Dept.%20of%20Computer%20Science%20

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Interaction of Overlay Networks Properties and
Control
Professor John C.S. Lui
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A Disruptive Technology
Because, sometimes, the Internet doesnt quite
work
-- MIT RON (Resilient Overlay Networks) Project
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A Disruptive Technology

• Growing trend of setting up overlay or
  peer-to-peer networks
• BitTorrent
• Resilient Overlay Network
• Akamai
• PlanetLab
• Skype

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Roadmap

• How do overlay networks co-exist with each other?
• What is the implication of interactions?
• How to regulate selfish overlay networks?

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Outline

• Overlay Networks Preliminary
• Motivation
• Mathematical Modeling
• Overlay Routing Game
• Implications of Interaction
• Pricing
• Conclusion

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Internet as an Overlay

• Internet an overlay on telephone networks
• Success of the Internet
• IP protocol
• End-to-end design philosophy

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Internet Clouds
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What is an overlay network?

• Definition

An overlay network is a set of nodes (servers)
that

• uses the existing Internet paths between end
  hosts as virtual links
• Creates a virtual topology
• Forwards and handles application data
• Provides infrastructure to applications on top of
  it.

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Overlay Network an Example
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J
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G
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Benefits of Overlay Networks

• Path diversity
• Support of specific application (QoS)
  requirements
• Quick deployment of new protocols

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Taxonomy
Category Functionality Purpose Example
Peer-to-peer (P2P) File sharing distribution BitTorrent, Gnutella
Routing Overlay Enhance IP-routing, reduce routing delay, improve resilience, etc Resilient Overlay Network (RON)
Content Delivery Network (CDN) Distributed content caching Akamai, Chord, Pastry, CAN
Multicast Overlay Multicast End System Multicast, Mbone
Others Various Purpose Security VPN, SOS Experimental PlanetLab, I3 VoIP Skype.
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Navigation

• Overlay Networks Preliminary
• Motivation
• Mathematical Modeling
• Overlay Routing Game
• Implications of Interaction
• Pricing
• Conclusion

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Motivation

• Overlays provide a feasibility for people to
  control their own routing.
• Routing becomes an optimization problem.
• Interaction occurs.
• Interaction between one overlay and underlay
  traffic engineering, Zhang et al, Infocom05.
• Interaction between co-existing overlays ?

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Performance Characteristics

• Objective minimize end-to-end delay
• Delay of a physical link e
• Performance Characteristics (Underlay)

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Performance Characteristics

• Objective minimize end-to-end delay
• Delay of a physical link e
• Performance Characteristics (Underlay)

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Performance Characteristics

• Objective minimize end-to-end delay
• Delay of a physical link e
• Performance Characteristics (Underlay)

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System Objectives

• Network Operators
• Min average delay in the whole underlay network
• Overlay Users
• Min average delay experienced by the overlay

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How do Overlays Interact?

• Overlapping physical links.
• Performance dependent on each other.
• Selfish routing optimization.
• Overlays are transparent to each other.

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Contribution

• What is the form of interaction?
• Is there routing instability (oscillation)?
• Is the routing equilibrium efficient?
• What is the price of anarchy?
• Fairness issues
• Mechanism design can we lead the selfish
  behaviors to an efficient equilibrium?

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Navigation

• Overlay Networks Preliminary
• Motivation
• Mathematical Modeling
• Overlay Routing Game
• Implications of Interaction
• Pricing
• Conclusion

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Mathematical Modeling

• Overlay routing An optimization problem

• Decision variable routing policy

s overlay f flow r path
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Mathematical Modeling

• Overlay routing An optimization problem

• Objective average weighted delay

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Overlay Routing Optimization

• Convex programming

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Algorithmic Solution

• Unique optimizer
• Convex programming
• feasible region convex
• delay function continuous, non-decreasing,
  strictly convex
• Solution
• Apply any convex programming techniques.
• Marginal cost network flow (probabilistic routing
  ICNP04).

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Navigation

• Overlay Networks Preliminary
• Motivation
• Mathematical Modeling
• Overlay Routing Game
• Implications of Interaction
• Pricing
• Conclusion

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Overlay Routing Game
Strategic Game GoverlayltN, (Gs), (s)gt

• Nash Routing Game
• Player -- N
• all overlays
• Strategy -- Gs
• feasible routing policy feasible region of
  OVERLAY(s)
• Preference relation -- s
• low delay players utility function is -delay(s)

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Illustration of Interaction
Aggregate traffic on physical links
Routing decision on logical paths in overlay 1
Delay of logical paths in overlay 1
Overlay 1
Routing decision on logical paths in overlay 2
Delay of logical paths in overlay 2
Overlay 2
Overlay probing
Aggregate overlay traffic

?
Routing Underlay
Underlay (non-overlay) traffic

Overlay n
Routing decision on logical paths in overlay n
Delay of logical paths in overlay n
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Why Nash Routing Game?

