On Self Adaptive Routing in Dynamic Environments

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On Self Adaptive Routing in Dynamic Environments

• -- A probabilistic routing scheme
• Haiyong Xie, Lili Qiu, Yang Richard Yang and Yin
  Zhang_at_ Yale, MR and ATT
• Presented by Joe, W.J.Jiang
• 28-08-2004

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Outline

• Overview of Adaptive Routing
• Related Work
• Probabilistic Routing Scheme
• Convergence Analysis
• Simulation Results
• Conclusion

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Where are you?

• Overview of Adaptive Routing
• Related Work
• Probabilistic Routing Scheme
• Convergence Analysis
• Simulation Results
• Conclusion

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Introduction to adaptive routing

• Routing in the Internetinterior gateway routing
  OSPFexterior gateway routing BGP
• Static routing, based on hop counts
• There is an inherent inefficiency in IP routing
  from users perspective latency, bandwidth, loss
  rate, etc
• Adaptive routing, allowing end hosts to select
  routes by themselves.

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Selfish Routing (user-optimal routing)

• Each end host selects a route with minimum
  latency.
• Shortest path routing, metric -- latency,
  additive
• Two approachessource routing -- Nimrodoverlay
  routing -- Detour, RON
• Selfish by nature -- selfish routing

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Illustration of source routing
n1-n2-n3-n4-n5
n1
n2
n3
n4
n5
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Illustration of overlay routing
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Problems I -- Oscillation

• Ring Network (Data Networks)
• Simultaneous Overlay Network

1? Mbps (L2)
Primary Paths
Alternate Paths
2 Mbps L1
Sources
Bottleneck Phy. Link
Destinations
1 Mbps (L3)
Ov.Nw. Nodes (2 Ovns)
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Problem II -- Performance Degradation

• Nash Equilibrium
• Well known that Nash Equilibrium do not in
  general optimize social welfare.
• Braesss Paradox

1
x
1
Performance degradationselfish routing global
optimal 2/(0.51) 4/3
1/2
0
s
t
1/2
x
1
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Where are you?

• Overview of Adaptive Routing
• Related Work
• Probabilistic Routing Scheme
• Convergence Analysis
• Simulation Results
• Conclusion

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Related Work

• Wardrop equilibrium a research aspect in
  economics of transportation.
• The proof of existence of unique equilibrium and
  some extensions.
• Network optimal routing - Data Networks-
  Frank-Wolfe Method- Projection MethodThese are
  centralized algorithms.
• Distributed version for optimal routing -
  Parallel and Distributed Computation

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Related Work (Cont)

• How bad is selfish routing?- There exists
  unique Nash Equilibrium for selfish routing under
  network flow model.- The performance (average
  delay) ratio between selfish routing and global
  routing could be unbounded for arbitrary
  network.- The upper bound for network with
  linear delay function is 4/3.
• On selfish routing in Internet-like
  environment- Based on simulation, selfish
  routing and global optimal routing exhibit
  similar performance, under different network
  topology and traffic models.

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Related Work (cont)

• If individual users are allowed to select routes
  selfishly without coordination, how to ensure
  these behaviors will converge to an equilibrium?
• Dynamic Cesaro-Wardrop equilibration in
  Networks- a model to ensure the convergence of
  probabilistic routing scheme
• On self adaptive routing in dynamic
  environments

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Where are you?

• Overview of Adaptive Routing
• Related Work
• Probabilistic Routing Scheme
• Convergence Analysis
• Simulation Results
• Conclusion

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Routing Scheme - Data Path Component

• Data path component- similar to distance
  vector routing- destination could be all overlay
  nodes.- - a generalization of normal Internet
  routing.

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Routing Scheme - Control Path Component

• Control path component - how routing
  probabilities are updated.
• Selfish routing, Wardrop routing, user-optimal
  routing
• property - Given a source-destination pair with a
  given amount of traffic, the routes with positive
  traffic should have equal latency, no larger than
  those unused routes for this source-destination
  pair.

