How to Approach New Industries and Gain Insights Into Their
Development Dynamics
- Examples of the German Aviation Industry
Friederike Behrens
friederike.behrens @ecad-aviation.de
Eva-Maria Cronrath
eva.cronrath @ecad-aviation.de
Alexander Zock
alexander.zock @ecad-aviation.de
* European Center for Aviation Development - ECAD GmbH
Lise-Meitner-StraBe 10
D-64293 Darmstadt
Phone +49 6151 3605 400
Fax +49 6151 3605 490
In today’s business environment it is essential to be able to gain insights in a yet unfamiliar
industry under tough time constraints. The 7 step framework we suggest addresses this issue.
Following the standardised sequence of steps will direct the user to identifying the industry’s
main influencing factors. The historical development of the industry’s output variable will be
approximated by model simulations. An analysis of the peaks in relative deviations between
real and simulated data will spotlight the industry's significant events and influencing
factors. Compared to traditional market and environment analysis techniques our
framework takes the particular industry’s development dynamics into account. Thus we
choose System Dynamics as underlying methodology which has already proven useful for
understanding market dynamics and gaining structural insights. The 7 step framework will
be illustrated with the development of passenger traffic at German airports.
Keywords: Industry Dynamics, Air Transport, Airports, Peak Travel
Today’s business world consists of various industries in which we observe diverse
developments. Therefore, decision makers such as politicians, managers, consultants,
methodology specialists, or researchers can often find themselves confronted with the
demand to gain insights in an industry they are not familiar with. The question is, how to
approach an industry you cannot enlighten drawing from your experience. How can you
achieve a general understanding of that industry given the usual tight time constraints? We
aim to give a framework to address this issue using the civil air transport industry in
Germany as an example.
The literature in the field of market and environment analysis is extensive though mostly
building on a_ selection of traditional techniques (see e.g. Mintzberg, 2005;
Homburg/Krohmer, 2003; Johnson/Scholes, 2002). Among those are Porter’s (1979; 1980)
five forces industry analysis and the strategic group analysis (Porter, 1980; Welge/Al-
Laham, 2008) which aim to understand the situation within an industry. Besides approaches
such as the SWOT analysis (Sudharshan, 1995; Chermack/Kasshanna, 2007) and the
PEST(EL) framework (Johnson/Scholes, 2002) are intended to also include information
about political, economic, social, technological, environmental and legal influences on an
industry.
Using these traditional techniques when faced with the need to develop an understanding for
a new industry promises a sound comprehension of the market, its mechanisms and the
future opportunities and threats it yields. However, there are disadvantages attached to the
traditional techniques. First, they require a large amount of data and moreover time
investment. For a person without experience in the particular industry a compilation of the
PESTEL factors, for example, is probably as time consuming as evaluating the threat of
substitute products or the degree of competitive rivalry as forces in the yet unfamiliar
market. In practise both time and data resources are usually scarce. Secondly, the traditional
techniques are static. The analyses look at the market’s present situation only and try to
incorporate possible future scenarios based on foreseeable events. The market’s development
dynamics up to the present day are not taken into account.
The question is, given time and data constraints how can we ensure to capture the important
facts concerning the new industry? How can we understand the industry’s development
dynamics? In this paper we suggest a framework for getting insights into new industries that
(1) directs the user straight to significant events and influences and (2) accounts for the
particular industry’s dynamics. The framework is a 7 step approach as illustrated in Figure 1.
The underlying methodology is System Dynamics as it allows parameter-based simulations
and has already proven useful for understanding market development dynamics and gaining
structural insights (see e.g. Lyneis, 2000).
Step | What to do
1 Define industry’s output variable according to your interest
2 Observe general trend in the historical development of the
industry’s output variable
Reduce complexity by focussing on the main players
4 Approximate the industry’s growth pattern
5 Analyse differences between modelled and historical behaviour
of output variable
6 Iterative process: Insert learnings in the model and analyse
variances
7 Recapture your insights
Figure 1: Illustration of the framework
Step 1: Define industry’s output variable
The first step to understanding an industry is to define its output variables of interest. In our
example of air transportation the output could be measured in terms of passengers and
freight transported at German airports. However, in this paper we assume to have an interest
in passenger traffic at airports only’.
