Table of Contents
Modelling the Telecommunication Market
Douglas Franco,
CANTY, Interconexion, Ave Libertador, Edif NEA, Piso 20, Caracas, Venezuela
00582512518117 Fax 00582512520250
dfranco@cantv.net
Abstract
Managing a telecommunication company requires, among others things, to evaluate the
consequences of different alternatives to interconnection agreements and also design
policies to improve profits from incoming calls. Product pricing and capacity acquisition
are complex issues, because competitor’s assets are complementary, as they bring more
people to call and more calls back. Economies of scale and scope are also present because
high investments are involved and firms trade between leaving “money on the table” or
optical fiber underground, as market saturates. The conditions for the misperception of
feedbacks, MOF, are all present (Sterman 1998), exacerbated by call back misperception
COM, when outgoing calls bounce back from other networks; so, additional charges to
compensate expenses for calls terminating elsewhere, unexpectedly deteriorate net
revenues. In order to understand this complexity a System Dynamics model of the
telecommunication market was constructed, where customers choose among alternatives to
call, mobile and fixed operators grow, merge, offer services and set prices. Regulators
control prices for call termination and fixed telephony. Model generates profits, levels of
consumption and surprises. Calling Party Pay billing practice is assumed, but it is easy to
adapt the model to RPP (Receiving Party Pays) billing. The model is implemented in
Vensim with data gathering in Microsoft Excel spreadsheet linked to corporate databases.
Economy applies optimization, which is a powerful tool when used as a module of a SD
model. Otherwise, it does not go beyond sub optimization: better parts and worse whole.
But, Economy helps to choose the variables and table functions in the system and System
Dynamics fine tune economic models to specific problems. Both disciplines work together
to improve understanding of socio economic systems; so, changes are focused toward high
leverage variables.
Economic models are useful, as long as System Dynamics never give up being the Fifth
Discipline.
(Simulation, telecommunication, market, wireless, socioeconomic)
Industrial Dynamics was originally conceived to model a problem, but in the seventies Jay
Forrester starts modelling a system: the National Model of US Economy. Such initiative
improves the discipline, because the adopted system approach promotes the inclusion of
levels and links that are not necessarily part of the problem but they are part of the solution.
Economy considers managers and customers as profit or utility maximizers; but, alternative
behaviors are studied by System Dynamics; so, economic solutions are fine tuned to real
operations. In the economic systems, variables and table functions have definite forms,
although they are not meant to solve specific problems.
The supply and demand of telecommunication services are simulated. Elasticity and
substitution parameters are calibrated. Marketing decisions are modelled, clients of
different operators grow, prices for outgoing and incoming calls are set, monthly profits
and minutes of consumption are calculated.
There are a lot of SD models regarding telecommunication business, but none that I know
off address the problem of interconnection explicitly; however, their ideas certainly
influence this work.
The model is implemented in Vensim, with data gathering from Microsoft Excel
spreadsheet linked to corporate databases.
The Market Sector
Several operators participate in the Telecommunication Market offering fixed and mobile
services. Customers of any operator may call to competitor’s clients.
Operators expand capacity in order to preserve service quality at peak time. Usually,
periods of expansion are followed by periods of lower prices, as operators use their spare
capacity to attract new clients (Evans 2000, Baumol 1994). Feedbacks due to network
positive externalities (Arthur 1994) are explicitly modelled.
A price is charged per outgoing minute to the party who makes the call, CPP. However,
other billing practices charging calls to receiving party, RPP, are also used by mobile
operators. Calls originate in an operator i and terminates in operator j. Demand is
represented by monthly consumed minutes, Mij, from operator i to j.
Revenues for outgoing calls of the operator i are: ROi = SUM( Mij*Pij ), where Pij is the
price per minute of the call from i to j.
Interconnection Charges
There is a price, ij, for call termination fro
minute that ends in its network. Naturally,
ito j. Thus, j receives a payment for every
is zero because the call is internal.
There are minutes from the rest of the operators that end in i. Those minutes pay a toll to
terminate the call in i; so, revenues also come from incoming calls:
Ri = SUM ( Mji*Iji ), where Iij is the charge to terminate a call from j to i.
Charges for call termination Iij are negotiated between operators as a part of the
interconnection agreements. Sometimes, there is a different peak and off peak rate. Usually,
long distance calls are part of the deal. The lij pricing is a critical issue in the company
survival (Salanie 1999).
The economic problem of improving profits is more complex than making our own
decisions; because growth and prices set by competitors also affect our own results.
Besides, there is a trade off between short and long term performance.
Customer Call Decision
Customers make calls influenced by Pij prices and their preferences (Laffont 2000).
