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SIMS Hal Varian
November 1999
Pravin Varaiya, Hal VarianRichard Edell, Karyen Chu, Walter Beckert
EECS, SIMS, Economics at UC Berkeley
INDEX: a status report
INDEX Hal VarianPage 2
Internet use currently has zero marginal cost for useResult: congestion (see next slide)
Internet currently uses one quality of service (QoS)Differential quality of service requires differential pricing
Research on QoSHow to engineer QoS: a lot of workWhat QoS costs: a little workHow users value QoS: nothing
Goal of INDEX project: measure how users value QoS
Motivation
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Modem use by day and user
0
20
40
60
80
100
120
140
160
180
200
220
240
260
Time of day
Mod
ems
02 04 06 08 10 12 14 16 18 20 22 00 02
256 14.4 Kbps
112 2.4 Kbps
60 1.2 Kbps
32 19.2 Kbps (15min limit)
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
100
% Users
% T
ime
51.2%
69.8%
INDEX Hal VarianPage 4
INDEX = Internet DEmand eXperiment
Web page: http://www.index.berkeley.edu
Support: Cisco Systems, Pacific Bell, Hewlett Packard,and National Science Foundation.
Information about INDEX
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Goal: Measure how much users are willing to pay forInternet Quality of Service (QoS).
Dimensions of QoSbandwidth (symmetric and asymmetric)volumecongestiondelay to connectetc.
What is our goal?
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•Give 150 Berkeley people "free" ISDN servicehardware and setup costs are freewe cover PacBell’s monthly charges
•Offer them different QoS for different prices•Simulate the QoS
same QoS choices for several weeksdifferent prices each week
•Note: real money, simulated service
How do we do it?
INDEX Hal VarianPage 7
Architecture
CampusNetwork
&Internet
Cisco 7200(DCNS maintains)
BGW(Intel PCs)
OfflineAnalysis
Supervisor
(also WWW& DBMS)
Cat 5000SwitchedEthernet NMAS
Cisco7513
PSTN
Cisco762s
Cisco7507
ISDN PRIs
ISDN BRI
1 2 3 4
IP IP
PPPUDP
IP
PPP
IP
4
4
1
4
4
2
2
2
3
3
3
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Interface for INDEX: settings
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Interface: experiment
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Interface: pricing
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Interface: choices
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Interface: asymmetric BW
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Interface: volume pricing
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Interface: billing
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Started providing service April 1, 1998have about 70 subjectssubjects proceed through experiments asynchronously
Have runsymmetric bandwidthasymmetric bandwidthvolume pricingbandwidth + volume mixture (predetermined +self-selected)pay upfront for flat pricing
Where we are
INDEX Hal VarianPage 16
Usage overall:
Symmetric bandwidth
8 kbs
16 kbs
32 kbs
64 kbs
96 kbs
128 kbsNote: 8 kbs is free
INDEX Hal VarianPage 17
Scatter plots
1000 2000 3000 4000u16
0.5
1
1.5
2
2.5
price
5000 10000 15000 20000 25000u32
1
2
3
4
price
16 Kbps 32 Kbs
INDEX Hal VarianPage 18
Scatter plots, continued
2500 5000 7500 10000 12500 15000 17500u64
2
4
6
8
10
price
2000 4000 6000 8000u96
2
4
6
8
10
12
14
price
2500 5000 7500 10000 12500 15000 17500u128
2.5
5
7.5
10
12.5
15
17.5
price
64 Kbs96 Kbs
128 Kbs
INDEX Hal VarianPage 19
Reduced form: estimate demand as a function of priceamount consumed = function of prices and individualcharacteristics
Structural: estimate parameters of utility functionchoice of bandwidth depends on value of time, urgency,etc. as well as price and characteristics
First look at reduced form, then examine some options forstructural estimates
Demand estimates
INDEX Hal VarianPage 20
u128= -2.0p128 +. 80p96 +.25p64 -.02p32 -.16p16
u96 =+1.7p128 -3.1p96 +.43p64 +.19p32 +.18p16
u64 = +.77p128 +1.8p96 -2.9p64 +.59p32 +.21p16
u32 = +.81p128 -1.0p96 +1.0p64 -1.4p32 +.15p16
u16 = +0.2p128 -.29p96 +.04p64 +1.2p32 -1.3p16
Red = negative own price effectLight = not statistically significant
Lesson: large negative own price effect, positive cross priceeffect
Log Regressions
INDEX Hal VarianPage 21
R2
ISE no ISEu128 .95 .11u96 .93 .25u64 .92 .18u32 .95 .14u16 .90 .17
ISE = "individual specific effect"; interpretationConclusion: very good fits!
