Applications of Diffusion Models in
Telecommunications
Nigel Meade
2
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
3
Recent examples of diffusion in telecomms - 1
Financial Times
20/9/2004
4
Recent examples of diffusion in telecomms – 1a
Potential penetration of 20 million households
Rapid Growth
Gradual growth
Growth quickly evapoarates
Financial Times
20/9/2004
5
Recent examples of diffusion in telecomms - 2
Financial Times
22/9/2004
6
Recent examples of diffusion in telecomms – 2a
No obvious limit to potential penetration
Rapid Exponential Growth
Gradual linear growth
Growth to a saturation level
Financial Times
22/9/2004
7
Recent examples of diffusion in telecomms - 3
Financial Times
21/9/2004
8
Recent examples of diffusion in telecomms - 4
3G starts to
attract 2G
customers
Forbes
20/9/2004
9
Definition of Diffusion models
• A new technology diffuses
into a population
Early Majority
Cumulative Adoption
Early Adopters
Saturation level
Laggards
Adoption per Period
Late Majority
0
10
20
30
40
50
Time
60
70
80
90
100
10
Example – UK Colour TV
UK Adoption of Colour TV
Early Majority
Cumulative Adoption
Early Adopters
Laggards
Adoption per Period
Late Majority
0
5
10
15
20
25
Time
30
35
40
45
11
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?
12
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
13
A selection of diffusion models
Gompertz
1
0.8
0.8
0.8
0.6
0.4
Penetration (Xt)
1
0.6
0.4
0.2
0.2
0
10
20
30
40
10
20
30
40
50
Cumulative Lognormal
0.6
0.4
0.2
0
1
1
0.8
0.8
0.6
0.4
40
50
40
50
30
40
50
0.6
0.4
0.2
0
0
30
30
Weibull
0.2
Time (t)
20
Time (t)
Penetration (Xt)
Penetration (Xt)
0.8
20
10
Extended Logistic (A)
1
10
0
Time (t)
Time (t)
0
0.4
0
0
50
0.6
0.2
0
0
Penetration (Xt)
Log Reciprocal
1
Penetration (Xt)
Penetration (Xt)
Logistic
0
10
20
30
Time (t)
40
50
0
10
20
Time (t)
14
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
15
Forecasting Cable Television Penetration in US
0.6
Forecast
Region
CATV Penetration in US
0.5
Forecast of
Best fitting model
Estimation Region
0.4
Combined
Forecast
0.3
0.2
0.1
0
0
5
10
15
20
Time
25
30
35
16
Applications in Telecomms
Variable
Fixed line telephone
penetration
Business
Telephones
Author
Model
Chaddha &
Chitgokepar (1971)
Logistic
Hyett & McKenzie
(1975)
Logistic
Bewley & Fiebig
(1988)
Flexible logistic
Lee et al (1992)
Non-linear growth
Meade & Islam
(1995)
Comparison of 14
models
Meade & Islam
(1996)
Growth +
econometric
17
Modelling approaches
• Extrapolate from available data
UK Business Telephones (Mil)
12
10
8
Fixed Saturation Level
6
4
Actual Telephones
2
0
1955
1960
1965
1970
1975
Date
1980
1985
1990
1995
18
Modelling approaches
• Dynamic saturation level by relation to environmental variables
12
UK Business Telephones (Mil)
Implied Saturation Level (local logistic)
10
8
Fixed Saturation Level
6
Implied Saturation Level (NSRL)
4
Actual Telephones
2
0
1955
1960
1965
1970
1975
Date
1980
1985
1990
1995
19
Multi – national models
• Pooling data series from several countries
is used to overcome data shortage
The diffusion of Digital Cellular Telephones (DCT)
17
16
15
14
Ln(no. of DCTs)
See
• Gatignon
et al
(1989)
• Islam et
al (2002)
13
12
Belgium
11
Norway
10
Portugal
Sweden
9
Switz.
8
UK
Hungary
7
Turkey
6
Mar-92
Mar-93
Mar-94
Mar-95
Mar-96
Mar-97
Mar-98
Mar-99
20
Multi – generation models
Successive Generations of Technology
Islam & Meade (1997)
Third
Generation
Adopters
Second
Generation
Adopters
First
Generation
Adopters
Time
21
3 Generations of Austrian Mobiles
Generation 1: nmt - 450
Generation 2: TACS
Generation 3: GSM
200
150
50
100
50
0
Dec-84
Dec-85
Dec-86
Dec-87
Dec-88
Dec-89
Dec-90
Dec-91
Dec-92
Dec-93
Dec-94
0
Dec-95
Third Generation Subscribers
100
First & Second Generation Subscribers
(000)
250
22
Multi – technology models
• Forecast international adoption of technology B using
history of adoption of technology A (Meade & Islam, 2003)
0.70
0.60
4
2
018
20
Hazard Rate - h(t)
6
Frequency (%
)
Conditional hazard t1 = 4
0.50
0.40
Marginal hazard
0.30
0.20
14
Conditional hazard t1 = 14
14
10
8
2
2
Ce
llp
ho
ne
X
FA
6
Bivariate histogram of adoption times
0.10
0.00
0
5
10
15
20
25
30
Time to adoption t
Hazard rates for early and late adopting countries
23
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
24
The end