Cheaper fixed to mobile calls substitute mobile to mobile when possible. From the cost
perspective the fixed mobile route use only one voice channel and the mobile mobile use
two voice channels; therefore, calls fixed to mobile are cheaper than mobile to mobile.
Elasticity and substitution parameters regulate those effects.
The following influences are explicitly considered:
Change in Clients From
More clients from, increase calls to other operators.
Change in Share To
The outgoing minutes from i, may go to several destinations j. More called client’s fraction
implies more minutes going to them. So, Mij minutes increases when j market share
increases.
Change in MOU From
Usually higher consuming clients are enrolled first. As the penetration or % of clients is
increased, the new clients tend to consume less. Therefore, the Minutes of Use per client
per month, MOUi, decreases with penetration. As the company grow, the consumption per
client goes down.
Changes in Price Gap From To
There is a gap between the call price from a mobile phone and the same call made from a
fixed phone; usually, mobile to mobile calls are more expensive. Therefore, when possible,
a fraction of mobile to mobile calls are substituted by fixed to mobile alternatives.
Changes in Price From To
Higher prices decrease the number of calls from to.
Minutes From to
Clients of company i call Mi minutes a month to all destinations j, the minutes from i to j
are Mij. Therefore,
Mi = SUM (Mij), for all j destinations.
But, Mi (t) = Ni(t)* MOUi(t),
Where, Ni is the clients of company i, and MOUi are minutes per month per client.
In general, Mij = Mi*fj, where fj is the fraction of minutes coming from i, that goes to j,
if prices and preferences are equal to all destinations; then, the fraction of outgoing minutes
from i to j is similar to j’s market share: fj = MSj = Nj(t)/N(t), however, customer
preferences may require a correction factor, Pref ij,
So, outgoing minutes from i to j, at time t are:
Mij(t) = Ni(t)*MOUi(t)* ( Nj(t)/N(t) )*Prefij
Where, N(t) is the total number of lines.
At t-1:
Mij(t-1) = Ni(t-1)*MOUi(t-1)* ( Nj(t-1)/N(t-1) )* Prefij
So,
Mij(t) =
Mij(t-1)* ( Ni(t)/Ni(t-1) )* ( Nj(®)/Nj(t-1) )* ( MOUi(t)/MOUi(t-1) )*( N(t-1)/N(®) )
Or Mij(t-1)* Growth i * Growth j * Growth MOUi / GrowthMarket
Minutes from to grow with origin, destination, MOU and decrease with market growth.
Note that Pref disappears imbedded in Mij. So, calls’ inertia rises minutes, as shares and
consumption grow.
Price Elasticity and Substitution
The quantity of minutes from i to j, Qij, depend upon changes of price Pij. Lower prices
increase calls. Duration of calls increases with flat rates, but it is relatively insensitive to
price changes. Some calls made from mobiles are substituted by calls from fixed, at higher
price gaps between mobile_mobile and fixed_mobile.
Let Alfa be the price elasticity and Beta the substitution elasticity.
Let the sub index 2 designates the fixed network.
Substitution at Call Destination:
Qij = Mij *( Factor Price ) * (Factor Substitution )
Qij = Mij*(Price(t-1)/Price(t)) * Alfa * (PriceGap(t-1)/PriceGap(t) ) * Beta
Qij = Mij *( Price(t-1)/Price(t))) * Alfa * ( (P(t-1)ij / P(t-1)2j )/ (P(tij / P(t)2j ) ) * Beta
Fixed network is represented by 2. If i=2, then the formula reads:
Qij = Mij *( P(t-1)2j /P(H)2j ) * Alfa
So fixed network elasticity has no substitution effect.
Mij(t) = Mij(t-1)* (Ni(®/Ni(t-1))* (Ni(O/Nj(t-1))* ( MOUi(Q/MOUi(t-1))*
*(N(t-1)/N()*(P(t-1)ij /P(Hij) * Alfa * ((P(t-1)ij / P(t-1) 2) )/ (P(Hij / P(t)2))) * Beta
Mij(t) = Mij(t-1)*(Ni(®/Ni(t-1))* (Nj(®/Ni(t-1))* (MOUi()/MOUI(t-1))*( N(t-D/N() )*
*( P(t-1)ij /P(Oij ) *( Alfat+Beta)*( P(t)2j / P(t-1) 2j )*Beta
Fixed to Mobile calls substitutes Mobile to Mobile calls, when possible and cheaper.
But there is also a substitution at the origin; so, calls Mobile to Mobile are also substituted
by Mobile to Fix, when possible and cheaper, especially indoors.