• Strategic game (not repeated game)
• Multiplayer Game
• Asynchronous routing update
• Limited information
• Strategic game

Nash Equilibrium
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Existence of Nash Equilibrium

• Definition Nash equilibrium point (NE)

A feasible strategy profile y(y(1),, y(s),,
y(n))T is a Nash equilibrium in the overlay
routing game if for every overlay s?N,
delay(s)(y(1),y(s),y(n))
delay(s)(y(1),y(s),y(n))for any other
feasible strategy profile y(s) .
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Existence of Nash Equilibrium

• Theorem

In the overlay routing game, there exists a Nash
equilibrium if the delay function
delay(s)(y(s) y(-s)) is continuous,
non-decreasing and convex.
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Fluid Simulation
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Overlay performance
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Overlay routing decisions
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Navigation

• Overlay Networks Preliminary
• Motivation
• Mathematical Modeling
• Overlay Routing Game
• Implications of Interaction
• Pricing
• Conclusion

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The Price of Anarchy
Global Performance (average delay for all flows)
Efficiency Loss ?

• GOR Global Optimal Routing
• NOR Nash equilibrium for Overlay Routing Game
• NSR Nash equilibrium for Selfish Routing

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Selfish Routing

• (User) selfish routing a single packets
  selfishness
• Every single packet chooses to route via a
  shortest (delay) path.
• A flow is at Nash equilibrium if no packet can
  improve its delay by changing its route.

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Selfish Routing

• Also a Nash equilibrium of a mixed strategic game
• Player flow f
• Strategy p ?Pf
• Preference low delay
• System Optimization Problem

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Performance Comparison
Overlay One Overlay Two Average Delay
Centralized Global Optimal Routing 2.50 2.38 2.46
NE of Overlay Optimal Routing 2.46 2.53 2.50
NE of Selfish Routing 2.63 2.75 2.68
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Inspiration

• Is the equilibrium point efficient (at least
  Pareto optimal) ?
• Fairness issues of resource competition between
  overlays.

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Example Network
y1
1-y1
y2
1-y2
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Sub-Optimality
physical link delay function de(le)
1-5 1l
3-4 l
2-6 2.5l
y1
y2
Non Pareto-optimal !
Routing (y1, y2) Average Delay (overlay1, overlay2 )
NE (0.5, 1.0) (1.5, 1.5)
Pareto Curve (0.4, 0.9) (1.4, 1.4)
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Fairness Paradox
physical link delay function de(le)
1-5 al
3-4 bla
2-6 cl
y1
y2

• a, b, c, aare non-negative parameters
• Everything is symmetric except two private links
  a c

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Fairness Paradox
physical link delay function de(le)
1-5 al
3-4 bla
2-6 cl
y1
y2
a lt c
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Fairness Paradox
physical link delay function de(le)
1-5 al
3-4 bla
2-6 cl
y1
y2
a lt c ? delay1 gt delay2
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Fairness Paradox
y1
y2
Unbounded Unfairness
a lt c ? delay1 lt delay2
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War of Resource Competition
1 unit
1 unit
USA
China
poil(y1y2)
pusa(1-y1)
pchn(1-y2)
pusalt pchn
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War of Resource Competition
1 unit
1 unit
y1
USA
China
poil(y1y2)
Min Costchn(y2 y1) y2poil(y1y2)(1-y2)pchn(
1-y2)
pusa(1-y1)
pchn(1-y2)
pusalt pchn
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War of Resource Competition
1 unit
1 unit
USA
poil(y1y2)
China
pusalt pchn ? Costusa gt Costchn
pusa(1-y1)
pchn(1-y2)
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Navigation

• Overlay Networks Preliminary
• Motivation
• Mathematical Modeling
• Overlay Routing Game
• Implications of Interaction
• Pricing
• Conclusion

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Pricing
Mechanism Design
Inefficient Nash equilibrium
Desired equilibrium
payment
new Nash equilibrium
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Pricing I Improve Delay

• Objective to achieve global optimality

• NE of overlay routing game

• Global optimal

le(s) traffic of overlay s le(-s) traffic
other than overlay s
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Pricing I Improve Delay

• Objective to achieve global optimality

• New NE of overlay routing game

• Global optimal

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Pricing I Improve Delay

• Global optimal

• New NE of overlay routing game

KKT condition
KKT condition
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Pricing II improve fairness

• Cause of unfairness
• Over-utilize good common resources
• Unfair resource (bandwidth) allocation
• Pricing Scheme

price p
ISP
Overlay
Improve performance Reduce cost
maximize profit
routing decision
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Incentive Resource Allocation

• For overlays

new Nash equilibrium ? le
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Revenue Distribution

• For ISPs (links)

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Interpretation of Price
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Effectiveness of Pricing
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Conclusion

• Study the interaction between multiple
  co-existing overlays.
• Non-cooperative Nash routing game.
• Prove the existence of NEP.
• Show the anomalies and implications of the NEP.
• Present two pricing schemes to address the
  anomalies.

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Thanks for your attention!

• Comments
• Q A

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Backup Slides