Applications of Diffusion Models in Telecommunications Nigel Meade - - PowerPoint PPT Presentation

Applications of Diffusion Models in Telecommunications Nigel Meade

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Introduction

• Recent examples of diffusion in telecomms
• Definition of diffusion model
• Survey of telecomms applications
• Extrapolation
• Use of explanatory variables
• Inter-market models
• Multi - national
• Multi - generation
• Multi - technology
• Strengths
• Weaknesses

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Recent examples of diffusion in telecomms - 1

Financial Times 20/9/2004

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Recent examples of diffusion in telecomms – 1a

Financial Times 20/9/2004 Potential penetration of 20 million households Rapid Growth Gradual growth Growth quickly evapoarates

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Recent examples of diffusion in telecomms - 2

Financial Times 22/9/2004

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Recent examples of diffusion in telecomms – 2a

Financial Times 22/9/2004 No obvious limit to potential penetration Rapid Exponential Growth Gradual linear growth Growth to a saturation level

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Recent examples of diffusion in telecomms - 3

Financial Times 21/9/2004

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Recent examples of diffusion in telecomms - 4

Forbes 20/9/2004 3G starts to attract 2G customers

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Definition of Diffusion models

• A new technology diffuses

into a population

10 20 30 40 50 60 70 80 90 100 Time Adoption per Period Cumulative Adoption Early Adopters Early Majority Late Majority Laggards

Saturation level

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Example – UK Colour TV

UK Adoption of Colour TV

5 10 15 20 25 30 35 40 45 Time Adoption per Period Cumulative Adoption Early Adopters Early Majority Late Majority Laggards

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Forecasting Issues of Interest

• What will the rate of adoption be at a

particular time?

• How many potential adopters are there in

total?

• When will peak demand occur?
• How high is peak demand?

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Problems in Forecasting

• Identify the appropriate model
• Estimate its parameters
• Predict future adoption

– (with a prediction interval).

• Model identification is crucial

– the literature reveals 29 possible models – there is no best single model

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A selection of diffusion models

Logistic 0.2 0.4 0.6 0.8 1 10 20 30 40 50 Time (t) Penetration (Xt) Gompertz 0.2 0.4 0.6 0.8 1 10 20 30 40 50 Time (t) Penetration (Xt) Log Reciprocal 0.2 0.4 0.6 0.8 1 10 20 30 40 50 Time (t) Penetration (Xt) Cumulative Lognormal 0.2 0.4 0.6 0.8 1 10 20 30 40 50 Time (t) Penetration (Xt) Extended Logistic (A) 0.2 0.4 0.6 0.8 1 10 20 30 40 50 Time (t) Penetration (Xt) Weibull 0.2 0.4 0.6 0.8 1 10 20 30 40 50 Time (t) Penetration (Xt)

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Model identification

• Meade & Islam (Management Science 1998)
• The best fitting model is not necessarily the best

forecasting model

• They propose combining criteria based on:

– Model fit (measured by R2 – Model stability (looks at one step ahead forecasts)

• These criteria suggest a subset of models which

are used to produce a combined forecast

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Forecasting Cable Television Penetration in US

0.1 0.2 0.3 0.4 0.5 0.6 5 10 15 20 25 30 35

Time CATV Penetration in US

Estimation Region Forecast Region Forecast of Best fitting model

0.1 0.2 0.3 0.4 0.5 0.6 5 10 15 20 25 30 35

Time CATV Penetration in US

Estimation Region Forecast Region Forecast of Best fitting model Combined Forecast

0.1 0.2 0.3 0.4 0.5 0.6 5 10 15 20 25 30 35

Time CATV Penetration in US

Estimation Region Forecast Region Forecast of Best fitting model Combined Forecast

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Applications in Telecomms

Logistic Chaddha & Chitgokepar (1971) Fixed line telephone penetration Logistic Hyett & McKenzie (1975) Flexible logistic Bewley & Fiebig (1988) Non-linear growth Lee et al (1992) Comparison of 14 models Meade & Islam (1995) Growth + econometric Meade & Islam (1996) Business Telephones Model Author Variable

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Modelling approaches

• Extrapolate from available data

2 4 6 8 10 12 1955 1960 1965 1970 1975 1980 1985 1990 1995

Date

UK Business Telephones (Mil) Actual Telephones Fixed Saturation Level

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2 4 6 8 10 12 1955 1960 1965 1970 1975 1980 1985 1990 1995

Date

UK Business Telephones (Mil) Actual Telephones Implied Saturation Level (local logistic) Implied Saturation Level (NSRL) Fixed Saturation Level

Modelling approaches

• Dynamic saturation level by relation to environmental variables

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Multi – national models

• Pooling data series from several countries

is used to overcome data shortage

The diffusion of Digital Cellular Telephones (DCT)

6 7 8 9 10 11 12 13 14 15 16 17 Mar-92 Mar-93 Mar-94 Mar-95 Mar-96 Mar-97 Mar-98 Mar-99 Ln(no. of DCTs) Belgium Norway Portugal Sweden Switz. UK Hungary Turkey

See

• Gatignon

et al (1989)

• Islam et

al (2002)

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Multi – generation models

Successive Generations of Technology Islam & Meade (1997)

First Generation Adopters

Second Generation Adopters

Third Generation Adopters

Time

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3 Generations of Austrian Mobiles

50 100 150 200 250 Dec-84 Dec-85 Dec-86 Dec-87 Dec-88 Dec-89 Dec-90 Dec-91 Dec-92 Dec-93 Dec-94 Dec-95

First & Second Generation Subscribers (000)

50 100

Third Generation Subscribers

Generation 1: nmt - 450 Generation 2: TACS Generation 3: GSM

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Multi – technology models

• Forecast international adoption of technology B using

history of adoption of technology A (Meade & Islam, 2003)

2 8 14 20 2 6 10 14 18 2 4 6 F r e q u e n c y ( % ) FAX Cellphone

Bivariate histogram of adoption times

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 5 10 15 20 25 30

Time to adoption t Hazard Rate - h(t)

Marginal hazard Conditional hazard t1 = 14 Conditional hazard t1 = 4

Hazard rates for early and late adopting countries

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Conclusions

• Strengths

– Intrinsic saturation level – Data based – forecasts grounded on actuality – Prediction intervals can be provided

• Weaknesses

– Data based – models prefer more data to less – Forecasts made before point of inflexion have high uncertainty

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The end