On Selfish Routing In Internetlike Environments

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On Selfish Routing In Internet-like Environments

• Lili Qiu (Microsoft Research)
• Yang Richard Yang (Yale University)
• Yin Zhang (ATT Labs Research)
• Scott Shenker (ICSI)

University of California, San Diego
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Selfish Routing

• IP routing is sub-optimal for user performance
• Routing hierarchy and policy routing
• Equipment failure and transient instability
• Slow reaction (if any) to network congestion
• Autonomous routing users pick their own routes
• Source routing (e.g. Nimrod)
• Overlay routing (e.g. Detour, RON)
• Autonomous routing is selfish by nature
• End hosts or routing overlays greedily select
  routes
• Optimize their own performance goals
• without considering system-wide criteria

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Bad News

• Selfish routing can seriously degrade performance
  Roughgarden Tardos

• Worst-case ratio is unbounded
• - Selfish source routing
• All traffic through lower link
• ? Mean latency 1
• Latency optimal routing
• To minimize mean latency, set x 1/(n1) 1/n
• ? Mean latency ? 0 as n ? ?

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Questions

• Selfish source routing
• How does selfish source routing perform?
• Are Internet environments among the worst cases?
• Selfish overlay routing
• How does selfish overlay routing perform?
• Does the reduced flexibility avoid the bad cases?
• Horizontal interactions
• Does selfish traffic coexist well with other
  traffic?
• Do selfish overlays coexist well with each other?
• Vertical interactions
• Does selfish routing interact well with network
  traffic engineering?

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Outline

• Our approach
• Performance results
• Physical routing
• Overlay routing
• Multiple overlays
• Interaction with traffic engineering
• Summary
• Ongoing and future work

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Our Approach

• Game-theoretic approach with simulations
• Equilibrium behavior
• Apply game theory to compute traffic equilibria
• Compare with global optima and default IP routing
• Intra-domain environments
• Compare against theoretical worst-case results
• Realistic topologies, traffic demands, and
  latency functions
• Disclaimers
• Lots of simplifications assumptions
• Necessary to limit the parameter space
• Raise more questions than what we answer
• Lots of ongoing and future work

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Routing Schemes

• Routing on the physical network
• Source routing
• Latency optimal routing
• Routing on an overlay (less flexible!)
• Overlay source routing
• Overlay latency optimal routing
• Compliant (i.e. default) routing OSPF
• Hop count, i.e. unit weight
• Optimized weights, i.e. FRT02
• Random weights

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Internet-like Environments

• Network topologies
• Real tier-1 ISP, Rocketfuel, random power-law
  graphs
• Logical overlay topology
• Fully connected mesh (i.e. clique)
• Traffic demands
• Real and synthetic traffic demands
• Link latency functions
• Queuing M/M/1, M/D/1, P/M/1, P/D/1, and BPR
• Propagation fiber length or geographical
  distance
• Performance metrics
• User Average latency
• System Max link utilization, network cost FRT02

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Outline

• Our approach
• Performance results
• Physical routing
• Overlay routing
• Multiple overlays
• Interaction with traffic engineering
• Summary
• Ongoing and future work

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Source Routing Average Latency
Good news Internet-like environments are far
from the worst cases for selfish source routing
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Source Routing Network Cost
Bad news Low latency comes at much higher
network cost
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Selfish Overlay Routing Full Overlay Coverage
Overlay source routing perform similarly as
source routing (except for very bad weight
settings)
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Selfish Overlay Routing Partial Overlay
Coverage (only edge nodes)
The effects of partial overlay coverage is
insignificant in backbone topologies.
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Horizontal Interactions(Two Overlays)
Different routing schemes coexist well without
hurting each other.
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Horizontal Interactions (Two Overlays) (Cont.)
With bad weights, selfish overlay improves the
performance of compliant traffic as well as its
own.
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Horizontal Interactions (Many Overlays) (Cont.)
Performance degradation due to competition among
overlays is insignificant.
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Vertical Interactions

• An iterative process between two players
• Traffic engineering minimize network cost
• current traffic pattern ? new routing matrix
• Selfish overlays minimize user latency
• current routing matrix ? new traffic pattern
• Question
• Does system reach a state with both low latency
  and low network cost?
• Short answer
• Depends on how much control underlay has

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Selfish Overlays vs. OSPF Optimizer
OSPF optimizer interacts poorly with selfish
overlays because it only has very coarse-grained
control.
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Selfish Overlays vs. MPLS Optimizer
MPLS optimizer interacts with selfish overlays
much more effectively.
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Conclusions

