Oct 17 2003 SOM Brownbag
Mechanics of Internet Diffusion
Amitava DuttaGeorge Mason University
Rahul RoyIndian Institute of Management, Calcutta
Oct 17 2003 SOM Brownbag
Agenda
• The problem and motivation to examine it• Current understanding of Internet diffusion• Causal Model based on System Dynamics• Model Validation• Advantages and disadvantages of SD• How will validated model inform us?
Oct 17 2003 SOM Brownbag
The Problem & Motivation to Examine it
• The problem– Diffusion, Internet, Mechanics– spread, proliferation, dispersion of the ‘Internet’ over space/time– Don’t just characterize the dispersal pattern, identify the
underlying mechanics (how)
• Motivation– interactions between technology and non technology factors. – Service providers, infrastructure planning– To affect diffusion through policy, need to know mechanics
Oct 17 2003 SOM Brownbag
Oct 17 2003 SOM Brownbag
Oct 17 2003 SOM Brownbag
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Current Understanding
• Lots of descriptive statistics on host growth• Usage patterns (email, chat newsgroups etc.)• Some correlational studies• Growth curve estimation models
Oct 17 2003 SOM Brownbag
One Missing Piece
• None of the previous work tells much about underlying mechanics.
• “When changing behavior is your aim, causation must be your game”
• Once we know the underlying mechanics, we can analyze the impact of ‘turning’ different knobs and see what that does to behavior (diffusion).
Oct 17 2003 SOM Brownbag
Methodology
• System Dynamics (Forrester 1959)– Stocks and Flows– Physical and Information Flows– Feedback Loops– Nonlinear relationships
• Policy Analysis• New Product Diffusion• Technology Management
Oct 17 2003 SOM Brownbag
Simple Contagion Model of DiffusionN
t
dx/dt = (a + bx)(N-x)a= coeff of innovationb= coeff of imitationN= market size
Potcust CBought
Buying
ConstA ConstB
CBought(t) = CBought(t - dt) + (Buying) * dt
INIT CBought = 0
INFLOWS:
Buying = (ConstA+ConstB*CBought)*Potcust
Potcust(t) = Potcust(t - dt) + (- Buying) * dt
INIT Potcust = 10
OUTFLOWS:
Buying = (ConstA+ConstB*CBought)*Potcust
ConstA = .01
ConstB = .02
PotCust CBought
Buying
ConstA ConstB+ +
+
-
+
+
Oct 17 2003 SOM Brownbag
System Dynamics Model Simulation Run
1:25 AM Wed, Oct 08, 2003
Diffusion Curve
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Time
1:
1:
1:
0
50
100
1: CBought
1
1
1
1
Oct 17 2003 SOM Brownbag
Actual Adopters
No. of AdoptersPer Period
ImitatorFraction
InformationValue
Economic ActivityLevel
Human DevelopmentIndex
++
+
+
+
InnovatorFraction
+
Population Growth
PotentialAdopters
+
+
+
Security ThreatLevel
-
ApplicationVariety
InterOperability
InfrastructureUtilization
-
-
CapacityShortfall
InfrastructureCapacity
++
-
Number ofProviders
AccessPrice
-
+
+
+
+
+
-
+
+
+
+
+
+
- +
+
+
Level of Competition
+
ContagionEffects
Social, Economic FactorsTechnology Factors
InfrastructureFactors
Oct 17 2003 SOM Brownbag
Feedback Loops
Adopters PerPeriodInnovator
Fraction
ActualAdoptersInfrastructure
Utilization
+
+
+
-
Adopters PerPeriodInnovator
Fraction
ActualAdopters
+
+
InformationValue
+Economic
Activity Level
Human DevelopmentIndex
+
+
+
Oct 17 2003 SOM Brownbag
Feedback Loops (contd.)Adopters Per
PeriodInnovatorFraction
ActualAdopters
+
+
InformationValue
+
Economic Activity Level
Human DevelopmentIndex
+
+
+
Application Variety
SecurityThreat
-
+
+
+
Adopters PerPeriod
AccessPrice
ActualAdopters
Number ofProviders
-
++
-
ImitatorFraction
+
Level ofCompetition
+
Oct 17 2003 SOM Brownbag
Functional FormsAdopters Per
PeriodInnovatorFraction
ActualAdoptersInfrastructure
Utilization
+
+
+
-
InfraUtil = ActualAdopters * AvgTraffic/Capacity
InfraUtil
Perf
orm
ance
Performance
Inno
vFra
ctio
n
Oct 17 2003 SOM Brownbag
Functional Forms (contd.)Adopters Per
PeriodInnovatorFraction
ActualAdopters
+
+
InformationValue
+
Economic Activity Level
Human DevelopmentIndex
+
+
+
Application Variety
SecurityThreat
-
+
+
+
∆InfoValue = InfoValue*(AAeff + AVeff –STeff)Why linear? Other functional alternatives?
Oct 17 2003 SOM Brownbag
Other Functional Forms
Actual Adopters
Secu
rity
Thr
eat
Price
Imita
tion
Frac
tion
US
India
Info Value
Imita
tion
Frac
tion
HDI
Pot A
dopt
ers
Oct 17 2003 SOM Brownbag
US DataActual vs. Predicted Hosts (US)
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
90000000 9 18 27 36 45 54 63 72 81 90 99 108
117
126
135
144
153
162
Time in Months Starting From 1981
Hos
ts
ACTUAL
SIMULATED
Oct 17 2003 SOM Brownbag
India Data (a)
0200,000400,000600,000800,000
1,000,0001,200,0001,400,0001,600,0001,800,0002,000,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time (Quarter)
No.
of S
ubsc
riber
s
Obeserved Simulated
Oct 17 2003 SOM Brownbag
India Data (b)
0.0000.100
0.200
0.300
0.4000.500
0.6000.700
0.800
0.900
1.000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time (Quarter)
Frac
tion
Gro
wth
Observed Simulated
Oct 17 2003 SOM Brownbag
Validating SD Models
• There are no fully valid models. Models are valid when they can be used with confidence.
• Model structure tests. Every element of model must have real-world counterpart. Every important factor in the real system should be reflected in the model. Based on data, physics, judgment and intuition.
• Parameter tests. Based on historical data, soft variable scaling and relationships
• Boundary adequacy tests• Replicate reference mode behavior• Anomalous behavior tests
Oct 17 2003 SOM Brownbag
How will the validated model be used?
• We have a computational microworld, within which policy alternatives can be tried out
• The microworld can be used to learn about important diffusion mechanisms using dominant loop analysis
• The causal loop diagrams give a pictorial way for modelers and policy makers to share mental models
• Loop gain analysis can be used to determine which policy actions might have the most impact
Oct 17 2003 SOM Brownbag
Management Flight Simulator
Graph 1Table 1
2.70SSEGrowth
0.1SSEUsers
1,779,897SubscriberSim INITPUSR 0.016INITINCF 0.002INITIMCF 0.474PUGRFX 0.015
U Initial Values
1:23 AM Wed, Oct 08, 2003
Untitled
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Quarters
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0
1000000
2000000
0.10
0.55
1.00
0.05
0.35
0.65
0.00
25.00
50.00
1: SubscribersActual 2: SubscriberSim 3: GrwthRateObsvd 4: GrwthRateSim 5: IPRIC
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