How good is the fit?
INDEX Hal VarianPage 22
Notationb = bandwidth chosenx = bits transferredt = time at bandwidth b = x/b
p(b) = price of bandwidth bUtility
u(x) - [c+p(b)]t
c is value of time; varies with circumstancesf(c) is probability distribution of c
Structural estimates
INDEX Hal VarianPage 23
Let (x,b*) be choice. Optimization requires:
Rearrange to find
Note that this gives upper and lower bounds on cost of time.
Choice model
minb∗<b
p(b∗)b − p(b)b∗b∗ − b ≥ c ≥ max
b∗>b
p(b∗)b− p(b)b∗b∗ − b
u(x)− [c+ p(b∗)]x
b∗≥ u(x)− [c+ p(b)]
x
bfor all b.
INDEX Hal VarianPage 24
Plot K(c) = [c + p(bi)] (1/bi) for i = 1,...,n
Observe (cU,cL,f ) for i= 1,...,n
Picture of estimation method
c
totalcost
b1
b2
b3
cL cU
i i i
INDEX Hal VarianPage 25
Histograms for one user
2 4 6 8 10 12 14
0.2
0.3
0.4
0.5
2 4 6 8 10 12 14
0.1
0.2
0.3
0.4
0.5
2 4 6 8 10 12 14
0.2
0.4
0.6
0.8
2 4 6 8 10 12 14
0.2
0.4
0.6
0.8
INDEX Hal VarianPage 26
Can calculate average time cost for each individual usingthese frequency distributions.Table shows number of subject with average estimated timecost that falls in indicated range:
Distribution of time cost
Range 1 2 3 4 5 6 7 8 9 10 11 12
Upper bound 39 8 3 4 1 2 2 1 2 0 3 0Lower bound 63 3 0 0 1 0 0 0 0 0 0 0
Average 47 7 2 3 3 3 1 3 1 1 0 0
INDEX Hal VarianPage 27
Who has high WTP?
Prof Tech Admin StudentOccupation
2
4
6
8
Est. Time Cost
INDEX Hal VarianPage 28
Very low WTP for time (= 1/2 cent per minute)• very small charges induce large changes in behavior• lot of low-value traffic out there• admin/technical have highest WTP
WTP for population as a wholecLowMean = 0.02cUpMean = 0.40cLowStd = 0.07cUpStd = 1.11
Average cost of time
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Suppose frequencies drawn from prob distribution p(c,β)
Find distribution that is close to all the frequencies
Closeness = Kullback-Leibler entropy measure, Σ f log p
Parametric fit
maxβ
n∑i=1
fi log∫ ciU
ciL
p(x, β) dx
INDEX Hal VarianPage 30
µ=.487, σ=.32
mean = .52
Truncated Normal
0.5 1 1.5 2 2.5 3 3.5
0.2
0.4
0.6
0.8
1
INDEX Hal VarianPage 31
µ=.48, σ=.32 µ=.42. σ=.25
max entropy min SSR
Picture of CDF
0.5 1 1.5 2 2.5 3
0.2
0.4
0.6
0.8
1
0.5 1 1.5 2 2.5 3
0.2
0.4
0.6
0.8
1
INDEX Hal VarianPage 32
What about population as a whole?cLowMean = 0.02, cUpMean = 0.40cLowStd = 0.07, cUpStd = 1.11
Estimated parameters: µ=-.16, σ=.64, mean time cost = .18
Entire Population
0.5 1 1.5 2 2.5 3 3.5 4
0.2
0.4
0.6
0.8
1
INDEX Hal VarianPage 33
Possible explanations1. Our population is not representative
can look at demographics, e.g., income effects2. We only get lower bound on WTP for 128 kbs
but this is only about 1/6 of use3. We can’t control QoS outside of Berkeley network
high bandwidth isn’t worth much if congestion iselsewhere
4. We can only measure value of existing applications
Why such a low WTP?
INDEX Hal VarianPage 34
Two bandwidths8 Kbs for free128 Kbs for money
Price volume downloadedprices range from 1 to 20 cents per megabytemonthly expenditures similar in bandwidth and volumeexperiments
Volume experiments
INDEX Hal VarianPage 35
Scatterplot
INDEX Hal VarianPage 36
no ISE: u128 = -0.29 p128 R2 = 0.02
ISE: u128 = -0.24 p128 R2= 1.00
Interesting finding:amount transmitted is not sensitive to priceentire effect is individual-specific effect
Why? Probably choice offered is too extreme...
Log Regressions
INDEX Hal VarianPage 37
Current experiment: pay flat fee on Sunday to opt out ofmetered pricingMove to ADSL or cable modem?What are you interested in?
What’s next?
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