A BGPbased Mechanism for LowestCost Routing

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A BGP-based Mechanism for Lowest-Cost Routing

• By Feigenbaum,Papadimitriou,Sami,Shenker
• Presented by Namrata Rastogi

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Presentation Layout

• BGP Review
• Comparison with Related work
• Pricing Mechanism
• Game Model
• Distributed Price Computation
• Open Problems and Conclusions

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BGP Recap-I

• Internet viewed as collection of Autonomous
  systems (AS).
• Backbone of high bandwidth lines and fast routers
• Hooked to these backbones are regional networks
• Routing Algorithm within AS OSPF
• Interior Gateway protocol
• Routing between ASes BGP
• Exterior Gateway protocol

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BGP Recap-II

• EGP, IGP and Multiple AS

AS 100
AS 200
Router A
Router B
EGP
EGP
IGP
Router D
Router C
AS 300
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BGP Recap-III

• Why do we need different protocols for
  inter-domain routing and intra-domain routing ?
• Policies involving political,security and
  economic considerations
• Example traffic starting or ending at IBM
  should not transit Microsoft.
• AS willing to carry traffic for some who are its
  neighbors or have paid .
• Policy based routing
• Policies are manually entered into each BGP
  router (not part of protocol)

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BGP Recap-IV

• Path Vector protocol
• Instead of maintaining cost to each destination ,
  BGP router keeps track of exact path used.
• Periodically sends each neighbor the exact path
  it is using instead of just the cost to a
  particular destination. (incremental updates)

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BGP Example

• Information F receives from its neighbors about
  destination D
• From B I use BCD -From E I use EFGCD
• From G I use GCD
• From I I use IFGCD

C
B
A
Solves count-to-infinity problem (how?)
D
G
F
E
H
I
J
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Related work

• Nisan and Ronen
• Formulation of VCG pricing for routing
• Hershberger and Suri
• Centralized mechanism design
• incentive issues in route selection
• compute LCP and set of payments to links
• lacked in simulation of real-world routing
• Starting point of this work need for
  distributed algorithmic mechanism design (DAMD)

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Why incentives?

• AS incurs a per-packet cost for carrying traffic
• Compensation payment for transit traffic
  (price)
• Current implementation of inter-domain routing
  framework has no notion of incentives.
• BGP computes LCP given a set of AS costs.
• AS could lie !!
• Lower than truthful
• Higher than truthful
• Pricing scheme such that no incentive to lie
  about costs.

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Strategyproof Pricing Mechanism

• Pricing scheme should be strategyproof
• AS that carry no transit traffic receive no
  payment.
• Member of VCG class of mechanisms.

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More Realistic Model 3 ways

• Strategic agents
• Links intra-domain routing
• Nodes inter-domain routing
• computes LCP for all source destination pairs
• Solve N2 LCP instances
• Distributed algorithm for computation BGP
• Backward compatibility with existing internet
  protocol

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Network Model Game

• Routing Game

Strategic agents AS nodes
How to play? -node has to report transit cost
V (c) ? Tij ? Ik(ci,j)ck
k ? N
i,j ?N
Only way to minimize the overall cost is
incentivize the players to report true costs
VCG pricing!
Centralized vs Distributed Mechanism Design
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Model Limitations

• per-packet cost model
• Transit cost administrative in nature
• BGP general policy based routing
• LCP not commonly used policy
• no transit restrictions
• no general path costs in BGP currently
• our model assumes actual LCP (not based on
  number of AS hops)

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Assumptions

• biconnected graph
• cost independent of which neighbor k received the
  packet from and which neighbor k sends the packet
  to
• nodes carry no transit traffic receive no transit
  payment
• Cost of only transit node counted
• At most one link (bidirectional) between two ASs
• Intra-domain issues ignored

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Pricing Mechanism

• The following two requirements for pricing
  mechanism uniquely determines the mechanism we
  must use.
• strategyproof
• nodes with no transit traffic receive no payment
• payments as per-packet price depending on source
  and destination
• Pk ? Tijpijk
• where pijk is the per-packet price paid to
  node k for each transit packet from i to j.

i,j ? N
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Theorem 1.