Step 2: Observe general development trend
The next step is to observe a general trend in the historical development of the industry’s
output variable. Following our example, the progress of passenger traffic in Germany is
shown in Figure 2 (see German Federal Statistical Office, 1951-2007). The general pattern
we can observe is a growth trend. The data shows a steady growth pattern with short-term
periods of stagnation and a high concentration of passenger traffic onto the top 10 airports in
Germany. The curve further on displays a tendency towards different growth regimes (50s
and 60s, 70s, 1982 - today).
Step 3: Reduce complexity
Before starting to conduct an analysis we suggest to reduce complexity by focussing on the
industry’s main players and their contribution to the general development. For passenger
traffic in Germany we find that the top 10 airports in 2006 accounted for 92% of total annual
air passengers in Germany (see Figure 2). Thus, we will limit our further analysis to the
manageable number of 10 airports.
Passengers (m)
200
150
100
0
1951 1961 1971 1981 1991 2001
——Top 10 Total
Figure 2: Passenger traffic at German airports in the years 1951-2006
Step 4: Approximate industry’s growth pattern
To analyse the given growth data it was decided to employ a modelling approach that is not
targeted at explaining the observed growth characteristics in detail, but tries to identify the
: Passenger traffic at airports is defined as the sum of passengers that have embarked or disembarked at all
airports in a considered country.
Market Potential
(Initial Value) empliids
<Time>
Market .
Increase of | Potential Modulation by . time Offset
See | industry cycle
Fractional
increase rate
Period of
Cycle
Passengers
Passenger Decrease of
Increase x Passengers
Co Relative
alpha beta growth rate
Figure 3: Logical Structure of the applied system dynamics model of an extended “Bass-model’. In the
framework of this paper, only the basic version of the “Bass-Model” was used.
archetypical growth pattern underlying the data. Typical patterns that can be observed in
nature are for example linear, exponential, hyperbolic or logistic growth. Typically the first
three growth patterns are only observed over a limited time period, whereas logistic growth
might be applicable to quite longer time periods as its S-shaped growth characteristic reflects
both growth driving as well as growth limiting processes.
A typical application of the logistic model can be found in the literature on product diffusion
processes, e.g. the market penetration of a new electronic device in the market. The
fundamental paper describing such application was published by Bass in 1969 (Bass, 1969).
Bass incorporates in his model, which was consecutively also named “Bass-Model”, the
superposition of three processes: (a) a linear growth process proportional to a theoretical
market potential for a product, which describes the starting phase of the logistic growth and
might be identified for example with advertising efforts, (b) an exponential growth process
that is proportional to the number of customers of the product under investigation (this part
is often called the “word-of-mouth effect”) and (c) a hyperbolic or super-exponential process
that inhibits further growth and shows a square relationship to the number of customers
divided by the market potential. According to Sterman (2000) and Mahajan/Muller/Bass
(1990) the “Bass-Model” is the most widely used model to portray the diffusion of
products.’
2 Original notation (Bass 1969, 217): f(t\(1-F(t))=p+qF(t)=p+qY(t)/m with p and q as innovation and
imitation coefficient, F(t) as cumulative distribution function, and f(t) as probability density function of the
random variable f, the time of new product’s adoption. Y(t) as cumulative sales at time , and m as total
market potential.
A modified mathematical expression of the “Bass-Model” reflecting the above described
structure looks as follows:
=a-N+(B-a)-A- po
dt
with N being the market potential, A being the number of customers at a certain time and a
and f being parameters that are normally used to describe the effectiveness of advertising
and the “word-of-mouth” process. A depiction of the logical structure of the “Bass-Model” is
shown in Figure 3, which additionally shows potential extensions of the simple model
version in the form of inclusions of for example a variable potential market size or the
variation of the customer growth rate by a cyclical process (e.g. business cycle).
To apply the “Bass-Model” to the considered growth process in the German Aviation system
it is important to clarify the interpretation of the model structure in the framework of this
industry setting. Here we assume that the product, whose diffusion is modelled by the “B:
Model”, is the use of air transportation. This means that a given number of customers at a
certain moment in time will be interpreted not as identifiable individuals but simply as the
number of flying people, whereas this number might include multiple purchases of a flight
ticket by a certain individual as well as the exchange of customers in the course of time.
Given this understanding of the model structure, the number of customers A does reflect the
dynamic equilibrium number of passengers in the German Aviation system.
