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Modeling the Mobile Service Market of the Region
and Control Problems Solution
Alexander B. Blinov Andrey I. Koblov Vladimir I. Shiryaev
Adviser to the Director, Lecturer, Professor, Head of the
Uralsviazinform Applied Mathematics Dep., | Applied Mathematics Dep.,
161, Kirova Street, South-Ural State University South-Ural State University
Chelyabinsk, 76, Lenina Ave., 76, Lenina Ave.,
Russia, 454000 Chelyabinsk, Chelyabinsk,
Tel. +7 3512 63 65 47 Russia, 454080 Russia, 454080
Fax. +7 3512 66 67 04 Tel./Fax. +7 3512 679074 Tel./Fax. +7 3512 679074
alexandr.blinov @chel.usi.ru koblov@prima.susu.ac.ru vis @ prima.susu.ac.ru
Abstract
This paper presents a system dynamics approach for the analysis of the mobile
service competitive market model. The model evaluates dynamic competition between
major operators: the dominant operator and the others. Their market share, as per the
number of subscribers, is influenced by the pricing policy, service quality, subscriber
base, potential subscribers, marketing, etc. The method for the identification of the
market carrying capacity is considered and the problem of the optimal price
management is formulated. The obtained results can be used to forecast and improve
decision-making within the real dynamic systems.
Keywords: system dynamics, modeling, forecasting, mobile service market,
price strategy, management.
Introduction
The task of analyzing existing experimental data and building growth models to
illustrate the sales volume has a wide range of implications to be considered in various
areas [4]. The results of defining the market share carrying capacity and the synthesis
of the optimal price strategy for the competitive market can be used to understand the
managerial decision-making in complex dynamic systems.
The fist part of the paper describes a system dynamics model of the mobile service
market. The model displays a process of adoption of the mobile services on the
competitive market (Figure 1). It includes information about the popularity of the
mobile services, which provides the growth of the subscriber base at the initial stage,
when the number of subscribers is significantly smaller than the potential. Such
popularity is generated by marketing, price strategy, dumping, etc.
In the second part we present the method for constructing the growth model. The
approach taken is suitable for various initial conditions (when the number of people,
who have taken an interest in the new services on offer is small). Parts three and four
focus on the actual mobile service market model. The numerical results of the modeling
process are established and the comparison with the real experimental data is made. We
also describe different scenarios of the market development and formulate the problem
of the synthesis of the optimal price strategy for the company.
The paper continues the research [1] and develops approaches [4, 6].
Distribution Model of Mobile Services on a Competitive Market
Figure 1 shows a system dynamics model illustrating the distribution of cellular
communications company services in the regional competitive market. This model is
based on the John D. Sterman’s approach [4]. The total adoption rate is the sum of
adoptions resulting from the “word of mouth” and adoptions resulting from the
company’s marketing and communication services, advertising and other external
influences. Adoptions from the “word of mouth” are formulated exactly as in the
logistic innovation diffusion model or the Bass diffusion model. The probability of
adoption by potential users as a result of an exposure to a given amount of advertising,
the volume of advertising and other external influences at each period remain constant.
The initial growth is driven by feedbacks outside the boundary of the simple
logistics models. Existing subscribers of the company, having found out about
satisfactory services available, spread the information among the unaware potential
customers. As a result of such contact, there is a probability that new subscriptions will
be made. This probability (the efficiency of the distribution of the “word of mouth’)
depends on the important principle of estimating appropriate costs for the services of the
cellular communications operator. For example, the cost of calls made within the
network of the same operator is cheaper than those calls made to destinations outside of
the network (i.e. for calls between relatives, friends and immediate family it is cheaper
to use one communications company).
An important factor influencing the rate at which customers subscribe is to inform
potential subscribers of the services available which is usually done with the help of
advertising.
It is important to clarify what is meant under “potential subscribers.” Consumers or
other customers typically move through a chain of development [5]. The precise
character of customers in each of these stages and their detection vary from case to case.
