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Internet Congestion and Pricing
An Overview


Prof. David Bernstein
James Madison University

The Graduate Reading Forum
James Madison University

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Overview
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  • The current Internet service model
  • Offering different levels of service
  • Pricing of service levels
  • Pricing Internet congestion
Current Service Model
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  • Applications are given "Best Effort" service
  • All applications receive the same level of service
Hidden Levels of Service
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  • The Situation:
    • You buy a T3 connection (45mbps)
    • Your normal requirements are 15mbps
    • You sell 30mbps but give yourself priority
  • The Result:
    • There are two levels of service
Categorizing Existing Applications
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applications.gif
Corresponding Levels of Service
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  • One Approach: Shenker (1995)
    • Firm Delay Bounds
    • Loose Delay Bounds
    • Best Effort 1
    • Best Effort 2
    • Best Effort 3
  • Other Approaches are Possible
Offering Different Levels of Service
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  • The Result:
    • People will mark everything high priority
  • Possible Fixes:
    • Precedence Pricing (Bohn et al., 1994)
    • Packet Auctions
    • Smart Markets (MacKie Mason and Varian, 1995)
Precedence Pricing
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  • The Idea:
    • The government sets precedence numbers for different applications
  • The Criticisms:
    • Increased regulation
    • Maintenance difficulties (as applications change)
Packet Auctions
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  • The Idea:
    • Each packet has a "bid" field
    • Packets are processed in order of bid
    • Users are charged the bid
  • The Criticisms:
    • Users will tend to underbid
Understanding Packet Auctions
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  • Assume:
    • Two packets
    • Each packet can have a different "value" or willingness-to-pay
  • Notation:
    • wi denotes the maximum willingness-to-pay for packet i
    • bi denotes the bid of pay for packet i
    • xi denotes the excess value of packet i
Understanding Packet Auctions (cont.)
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  • Excess Value:
    • eq1.gif
  • Expected Excess Value:
    • eq2.gif
Understanding Packet Auctions (cont.)
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  • More Assumptions:
    • The willingness-to-pay of each packet is uniformly distributed on [0,1]
    • Each packet's bid is a percentage of its willingness-to-pay eq3.gif
Understanding Packet Auctions (cont.)
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  • Consider What Packet 1 Knows:
    • 2's highest possible bid is α 2
    • eq4.gif
Understanding Packet Auctions (cont.)
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  • Packet 1's Problem:
    • eq5.gif
  • Solution:
    • Differentiating (ignoring the constraint)
    • eq6.gif
    Expand
Understanding Packet Auctions (cont.)
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  • Packet 2's Solution:
    • eq7.gif
  • Making Them Both Happy:
    • eq8.gif
Smart Markets
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  • The Idea:
    • Packets are processed in order of bid
    • Users are charged the capacity-clearing price
  • The Criticisms:
    • Cost of micro-transactions
    • Might require packet sampling
    • Accounting problems (IP addresses aren't people)
Understanding Smart Markets
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  • Excess Value:
    • eq9.gif
  • Expected Excess Value:
    • eq10.gif
Understanding Smart Markets (cont.)
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  • Packet 1's Problem:
    • eq11.gif
  • Solution:
    • Packet 1 can only influence the probability, not the payoff
    • So the bid should be as large as possible
    Expand
Pricing Internet Congestion
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  • Some Observations:
    • The demand for Internet services depends on the time required to process requests
    • The performance of the system depends on the number of requets
  • The Result:
    • The Internet is over-used
Pricing Internet Congestion (cont.)
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  • Notation:
    • T denotes the service time function
    • R denotes the inverse request function
Pricing Internet Congestion (cont.)
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  • Equilibrium:
    • equilibrium.gif
Pricing Internet Congestion (cont.)
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  • The Optimal Usage:
    • eq12.gif
  • Solution:
    • eq13.gif
    Expand
Pricing Internet Congestion (cont.)
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  • Comparing the Optimum and Equilibrium:
    • optimum.gif
Pricing Internet Congestion (cont.)
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  • About the Comparson:
    • The Internet is over-used
    • Pricing can fix it
Conclusions
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  • There are several arguments for Internet pricing
  • Proper pricing may require complicated mechanisms
  • Internet applications may need to include pricing logic
There's Always More to Learn
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