To apply the “Bass-Model” to the given data it is necessary to estimate the market potential
for the considered market. This is a difficult task as there is no data available that can be
relied on. Nevertheless, there are some data sources available that can be used to get an idea
of the magnitude of the market potential e.g. the widely used traffic forecast by Intraplan
(2006) for German airports. Intraplan estimates the market size for air travel in Germany in
the year 2020 to be 307 million passengers. For the 10 biggest airports this number is
expected to be about 270 million passengers. As no exact data was available for the
theoretical market potential we used in the course of this work a rough estimation scheme in
combination with a sensitivity analysis. Other approaches for market potential estimation can
be found in the literature (see for discussion of methods e.g. Lee et al., 2007; Sakarya, 2006;
Thomas, 1985).
The initialised “Bass-Model” is fitted to the historical data displayed in Figure 2 via an
optimization routine that tries to minimise a so called pay-off-function that is a measure of
the model prediction error’.
When applied to the data, the analysis of the traffic at the top 10 airports in Germany shows
a strikingly good agreement between model and passenger data as well as the data for
+ The best fit between model curve and historical data is defined as having the maximum payoff. The payoff is
a single number that summarises a simulation by which model parameters are compared to historical data. To
find the maximum payoff, numerous simulations are run with varying diffusion parameters Alpha and Beta.
The parameters are set to be equally important, so that their weights for the payoff calculation are 1. At each
TIME STEP the historical data set is checked to see if a historical value is available. If it is available, the
difference between the data and the model simulation is multiplied by the weight specified and this product is
then squared. This number, which is always posit is then subtracted from the payoff so that the payoff is
always negative. Maximizing the payoff means getting it to be as close to zero as possible.
-5-
absolute growth and relative growth rates (the trend is captured over a period of 50 years) as
can be seen from Figure 4 and will be discussed in more detail in the following.
Comparison of Simulated and Historical Comparison of Simulated and Historical
Passenger Traffic Development Relative Growth in Passenger Traffic
2 250 120%
3
2 100%
5 200 nae ollcrisis_—_ "99 war
0 60%
100 40%
a 20%
0%
0 -20%
exesgeeresyengyene enesegenrsegegneg8ensg
BRRRRRRRREESSSSS RAaRaggagaagsgss
SLASAAAAASARRARK SASSARARAAARRRAR
—— Desiatis Data Opt. 300 = = *Opt.350 — opt. 300 ——Destatis Data
Comparison of Simulated and Historical Deviation between Simulated and Historical
Absolute Growth in Passenger Traffic Absolute Growth in Passenger Traffic
vw 8
& 6
54
2
0
2
4
6
8
-10
exexeveseeenegnone enegeengoeen eg
Opt.300 = = =Opt.350 Destatis Data “= Deviation Data - Opt. 300
Figure 4: Approximating the growth pattern of passenger traffic at German Airports in the years 1951-
2006 with an S-shaped growth pattern (based on a Bass-modelling approach): Historical data for
passenger number versus model simulation (top left), historical relative growth rates versus predicted
growth rate (top right), historical absolute growth rate versus predicted growth rate (lower left) and
absolute deviation between absolute growth rate and predicted growth rate (lower right).
Step 5: Analyse differences between modelled and historical behaviour
(a) Comparison of the absolute number of passengers in the German Aviation system
with the predicted number (Figure 4, top left):
From an overall perspective the agreement between historical passenger data and the
predicted values is quite satisfying with an extremely good fit in the time period from 1950
to the end of the 1960s. In the 1970s a prominent deviation appears before the oil crisis in
1973, which might be attributable to the suppressed growth rates in the time after the oil
crisis. For the period starting at about 1975 up to today it appears that the simulated curve
reflects an average development that does not fit the historical data in detail, which seems to
display a sequence of lower and higher growth rates if compared to the simulated curve.
Nevertheless, through the succession of these varying growth rates, the average trend of the
data is very well reflected in the simulated data as it was stated above. Interestingly, the
-6-
influence of a variation of the theoretical market potential between 300 and 350 million
passengers seems not to have a dramatic effect on the overall fit between the historical data
and the simulation. A notable difference becomes only visible for the time period between
2010 and 2020.