Rigorous market analysis methods should be applied to determine these customer
characteristics accurately.
Company
Company > Subscribers
Adoption > New Subscribers
from Rai xX,
Advertising Cheaper
SS
calls inside
the network Total
population
. ; Adoption Adoption é
Unit Services fam eS ee Experience
unit
al quality Word of Mouth <=
Contact
f Rate
Information.
Potential Adoption Rate Well-informed
Subscribers > People
No \ | x,
a
i Adoption ~ <———__ Population
Unit Services feck
quality Word of Mouth =. Adoption Experience
Fraction unit
Cheaper Contact
eee calls inside Rate
Adoption the network ie
from a
Advertising A ate 8 aie Rival’s
—> Subscribers
xX
Figure 1. Mobile Service Competitive Market Model
Dynamic Growth Models
The method of the growth model construction using the differential equation has
been proposed in [1]. This approach is suitable for describing the sales process where
mobile services are distributed into account for different initial conditions (when the
number of people who have taken an interest in new services is very small compared to
the actual market share carrying capacity). Different growth models are illustrated in
(1).
One of the possible market development models for a single service can be
described by the equation:
P. -1
AP = —™-exp| —], 1
At AZ] w
where P(t) — cumulative sales of the mobile services; P.,,, — estimation of the potential
market share carrying capacity, taking into account issues, specific to the socio-
economic factors of the region; A — parameter, which depends on the fractional growth
rate; f — time (days, months, years, etc.).
The next growth model of cumulative sales volumes can be described by the
differential equation:
dP
Fp 7 POI (Poa = PO), Q)
where @,, a, — parameters, depending on company marketing activity and the “word of
mouth” effect.
Figure 2 illustrates the real company statistical data (real subscribers) and the result
of modeling the mobile service market of the region with the help of different models.
Experimental data can be approximated with a high degree of accuracy through the
model identification.
Sabscriber base of the company
I I I I
—Real data
—— Differential equation [1]
—— Equation (1)
—— Equation (2)]
subscribers
0 5 10 15 20 25 30 35 40 45 50 55 60
time (month)
Figure 2. Growth Models and Experimental Data
Such modeling process allows estimating the market share carrying capacity P.,,. .
This method also enables us to forecast the demand for services. The receipt of new
sales volumes allows updating the model parameters continuously.
The next part of the paper is based on the system dynamics model (Figure 1) and
the equation (2).
Competitive Market Model
Consider conditions when the major operator is determined. This company has the
largest subscriber base. The model (Figure 1) includes dynamic competition between
major operators: the leader and the others. The pricing policy, service quality,
subscriber base, potential subscribers, marketing, etc influence their market share in
regards to the number of subscribers.
The system dynamic model from Figure | can be described by the set of equations:
d:
taal n,- -A(l K,)x,- eer [a,,x, +bu,];
o =a) N, -A(I-K. Za I [ayx, +ay,.x, +bu,]; (3)
aes
Bs al ros) 4,5)
al
where x,,i=1,2 — subscriber base of the i-operator, x, — number of people, who know
the actual situation (price, service quality, etc.); N, — estimation of the potential market
share carrying capacity, under a certain service price u,,i=1,2; K,,i=1,2 — service
quality function for i-operator; @,%,7,,A; 4,,,b, i=1,2, j=1,2,3 - parameters,
depending on the company’s marketing, price strategy, advertising, customers’ activity,
etc.
The service quality function can be described by the equations:
K,= As desir) T" =0.2H,/3; z,=H,-xt; H,,,=H,+a"/365+H,. (4)
The system usually dedicates a single radio channel to a local group of subscribers
who share it. There is an optimal number of subscribers H, using an i network witha
normal connection quality K,. If more subscribers use one channel of an i network,
the connection cannot be guaranteed.
Different scenarios of the market development are illustrated in Figures 3 and 4.
Experimental data are displayed by the dotted line. The parameters of the model (3) and
equations (4) are described in the top left corner of the Figures 3 and 4.
