Dynamic Modelling to assist in the Understanding of
Consumer Take-up and the Diffusion of New
Telecommunications Services
Jo Osborne
BT Labs
Admin 2 OP7, BT Labs, Martlesham Heath,
Ipswich, Suffolk. IPS 3RE
Tel: + 44 (0) 1473 643677 Fax: + 44 (0) 1473 643392
E-mail: jo.osborne @bt.com
With the approaching new Millennium, the rate of telecoms evolution is continuing to
grow with business and market opportunities in abundance. This in turn creates a
necessity to understand the success or otherwise of the temporal take-up by
consumers of new products and services, (innovations). Such issues not only have
serious implications for the fundamental network infrastructure, dimensioning and
traffic, but also for profitable revenue generation.
Traditionally, the Bass diffusion curve has been used to simulate customer take-up.
This paper investigates the use of alternative methods to create different types of
diffusion curves to simulate the take-up of an innovation by a customer base. A
System Dynamics approach has been taken to examine the effect of different market
diffusion processes on the take-up of innovations. Successful diffusion and take-up of
any new innovation depends on a large number of attributes, such as perceived
quality, perceived need, actual quality and actual need. One System Dynamics
methodology discussed examines the drivers and attributes, which determine the
particular type of diffusion curve that a new innovation will probably follow. This
then indicates the likely success or otherwise of that innovation in the marketplace.
The paper also suggests future developments of the work, within the
Telecommunications environment. This is to assist in the creation of models that are
more accurate in modelling the diffusion of products and services into the UK market.
1 Introduction
Until recently, many of the System Dynamics models created in the telecoms
environment, had based their product diffusion on the Bass model of innovation and
imitation. The work described here attempts to progress that model further by
suggesting alternative mathematical options to the Bass model.
With respect to this work, the diffusion of telecoms products and services is based on
the assumption that: they are not substituting products/services already in the market,
nor repeat purchases, nor Me2' products or services. This is an unrealistic situation.
However, the importance here is to accurately model product diffusion before
incorporating too many outside factors that are beyond the telecoms providers'
immediate control. Similarly, competition has been excluded. This is to enable the
investigation of effective modelling of a company's own products/services and their
diffusion process before attempting to model the effects of the competitions'
products/services.
This paper focuses particularly on the diffusion equations that could be used in
Telecoms System Dynamics modelling and how they could be modified within the
model to give a more realistic diffusion model of consumer take-up of telecoms
products and services.
One of the main drivers for this research is that when a new product or service is
launched, it is of great importance to understand the consequent effects on the
network infrastructure, cost, revenue, etc. Therefore, accurately modelling of the
diffusion process is essential when trying to manage issues such as the cost base and
ensuring network availability.
Unfortunately, the methods used to model the diffusion of products/services within
the telecommunications System Dynamics arena are often overly simplistic, leading
to errors in the scenarios modelled.
Having recognised that there are weaknesses in the product/service diffusion
methodology often used by telecoms modellers, some investigation into other
methods has been undertaken. Alternative methods of modelling the diffusion of
innovation are discussed in this paper. Please note that this paper is put forward as a
discussion tool, it is intended to stimulate debate and invoke research into this area.
2 System Dynamics & Diffusion Curves in Telecoms Models: Factors Affecting
Diffusion
There are a large number of issues, (both internal and external to the telco), that can
affect product/service diffusion. A few of the external issues are shown in figure
2.0.1. An issue to note is that not only do they all affect the diffusion process in
different ways, but do so by varying amounts. To accurately model the effects of
certain issues on diffusion, it is important to state the assumptions that are being made
and to justify why those being modelled have been chosen and why others have been
left out.
Figure 2.0.1 External Factors Affecting Diffusion
In addition to these external issues, there are a large number of company internal
issues that contribute to the diffusion of innovation. For example, time to market,
distribution channels, network capabilities. The internal factors are to an extent, easier
to model than external ones. This is because internal information, (e.g. costs and
provisioning), is easier to obtain than external information, (e.g. customer perception).
3 Bass Diffusion in Telecoms Models
The Bass diffusion equation is the most commonly used method of simulating the
diffusion of innovation through a population or the flow of customers from one
telecoms company to another. However, it is recognised that this is not a particularly
accurate method of simulating diffusion, it uses the same curve, which is flexed, for
each diffusion process. The diffusion equation used in most telecoms SD models can
be seen in figure 3.0.1, (where "Att" represents the attractiveness of the
product/service to the customer).
Product/Service Take-Up =
((Non_Customer * Customer_Att) - (Customer * Non_Customer_Att)) * Inertia
Figure 3.0.1 Traditional Diffusion Equation
This equation calculates the flow from being a customer without the product/service
to becoming a customer with that product/service. This flow is determined by the size
of the customer base having the product and the relative attractiveness of the service.
This relative attractiveness of the product/service could be determined by a number of
internal and external factors. The factors either have a positive or negative effect on
the product/services relative attractiveness.
Non_Cust_to_Cust
Non_Cust Customer
Non_Customer_Att | Customer_Att
Inertia
Figure 3.0.2 Powersim Model Structure
The model segment shown in figure 3.0.2 is the structure of that part of the model for
the equation in figure 3.0.1.