(b) Comparison of the relative passenger growth rates in the German Aviation system
with the predicted relative growth rates (Figure 4, top right):
If one considers the overall trend in the development of the relative growth rates for
passengers in the German Aviation system it is interesting to note that the growth rates show
a continuous decline over the last 50 years. This does not reflect a slow down in the growth
dynamics (as can be seen from the discussion in the next section), but is merely the result of
the fact that it is easier to grow at high rates when the base of the growth is smaller than
when the base has grown to larger numbers. This phenomenon is often overlooked for
example in the low cost discussion, where the higher growth rates of low cost carriers are
often mistaken for higher absolute growth in passenger numbers when compared to classical
carriers. Another interesting observation can be made if one concentrates on the dips in the
historical data curve as these dips are clearly correlated to external factors as the first oil
crisis (1973), the 80s recession, the second gulf war (1991), the Asia crisis (1997) and the
events around 9/11. This correlation seems mainly to stem from the high correlation of
industries growth to developments of the GDP (Helenius, 2003; Hamburg Airport, 2008;
Pompl, 2006). Other influencing factors can be found in political events as for example in
1972 when the so called transit agreement between the Federal Republic of Germany and the
former Soviet Union guaranteed landside access to West Berlin so that the airside connection
between West Berlin and for example Hannover lost most of its importance and the overall
growth rate of the top 10 airports in Germany declined sharply (see Treibel, 1992). All these
events are clearly visible in the data and therefore show that the growth rates in the aviation
industry are extremely sensitive to such events. Despite the fact that these dips are not
reflected in the simple growth model that we applied here, it is encouraging to see that the
overall average trend of the growth rates can be captured by the model quite nicely with
deviations in both directions (under- and overestimation); an observation already described
in the last section. Based on this finding a last interesting feature can be seen in the displayed
curves, which is the continuous decline in growth rates predicted for the time period after
2008. According to the model the growth rates in the system will continue to decline up to
the year 2020 and possibly onwards.
(c) Comparison of the absolute passenger growth rates in the German Aviation system
with the predicted absolute growth rates (Figure 4, lower left and lower right):
The absolute growth rates for passengers in the German Aviation system show in their
historic course an overall increase from the 1950s up to today. This overall growth trend is
superimposed with strong deviations into the positive and the negative direction. If one
compares these deviations with the external events described in the last section again a clear
correlation is visible as can be expected. It appears that the logic behind these deviations is
that an external crisis first hits the industry by suppressing the growth rates down to negative
growth numbers to be followed then by growth numbers that exceed the average growth
rates by far. This effect seems to reflect a tendency in the industry to catch up losses after a
crisis by growth numbers that are higher than the average long-term numbers. This
interpretation is further on corroborated by an analysis of the differences between the
historical data and the simulated trend, as this data series shows mainly variations around the
x-axis without any remaining clearly discernable trend.
If we summarise the findings described above it appears to be justified to put up the
hypothesis that passenger growth in the German Aviation system can be characterised by a
logistic-growth pattern. The deviation analysis further on spotlights the important influence
which political, economic, social, technological, environmental and legal factors have had
and will have on the growth pattern in the aviation industry. Based on these insights we will
focus in the next step on possible further analysis and derivation discussions that can be
performed on the basis of the above outlined hypothesis.
Step 6: Iterative process: Insert learnings in the model and analyse variances
In this step we will extend our analysis of the passenger data in the German aviation system
in two ways. First, we will use the logistic growth hypothesis to derive some non apparent
consequences for the aviation system if the system actually follows a logistic growth
trajectory. Secondly, we will have a closer look at the observed deviations between the
historical data and the simulated data to apply a time wise segmented growth simulation.
(a) “Peak Travel” analysis in the German aviation system:
A major drawback of the “Bass-Model” used in the last section has been its dependence on
the beforehand knowledge of a theoretical market potential of a considered market. As such
data is usually not available a detailed analysis of such a market is severely hampered.