A competitive market development for the condition bu, >> bu, in the long run is
illustrated in Figure 3 - the market share of the major operator demonstrates an increase.
If bu, = bu, and service quality of the major operator is decreased, the market share of
other operators increases (Figure 4).
36
‘Tou, =107000; bu, =12900;7~
[Ay =310°; a 22.10":
xi
T
1 -
a@=4.13-10°; | N,=1.2-10°;
Yo a2, = 055-405
a,=1.1; @,=0.005; a,=2.35;:
T T T T
T=045.
i i i i i i
i Ei) 1 160 20 260 a 360 a0
Figure 3. Results of subscriber base in case bu, >> bu,
i i i i i i
Ey 7 1 200 20 m0 x0 0
Figure 4. Results of subscriber base in case bu, = bu,
Scenarios of Regional Market Development
Here we present the result of a model simulation under two scenarios: monopoly
and real competitive market. Any regional mobile service market at the initial stage had
a dominant operator with a subscriber base of x, >>x,. Suppose, that other initial
conditions (such as price, service quality, marketing, etc.) are equal and the oldest
operator is the monopolist in the long run (Figure 5). The service price reduction allows
new operators to attract the subscribers. In this case, the market actively develops. The
distribution of new subscribers depends on the existing subscriber base of a less
dominant operator (Figure 6).
x10"
25
subscribers
0 700 Er) nr) 70 a0 ‘00 7
Figure 5. Market Growth: Monopoly
18 i i i i
cubetiors
Er)
Figure 6. Market Growth: Real Competitive Market
There is a possibility of an industry-wide “word-of-mouth” and other growth effects
(Figure 1). Simply put, the more subscribers already exist, the more new customers
become aware and actively consider using its services. Similarly, the increasing
awareness converts people who haven’t represented likely subscribers into a group of
those who are at least not being excluded. The influence of exogenous forces (political,
economic, social, and technological [1, 5]) must be added to this internal market growth
mechanism.
Control problems
Consider the problem of optimal management for a mobile operator on a
competitive market. The nonlinear model (3) includes control parameters bu,, bu, (in
Figure 1| it is called “Unit Price’). Let’s formulate control problems [1-3, 6]. Control
purposes for each mobile operator on different stages vary by: the subscriber base,
revenue, market share, minimized churn rate, increased revenue per user, net income,
improvement in financial efficiency, etc.
The obtained market share carrying capacity should be used for the analysis of the
market situation and the determination of the price strategy, which is optimal in the
sense of the firm development criterion [1]. Consider the control problem using the
nonlinear model (3). The model built is described by the following finite-difference
equations:
Xen = F(X pot) Buy +S > 6)
where X,€ R? is a state vector, describing the market behavior; u, € R® is a control
vector; w, € R® is a vector, describing current market situation; é; e€ R® is a vector,
characterizing inaccuracy of information about the parameters of the market; F()-a
nonlinear vector-function; B,— a constant matrix. It is assumed that all information
about operators is available for measurement.
Equation (5) is reduced to the linear one using a linearization procedure:
Xp = AX, + By +o, (6)
where A, is a constant matrix.
The use of control theory to solve management problems is considered e.g. in [6].
Conclusions
We presented the system dynamics approach for the analysis of the mobile service
competitive market. The model includes the description of the dynamic competition
between major operators: the leader and the others. The pricing policy, service quality,
subscriber base, potential subscribers, marketing, etc influence their market share with
regards to the number of subscribers.
In this paper, the method for the identification of the market carrying capacity is
described and the problem of the optimal price management is formulated. The
obtained results can be used in research to forecast and improve decision-making in real
dynamic systems. We also established the numerical results of the modeling process and
made comparisons with the real experimental data on the volume of sales of
communications services in the competitive market.
References
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Shiryaev V.L, Shiryaev E.V., Golovin LYa., Smolin V.V. 2002. Adaptation and
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