On Selfish Routing In Internet-like Environments

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On Selfish Routing In Internet-like Environments

• Lili Qiu
• Microsoft Research

March 18, 2004 University of Maryland
2
Todays Internet Routing

• Network in charge of routing
• Route selection affects user performance
• IP routing yields sub-optimal user performance

MSNBC
UMD
3
Deficiency in IP Routing

• IP routing is sub-optimal for user performance
• Routing hierarchy
• Policy routing
• Equipment failure and transient instability
• Slow reaction (if any) to network congestion

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Selfish Routing

• Selfish routing users pick their own routes
• Source routing (e.g., Nimrod)
• Overlay routing (e.g., Detour, RON)

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Source Routing
MSNBC
UMD
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Overlay Routing
MSNBC
Boston
Salt Lake
St. Louis
Phoenix
UMD
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Selfish Routing

• Selfish nature
• End hosts or routing overlays greedily select
  routes
• Optimize their own performance goals
• Not considering system-wide criteria
• Studies based on small scale deployment show it
  improves performance
• How well does selfish routing perform if everyone
  uses it?

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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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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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Source Routing Average Latency
Good news Internet-like environments are far
from the worst cases for selfish source routing
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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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Source Routing Network Cost
Bad news Low latency comes at much higher
network cost
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Selfish Overlay Routing

• Similar results apply
• Selfish overlay routing achieves close to optimal
  average latency
• Low latency comes at higher network cost
• The results apply when the overlay only covers a
  fraction of nodes
• Scenarios tested
• Random coverage 20-100 nodes
• Edge coverage edge nodes only

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Horizontal Interactions(Two Overlays)
Different routing schemes coexist well.
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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)
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 the network 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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Summary

• 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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Other Work

• Internet
• Fault diagnosis
• Web performance
• Congestion control
• IP telephony
• Wireless networks
• Model the impact of wireless interference
• Provision wireless networks
• Manage wireless networks

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Fault Diagnosis

• Server-based Inference of Internet Performance.
  IEEE INFOCOM 2003.(Joint work with V. N.
  Padmanabhan and H. J. Wang)

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Motivation
Web Server
Ethernet
ATT
CW
UUNet
Sprint
AOL
Qwest
Earthlink
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Network Diagnosis
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Problem Formulation

• (1-l1)(1-l2)(1-l4) (1-p1)
• (1-l1)(1-l2)(1-l5) (1-p2)
• (1-l1)(1-l3)(1-l8) (1-p5)
• Challenges
• Under-constrained system of equations
• Measurement errors

server
l1
l3
l2
l8
l7
l6
l4
l5
clients
p1
p2
p3
p4
p5
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Gibbs Sampling

• D
• observed packet transmission and loss at the
  clients
• ?
• ensemble of loss rates of links in the network
• Goal
• determine the posterior distribution P(?D)
• Approach
• Use Markov Chain Monte Carlo with Gibbs sampling
  to obtain samples from P(?D)
• Draw conclusions based on the samples

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Gibbs Sampling (Cont.)

• Applying Gibbs sampling to fault diagnosis
• 1) Initialize link loss rates arbitrarily
• 2) For j 1 warmup for each link i
  compute P(liD, li) where li is
  loss rate of link i, and li ?k?I lk
• 3) For j 1 realSamples for each link
  i compute P(liD, li)
• Use all the samples obtained at step 3 to
  approximate P(?D)

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Summary of Internet Fault Diagnosis

• Gibbs sampling yields a high coverage (over 80),
  and a low false positive rate (below 5-10)
• Two other inference techniques trade-off accuracy
  for speed

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Model the Impact of Wireless Interference

• Impact of Interference on Multihop Wireless
  Network Performance. ACM MOBICOM 2003. (Joint
  work with K. Jain, J. Padhye, and V. N.
  Padmanabhan)

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Motivation

• Multihop wireless networks
• Community networks, sensor networks, military
  applications
• Important to compute wireless network capacity
• Capacity planning
• Evaluate the efficiency of protocols
• A lot of research on capacity of multi-hop
  wireless networks
• Much of previous work studies asymptotic
  performance bounds
• Gupta and Kumar 2000 O(1/sqrt(N))
• We present a framework to answer questions about
  capacity of specific topologies with specific
  traffic patterns

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Community Networking Scenario
What is the maximum possible throughput?
Asymptotic analysis is not useful in this case
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Challenge

• Model the impact of wireless interference

1 Mbps
1 Mbps
B
C
A
Throughput 1 Mbps
B
A
C
1 Mbps
1 Mbps
Throughput 0.5 Mbps
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Overview of Our Framework

• Model the problem as a standard network flow
  problem
• Represent interference among wireless links using
  a conflict graph
• Derive constraints on utilization of wireless
  links using independent sets in the conflict
  graph
• Augment the linear program to obtain lower bound
  on optimal throughput
• Derive constraints on utilization of wireless
  links using cliques in the conflict graph
• Augment the linear program to obtain upper bound
  on optimal throughput

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Sample Results Using Our Framework
Houses talk to immediate neighbors, all links are
capacity 1, 802.11-like MAC, Multipath routing
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Sample Results Using Our Framework (Cont.)
Scenario Aggregate Throughput
Baseline 0.5
Double range 0.5
Two ITAPs 1
Two Radios 1
Houses talk to immediate neighbors, all links are
capacity 1, 802.11-like MAC, Multipath routing
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Future Work

• Trends
• Networks become larger and more heterogeneous
• Research problems
• Internet management
• End-user based approach
• Wireless network design management
• Error-prone physical medium
• Dynamic and unpredictable networks
• Accessible physical medium, vulnerable to attacks

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Future Work (Cont.)

• Trends
• Network protocols become more complicated, e.g.,
  various optimizations are proposed for different
  network layers
• Network users and providers have different and
  sometimes conflicting goals
• Research problems
• How to optimize network performance?
• Cross different network layers
• Satisfy the need of different users and network
  providers

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Thank you!
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Computing Traffic Equilibrium of Selfish Routing

• Computing traffic equilibrium of source routing
  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 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
• Each overlay computes its best response by fixing
  the other overlays traffic
• Merge the best response and the previous state
  using decreasing relaxation factors.

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Overlay Routing in Inter-domain
Selfish routing yields close to optimal latency,
and better than compliant routing.
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Advantages of Our Approach

• Real numbers instead of asymptotic bounds
• Optimal bound, may not be achieved in practice
• Useful for what if analysis
• Permits several generalizations
• Different routing
• single path or multi-path routing
• Different wireless interference models
• Different antennas/radios
• directional or unidirectional, different ranges,
  data rates, multiple radios/channels
• Different senders
• senders with limited (but constant) demand
• Different topologies
• Different performance metrics
• throughput, fairness, revenue

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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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Example Conflict Graph
Connectivity Graph
2
1
C
B
A
4
3
Conflict Graph
1
2
3
4