Fortunately it is possible to find in the literature a wealth of applications of the logistic-
growth model to real world data sets that try to deal with this problem. An especially
interesting application can be found under the term “Peak Oil” (see for example Hubbert,
1956; Deffeyes, 2001). The term “Peak Oil” relates to the phenomenon that the production
rate of oil is expected to peak long before the available resources of oil will be depleted. This
finding was first presented by M. King Hubbert in 1956 when he predicted that the US oil
production would peak in the early 1970s, what it ultimately did. Hubbert’s methodology
mainly comprised the use of the hypothesis, that the production of crude oil follows a
logistic growth pattern. Based on this assumption he derived from the mathematical
formulation of logistic growth an approximation that allows deriving from empirical data on
crude oil production the most likely point in time when “Peak Oil” will appear. This is done
in a two step process which first includes the empirical derivation of an estimate for the
overall size of the available oil resources and then based on that estimate the calculation of
the “Peak Oil” point based on the relationship that “Peak Oil” appears for logistic growth
patterns at the point in time, when half of the available resources of oil have been conveyed.
In practice this two-step procedure is based on a graph that relates the amount of conveyed
oil on the x-axis with the ratio of actual production divided by the cumulative amount of oil
that has already been conveyed. If one plots empirical data about oil production in this
graphs one gets for the long-term tail of the curve a straight line that intersects the x-axis at
exactly the point where the available resources have been depleted completely, i.e. the
theoretical size of the available resources.
The above explained scheme of “Peak Travel”-analysis can be applied to the aviation
industry in the following way. The cumulative amount of conveyed oil is equivalent to the
number of passengers one finds in the system at a certain point in time. This interpretation
means that at zero growth we will not have zero passengers in the system but will find an
equilibrium number of passengers that will continuously travel in the system. The ratio of
the actual oil production to the cumulative amount of conveyed oil can be translated to the
relative growth rate of passengers in the aviation system. Applying this translation scheme to
the data of the German aviation system yields to the results displayed in Figure 5.
-8-
90%
70% 4
50%
30%
10%
-10%
° ° ° i) =) re] °
n o 7) r=) 0 r=)
d d a a ”
Passenger [Millions]
* Destatis Data “==™Opt. 300
Figure 5: Comparison of a “Peak Travel’ analysis for the German Aviation System based on the historic
data displayed in Figure 4 in comparison to a simulated system growth trend using a “Bass-model”-
simulation with a theoretical market potential of 300 million passengers.
Looking at the data displayed in Figure 5 the visible match between the simulated growth
trend of the “Bass model” (assuming a market potential of 300 million passengers) and the
historic data is again quite well. Additionally, it is interesting to note that the travel data,
despite its noisy appearance, settles into a trend line as it would be expected based on the
“Peak Oil” observations. Given this finding it appears to be possible that the German
aviation system is heading for a “Peak Travel” point in the near future. If we assume market
potentials of about 300 or 350 million passengers, this would even translate into “Peak
Travel” points at around 2005 or 2007/2008. This result is also shown in Figure 4 (bottom
left) in the simulated data for the absolute growth numbers in the German aviation system as
these growth numbers clearly peak at the above stated points in time. Such findings are of
great interest if we aim at understanding the future growth trajectory of the aviation industry
in Germany, as a “Peak Travel” phenomenon would put highly challenging constraints on
growth strategies of airlines operating in such an environment. Therefore, it is important to
note that despite the apparent fit of the logistic growth model to the industry trend of the last
50 years, the mathematical consequences of such a similarity have so far not acknowledged.
For example the possible existence of a “Peak Travel” phenomenon in the German aviation
system, that might possibly appear in the near future, is not yet subject of discussions.
-9-
(b) Segmented growth modelling for the German aviation system:
In Step 5 in the course of the comparison of the historical data with the simulated data it was
found, that the simulated curve showed an extremely good fit to the empirical data in the
1950s and the 1960s. After that time the growth characteristic seemed to have changed
slightly so that as a consequence of this behaviour the fit in later years showed some higher
deviations from the historic curve. Based on these observations it appears promising to
compare the optimisation results that one would get if the analysis would be restricted to
defined periods of time, e.g. 1951 — 1971 and 1982- today. The results of such a calculation
are displayed in Figure 6. They show a strong deviation in the growth trend between both
curves, with much higher growth rates for the curve that was fitted to the time period from
1951 — 1971. According to this growth scenario, the 2006 passenger number in the German
aviation system would already have been reached at the end of the 1980s. Given these results
it seems that the growth pattern in the industry went through a huge change during the early
1970s until it settled again for a weaker overall growth from the 1980s onwards.