• Contributions
• Important questions on selfish routing
• Simulations that partially answer questions
• Main findings on selfish routing
• Near-optimal latency in Internet-like
  environments
• In sharp contrast with the theoretical worst
  cases
• Coexists well with other overlays regular IP
  traffic
• Background traffic may even benefit in some cases
• Big interactions with network traffic engineering
  
• Tension between optimizing user latency vs.
  network load

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Ongoing Work Dynamics of Selfish Routing

• Questions
• How are traffic equilibria reached?
• What routing protocols enable us to reach
  equilibria quickly?
• Solution A probabilistic routing protocol based
  on reinforcement learning
• Distributed algorithm
• Provable convergence and stability
• Quick response to changes

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Lots of Future Work

• Extensions
• Multi-domain IP networks
• Model topology and traffic demands
• Reduce computation complexity
• Different overlay topologies
• Tree, ring, power-law, exponential
• What overlay topology to form to improve
  performance and/or robustness?
• Alternative selfish-routing objectives
• Throughput, loss rate,
• Improve interactions
• Between selfish routing traffic engineering
• Bi-level programming?
• Estimate traffic demands

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Thank you!
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Computing Traffic Equilibrium of Selfish Routing

• Computing traffic equilibrium of non-overlay
  traffic
• Use the linear approximation algorithm
• A variant of the Frank-Wolfe algorithm, which is
  a gradient-based line search algorithm
• Computing traffic equilibrium of selfish overlay
  routing
• Construct a logical overlay network
• Use Jacob's relaxation algorithm on top of
  Sheffi's diagonalization method for asymmetric
  logical networks
• Use modified linear approximation algo. in
  symmetric case
• Computing traffic equilibrium of multiple
  overlays
• Use a relaxation framework
• In each round, each overlay computes its best
  response by fixing the other overlays traffic
  then the best response and the previous state are
  merged using decreasing relaxation factors.

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Selfish Overlay Routing (Full Overlay Coverage)

• overlay-src with opt-weight and hop-count
  performsimilarly as source routing
• overlay-src with random-weight performs much
  worse.

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Difference between Source Routing and Overlay
Routing

• Even if the overlay includes all network nodes,
  routing on an overlay is still different
• Network-level routing can prevent overlay traffic
  from using a link by setting the corresponding
  entry in routing matrix to 0 (in OSPF this is
  achieved by assigning a large weight)
• Certain physical routes cannot be implemented by
  any overlay routing
• Routing flexibility is further reduced when only
  a fraction of nodes belong to an overlay

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Selfish Overlay Routing (Full Overlay Coverage)

• Direct Link Shortest DLS
• For any physically adjacent nodes A and B, all
  the traffic from A to B is routed through the
  direct link AB without involving any other links.
  (e.g., hop-count-based OSPF)
• For an overlay that covers all network nodes and
  satisfies DLS
• routing on the overlay routing on the underlay
• Hop-count-based OSPF and optimized OSPF weights
  satisfy DLS ? they perform similarly as source
  routing
• Random OSPF weights violate DLS ? some links are
  pruned, and performance degrades

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Selfish Overlay Routing

• Similar results apply for overlay routing
• Achieves close to optimal average latency
• Low latency comes at higher network cost
• Even if overlay covers a fraction of nodes
• Random coverage 20-100 nodes
• Edge coverage edge nodes only

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One Round during Vertical Interaction

• T(t) Traffic matrix when routing matrix is
  R(t-1)
• R(t) OptimizedRoutingMatrix(T(t))
• Traffic engineering installs R(t) to network
• Selfish routing redistributes traffic to be
  T(t1)

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How to achieve traffic equilibria?

• Challenges
• Distributed algorithm
• Responsive to changes in traffic
• Approach
• Probabilistic routing based on distributed
  learning
• For each destination k, node i maintains a
  routing probability P(i, k, j) for each neighbor
  j

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How to achieve traffic equilibria? (Cont.)

• Protocol
• For every T seconds
• Send latency Lik(t) to all neighbors
• Receive latency Ljk(t) to all neighbors
• Compute Lik(t1)
• Update pikj(t1) for all neighbors j
• Properties
• Converge to Wardrop equilibria or global minimum
  latency
• Responsive to traffic stimuli (e.g., spike, step
  function, linear function)

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Selfish Overlay Routing (Partial Overlay
Coverage) (Cont.)
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Recap

• Good news
• Unlike the theoretical worst cases, selfish
  routing in Internet-like environments yields
  close to optimal latency
• The above result is true for both source routing
  and overlay routing
• Selfish routing can achieve good performance
  without hurting the traffic that is using default
  routing
• Bad news Selfish routing achieves low latency at
  the cost of overloading network