4 Logistic Curves
One way of expanding on the diffusion equation discussed above is to incorporate an
exponential element. The equation shown in figure 4.0.1 is a logistic curve with two
variables that can be altered depending the type of product/service that is being
offered.
-1*Gain*((AttCust/AttNon_Cust)-Barri
No. of Customers = Non_Cust*(1/(1 +e) Gan (Anca AtNon_Cus)-Barrier))))
. Cust* (1/1466 ain *(AtNon_Cust/AttCust)-Barrier)}))
Figure 4.0.1 Logistic Curve
The key variables are the Barrier and the Gain. They determine the barrier to moving
and the temptation to moving respectively. The Barrier moves the curve along the x-
axis of the graph, whereas the Gain changes the shape of the curve. The smaller the
Gain, the earlier the customer's take-up the product/service after it has been launched,
but at a slower rate than if the Gain was higher. By being able to change the Gain and
the Barrier, the different diffusion processes can be simulated through one equation.
However, this requires a good understanding of the product/service being launched,
so as to select the correct values for the Gain and the Barrier.
The graph shown in figure 4.0.2 plots a number of diffusion curves that have been
generated from the equation shown in figure 4.0.1. This shows how a range of
alternative diffusion equations could be easily incorporated into a model.
Figure 4.0.2 Outputs of the Logistic Equation
5 Other Techniques to Simulate Diffusion
An alternative method of generating new types of diffusion curves is based upon the
actual market performance of real existing products/services. These could be achieved
by creating a number of diffusion curves of different shapes based on the actual
diffusion of historic products. Then depending on issues such as coverage, cost,
customer base, QoS etc., the model would select the most likely historic diffusion
curve to simulate the diffusion of the new product or service. This would obviously
require a greater understanding of product diffusion of a number of analogous
products and services already in the market and the diffusion curves that they have
followed historically. Thus, further research into existing historic products and
services with similar attributes to the new products/services would be encouraged.
This new product/service would then be substituted into an adjusted version of the
diffusion curve for the older product. This methodology would facilitate the
modelling of the diffusion of products and services according to, which of the
different curves is most appropriate.
Another way of simulating diffusion would be to use a random selector to chose one
of a number of predefined diffusion curves for input into the simulation. Thus every
time the model is run there is a, say, one in six chance of having a different diffusion
curve. Obviously, to do this, 6 different diffusion curves would have to be
incorporated into the model. This could simulate the changing environment into
which the product/service is being launched and therefore the possible effects the
change of environment would have on the diffusion of the product or service.
6 Future Developments
A way of moving this work further could be to incorporate even more modelling
techniques into a System Dynamics model to simulate the diffusion process. This
could be achieved, for instance, by using an Agent Based modelling approach. The
agent model could simulate the product/service diffusing through a population and the
diffusion curve generated from the agent model could feed into the SD model. This
would assist in the simulation of the diffusion of a product or service, through a
modelling approach that treated each agent/customer as an individual entity, rather
than forcing segmentation patterns onto a population, (which is often how System
Dynamics’ is used to model customers/populations). This could be a more realistic
method of generating a diffusion curve.
Other methods of generating diffusion curves could be to learn lessons from the world
of diseases and Epidemiology, "A key feature of Epidemiology is the measurement of
disease outcomes in relation to a population at risk", [1]. Essentially, this quote
describes how many people in a population exposed to a disease are likely to succumb
to that disease. This could be analogous to the diffusion of a product/service through a
customer base. Consequently, the spread of diseases through a population is evidently
one way of progressing the understanding the diffusion of an entity through a
customer base. Further research into this field would appear to be very wise, in the
effort to improve the simulation of the diffusion of product/service innovation.
7 Summary
This paper has discussed the use of alternative diffusion curves in telecoms System
Dynamics models and has suggested how they could be improved through expanding
on the work previously carried out in the telecoms industry. The alternative methods
could include extending the use of Agent Based models and integrate them into to
System Dynamics models to develop a more detailed model of product/service
diffusion. Another route would be to investigate further the area of disease
propagation and Epidemiology to help understand how and why disease's and
therefore products and services spread throughout a population.
8 Acknowledgements
I wish to thank Ann Matthews for reviewing this paper and Mike Matthews for the
final review and authorising its publication. I also wish to thank Tony Reeder for
contributing to the modelling discussion.
9 References
[1] Coggon, D., Rose, G. & Barker D, J, P. (1997)"Epidemiology for the Uninitiated".
Fourth Edition. BMJ Publishing Group. Pg.1.
10 Other Reading
Journal Article
Bass, F. (1969) "A New Product Growth Model for Consumer Durables,"
Management Science, Vol. 15, pp 215 - 227.
Maier, F. H. (1998) "New product diffusion models in innovation management - a
system dynamics perspective". System Dynamics Review Volume 14 Number 4
Winter. WILEY.
Book
Kotler, P. (1996) "Principles of Marketing". Prentice Hall Europe.
Mahajan, V. & Peterson, R. A. (1985) "Models for Innovation Diffusion". Sage
Publication.
Thomas, R.W., (Editor), (1990) "Spatial Epidemiology". Pion Limited.
* A Me? product or service is one that enters the market in second place after another company already
has a version of the same product/service on the market.
