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

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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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1:

1:

2:

2:

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3:

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5:

5:

5:

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

1 11

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