d

                     3
       v(31d) = 10                          Dispute Cycle
       v(3d) = 5
                                                  Subpath
                                                  Preference
                                                                     18
                  Policy Consistency
                              Valuations are policy consistent
    R1                                iff, for all routes R1 and R2
                                            (whose extensions are
                   ....
                                   k               i   not rejected),
d
                        ...


                                                           THEN
            R2                                     vi((i,k)R1) > vi((i,k)R2)
                                      IF
(analogous to                   vk(R1) > vk(R2)
isotonicity [Sob.03])
                                                                               19
               Optimality

• Theorem: If the valuation functions are
  policy consistent and do not induce a
  dispute cycle, then BGP converges to the
  globally optimal routing tree.




                                             20
  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.
                                                21
             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.

                                             22
              Future Work

• Approximability of the interdomain-routing
  problem?
  – Without restrictions on policies, no good
    approximation ratio is achievable [FSS04].
• Remove bank?
• Optimal communication complexity?



                                                 23
             Technical Report

Full version of this paper is available as

  Yale University Technical Report
  YALEU/DCS/TR-1342

  http://www.cs.yale.edu/publications/
  techreports/tr1342.pdf




                                             24

				
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posted:7/27/2012
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