• When routing picks lowest cost paths, and the
  network is biconnected, there is a unique
  strategyproof pricing mechanism that gives no
  payment to nodes that carry no transit
  traffic.The payments to transit nodes are of the
  form
• pk ?i,j? N Ti,jpijk
• where pijk ckIk(ci,j) ?Ir(ck?i,j)cr -
  ? Ir(ci,j)cr
• Proof ?

r?N
r?N
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Claims of proof

• Payments do not depend on traffic matrix.
• prices pij are zero if LCP between i and j does
  not traverse k.
• prices depend on source and destination unlike
  costs
• Payment to a node k for a packet from i to j is
  determined by the cost of LCP and the cost of the
  lowest-cost path that does not pass through k.

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AS Graph sample calculation
Traffic X to Z LCP XBDZ Payment to
D (depends on LCP and lowest-cost k avoiding
path) Lowest-cost D avoiding path is XAZ
(transit cost 5) pd cD 5 - 3 3 Pb
cB 5 - 3 4
Z Cz4
D cD1
A cA5
Y cY3
B cB2
X cX2
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BGP Computational Model

• Every node i stores lowest-cost AS path for
  each j.
• A router stores
• O(nd) AS numbers , where d is the diameter of the
  network.
• O(n) path costs
• Routing table updates (incremental)
• Computation of a single router infinite
  sequences of stages
• complexity measures
• number of stages for convergence
• total communication

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Assumptions

• Nodes run synchronously
• BGP converges within d stages of computation.
• Each stage involves O(nd) communication on any
  link.
• Computation at node i in single stage O(nd x
  degree(i))
• Static environment

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Distributed Price Computation
Loop-free Tree formation
Z Cz4
Z Cz4
D cD1
D cD1
A cA5
A cA5
Y cY3
Y cY3
B cB2
B cB2
X cX2
X cX2
Tree T(Z)
AS Graph
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Distributed Price Computation

• 4 cases

Z cz4

• a is is parent in T(j)
• pijk lt pajk

ii)a is is child in T(j) pijk lt pajk ci
ca
D cD1
A cA5
Y cY3
iii)a is not adjacent to i in T(j) and k is on
P(ci,j) pijk lt pajk ca c(a,j) - c(i,j)
B cB2
X cX2
iv)a is not adjacent to i in T(j) and k is not
on P(ci,j) pijk lt ck ca c(a,j) - c(i,j)
Tree T(Z)
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Lemma 1

• Let ib be the first link on P-k(ci,j).Then, the
  corresponding inequality (1) to (4) attains
  equality for b.

P-k(ci,j) lowest-cost k avoiding path
Pk(ci,j) LCP from i to j for vector of
declared costs c b neighbor of i on
P-k(ci,j)
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Theorem II

• Our algorithm computes the VCG prices correctly,
  uses routing tables of size O(nd) (i.e., imposes
  only a constant-factor penalty on the BGP
  routing-table size), and converges in at most (d
  d) stages (i.e.,imposes only an additive
  penalty of d stages on the worst case BGP
  convergence time).

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Open Problems

• AS implement distributed algorithm different
  algorithm.
• Overcharging
• Convergence time

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Comments-I

• This paper considers distributed resource
  allocation problems
• Users are distributed
• Resources are distributed
• Computation is distributed
• Focus on Network complexity
• Assume that the economic mechanism involves a
  distributed computation carried out over a
  network.
• Network complexity measures the computational and
  communication efficiency of the distributed
  algorithm

Internet is the biggest and most successful
distributed system, making it a natural source
of DAMD problems.
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Comments-II

• Field still not mature
• No particularly compelling example yet
• Some isolated results, but no coherent framework
• Many fundamental issues unresolved
• Four examples
• Congestion Game
• Alternate Path Game
• Inter-domain Routing Game
• Multicast Cost Sharing Game

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Comments-III

• Common Features of such games
• Little information about infrastructure and
  other players.
• Dynamic Environment
• Asynchronous
• Computational Constraints
• Communication/computation costs are important
• Mechanisms should have low network complexity
• DAMD raises two types of issues
• Game-theoretic issues in distributed systems
• Distributed computational issues in resulting
  economic
• mechanisms