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Routing Scheme Notation

• lji the latency of link from node i to its
  neighbor j
• Ljik the estimated delay from i to destination k
  through node j
• qjik the internal probability from node i to
  destination k through neighbor j
• pjik the routing probability from node i to
  destination k through neighbor j
• qjik will converge to the Wardrop equilibrium
• pjik are e- approximate of qjik

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Update of routing probabilities (1)

• Node i first computes the new delay ?jik lji
  Ljk
• Ljk is the estimated latency from node j to node
  k
• node i update the new latency estimation Ljik
  (1-a(n)) Ljik a(n) ?jik
• a(n) is the delay learning factor.
• then node i computes its overall delay estimation
  Lik to destination k

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Update of routing probabilities (2)

• Node i reports Lik to its neighbors after some
  delay, and the delay is a random value between
  T/2 to T, to avoid synchronization.
• node i updates its internal routing
  probabilities
• ß(n) is routing learning factor
• ?jik is i.i.d uniform random routing vectors to
  add disturbance to avoid non-Wardrop solutions

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Update of routing probabilities (3)

• Projection node i projects the internal routing
  probabilities to the subspace of 0,1N(i), which
  is equivalent to solving the following problem

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Update of routing probabilities (4)

• Node i compute the routing probabilities

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Protocol to implement user-optimal routing
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Comments on measuring

• About measuring lji , two approaches- measured
  by node i- measured by node j
• The advantage of the second method- unnecessary
  for clock synchronization- ?jik lji Ljk,
  there is an offset which is just the clock
  difference between i and the destination,
  independent of j.- - overhead is to stamp
  packets

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Probabilistic Scheme for network optimal routing

• Overview of network optimal routingto solve the
  convex programming

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Probabilistic Scheme for network optimal routing
(cont)
Proved in How bad is selfish routing.
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Probabilistic Scheme for network optimal routing
(cont)

• For network optimal routing, replace lji with
  marginal cost function mcji lji fjisji
• sji is the rate of change in the latency from
  node i to node j at traffic amount fji
• Without knowing the analytical expression of
  latency functions.
• However, the paper does not mention the scheme to
  measure the rate of change in the latency.

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Where are you?

• Overview of Adaptive Routing
• Related Work
• Probabilistic Routing Scheme
• Convergence Analysis
• Simulation Results
• Conclusion

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Convergence analysis - Intuition

• Consider a network with only two links
• p1, p2 gt0, p1p21
• Five cases.- (a) link 1 has higher latency- (b)
  link 1 has lower latency- (c) link 1 and 2 has
  the same latency- (d) link 1 has all of the
  traffic- (e) link 2 has all of the traffic

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Convergence Analysis - Assumption

• A1 - latency function is continuous,
  non-decreasing and bounded.
• A2 - the updates are frequent enough compared
  with the change rate in the underlying network
  states.
• A3 -

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Convergence Analysis - Assumption

• A4 -

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Where are you?

• Overview of Adaptive Routing
• Related Work
• Probabilistic Routing Scheme
• Convergence Analysis
• Simulation Results
• Conclusion

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Evaluation Methodologies

• Network topologies ATT, Sprint, Tiscali
• Traffic demands
• Traffic stimuli- Traffic spike- Step
  function- Linear function
• Performance metrics- average latency- average
  convergence time- link utilization

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Dynamics of user-optimal routing and
network-optimal routing
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Conclusion

• Overview of Adaptive Routing
• Related Work
• Probabilistic Routing Scheme
• Convergence Analysis
• Simulation Results
• Conclusion

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Conclusion

• This paper introduces a probabilistic routing
  scheme to achieve both user-optimal (selfish)
  routing and network optimal routing.
• An application of enforcement learning.
• Not consider the issue of fairness between users
  (or overlays).

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• Thank you!