2 300
2
250
200 ca
150
100 +
so
1950
1980
1985
1990
1995
2000
2005
Destatis Data = = =Upto1971 —— =From19820n
Figure 6: Historical development vs. segmented simulation model of passenger traffic at German
airports for the time periods of 1951 — 1971 and 1982 onwards
If this segmentation approach is extended further to decrease the remaining deviations
between the empirical data and the simulated data, we settle with a model that uses four
segments between 1951 and 2006 that look as follows:
Segment 1: 1951-1972
Segment 2: 1973-1981
Segment 3: 1982-2001
Segment 4: 2002-2006
» 10+
Passengers (m)
200
FP=0,9635
150 A
lal
100 Z
fo
y
50 af
J
0
1951 1961 1971 1981 1991 2001
—— Passengers
Segmented Simulation Model
Figure 7: Historical development vs. extended segmented simulation model of passenger traffic at
German airports in the years 1951-2006
Using this segmented model, an even better fit between the empirical and the simulated data
can be achieved as can be seen in Figure 7. The four-segment model delivers an R’ of 0.96,
which reflects a high correspondence between the empirical data and the simulation data.
Step 7: Recapture your findings
Summarising the findings of the six steps that have been employed in the frame of this
paper, it can be stated that the proposed analysis scheme is capable of aiding a thorough
analysis of a key performance indicator of a complex industry like the aviation industry in a
way that enables the identification of significant insights. The basic insights into the German
aviation industry are:
e The growth pattern of the passenger number in the German aviation system can be
approximated for the time period of the last 50 years by a logistic growth model
(“Bass model”).
e The logistic growth model does not only suitably characterise the overall growth
trend in the passenger numbers of the German aviation system but is also capable of
providing a good fit to the absolute and relative growth numbers per year.
e Major deviations between the model and the given empirical data are always related
to external socio-economic or political influencing factors such as oil crises or
economic recessions.
e The application of a “Peak Travel” analysis on the German aviation system, i.e. the
assumption of a logistic growth pattern for passenger growth, enables the derivation
of further unexpected insights into the industry.
oy ie
e An extension of the simple modelling approach by a segmentation approach in time
is capable of increasing the quality of the fit between the model output and the
empirical data significantly.
Conclusions
The presented framework shall be understood as a complementary approach to various
business techniques for examining an industry, tailored to todays usually time constrained
situations. As opposed to many traditional techniques the framework focuses on gaining
dynamic insights into the respective industry by basing the analysis on time series
modelling. To conduct the analysis it is thus inevitable to have access to time series data on
the desired industry output.
When contemplating emerging markets, however, a lack of historical data and possibly also
difficulties in estimating a market potential will limit the frameworks applicability. Sakarya
et al. (2007) discuss the specifics of dealing with emerging markets and also give examples
of how to assess the market potential in such cases.
The framework is open to the users’ own ideas in terms of which generic growth pattern to
test for and how to insert learnings into the simulation model. To build on the “Bass model”
and then extend this approach to a “Peak Travel” analysis or a segmentation approach is only
one option. Another option could be to consider the influence of a business cycle in the
model (see e.g. Liehr et al., 2001; Jiang/Hansman, 2006).
In today’s business environment the demand to gain insights into a yet unfamiliar industry
under tough time constraints is increasingly high. Although the literature in the field of
market and environment analysis is extensive, the application of most traditional techniques
involves some disadvantages, especially under time and data constraints. The 7 step
framework we suggest addresses this issue.
Opposed to traditional techniques our framework puts its main focus on the particular
industry development dynamics and is thus very similar to the standard System Dynamics
modelling approach for dynamic problems (see for example Sterman, 2000).
By following a standardised sequence of steps the user will be able to identify the industry’s
main influencing factors. The historical development of the industry’s output variable will be
approximated by model simulations. A deviation analysis can then also reveal peak
deviations between the historical and simulated values and will thus draw the user’s attention
to important industry specific turning points. Interpreting the spotlighted events will enable
the user to improve the model and hence the approximation of the historical data. In addition
the use of a model might extend ones analysis capability by a modest forecasting possibility.
Future research could focus on integrating a business cycle into the model as well as time-
varying market potentials that would allow for an alternative incorporation of different
stages in the industry’s development. Lastly, it may also be worthwhile to replace the
employed “Bass Model” by an industry adjusted modelling approach that would allow a
more meaningful interpretation of used model parameters.
» 12«
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