Mij(t) = Mij(t-1)*(Ni(®/Ni(t-1))*(Nj@/Nj(t-)* (MOUi(®)/MOUi(t-1))*(N(ED/N(O)*
(P(t-Dij /P(Dij ) MC Alfa+Beta) * ( P(f)2j / P(t-1) 2j ) * Betal* (P(t)i2 / P(t-1) i2) * Beta2
Betal and Beta2 are not necessarily the same; but, empirical evidence rejects the
hypothesis that they are different.
In general, the minutes called from i to j, Mij change with time. From time, t-dt, to time t,
has the following influences:
Mij(t) = Mij(t-dt)* ChangeInClientsFrom*ChangeInShareTo*
ChangeInMOUfrom*ChangeInPriceGap/(ChangeInPriceGapTo*ChangeInPriceGapFrom)
Alternative Formulation to the Relationship between Variables
Economist usually represents the influence from X to Y as:
Y(t) = ¥(0)*( X(O/X(0))*E,
Where, E is the elasticity of the transmission of the changes from X to changes in Y. When
there are many X’s, like in the Cobb_Douglas function, factors are multiplied to make
production.
This formulation is entirely equivalent to the following one, where products are turned into
sums:
dY/dt = Y*E* (dX/dt)/X = Y*E*Fraccional Change Of X
This formulation is more appropriated for SD models, because it makes explicit that X and
Y are levels, so they may interact with each other by a dynamic usually missed in economy
For instance, the Cobb_Douglas production function uses labor and capital as factors.
James Lyneis 1980, describes how labor and capital interact to make production, a whole
lot of possible behaviors emerge from labor and capital being levels whose incoming and
outgoing rates are explicitly linked resembling the real productive activities.
In vensim, the previous expression reads, using company sub index to name operators:
The sub indexes from and to have to map to company, company<-> from and
company <-> to
Change Price [from, to] =
(New Price[from,to]-Prices[from,to])/TimeToPerceivePrice
~ |
FractionalChangeOFprice[from,to]=
ChangePrice[from,to]/Prices[from,to]
~ |
ChangeOfMinutes|[from,to]=
- FractionalChangeOFprice|from,to]* (Alfa+ Beta)
+ FractionalChangeOFprice[fixed1,to]*Beta
+ FractionalChangeOF price|from,fixed1]*Beta
+ FractionalChangeOfMOU[from]
+ FractionalChangeOfClients|from|+FractionalChangeOfClients{to]
- FractionalChangeOfTotalClients
Personal consumption MOU falls with penetration, TotalClients/Population, clients grow
at lower prices but fall with penetration, so the factors are far from being independent, a
bunch of interactions are present.
Alfa and Beta are calibrated to fit historical data.
Monthly consumption MOUi, is the average duration of the call multiplied by the number
of calls, MOU = Duration*Calls, where calls are sensitive to average per minute price,
and Duration is sensitive to marginal per minute price. So, flat rates encourage longer
calls. MOU is Gamma distributed with parameters Duration and Calls, where calls = (
MOU/Duration).
Telecommunication budget is a fraction of personal income, so when income increases
more calls are made. Therefore, calls tend to follow a statistical Paretto distribution
function, where, at higher prices fewer calls are made. The duration of the call tend to
follow an exponential distribution, at lower marginal prices the length of the call increases.
Price is usually organized in a monthly rent, a cost per minute and a lot of free minutes. The
average price is revenues divided by minutes. The marginal price is the cost per additional
minute. The Duration of the call is important because longer calls tend lo decrease service
quality in mobile services. The scarce resource is spectrum, longer calls occupy frequencies
for more time, so they are not available when new calls arrives. Calls are interrupted when
a person call from a moving object, because the phone needs a new frequency in the next
base station.
The model
The model receives data from the company databases to an Excel spreadsheet, and then
they are read by the vensim model.
Corporate ———+>| Excel Vensim
Databases © +————— | Spreadsheet
l~____| Model
It may sound complicated the lot of sub indexes used in the paper, but interconnection
requires the identification of the origin and destination of calls. In Vensim the model is very
simple, because its power to handle sub indexes.
The model has two views, the economic and the financial. In the economic view, customers
(demand) choose among alternatives offered by operators (supply). However, instead
demand or supply being a simple downward or upward slope curve, it is a complex
dynamic matrix of possibilities, where the choices of customers and services offered by
operators unfold into unexpected paths to the future. How your prices, growth,
consumption patterns, investments and other factors affect competition and how
competitors’ decisions affect your results, build a difficult game to play. Model allows
managers understand traffic data, to respond the moves of competition.
Tmigra
“a 2
oO Convinced
y
Sales Share ——migratio
available
Clients
NewAdds
Pal
<NewClients>
Figure 1. Growth, Penetration and Consumption
<FactorClients>
i RevenueOut Revenues <CostLines>
NewminutesA fectedByClients ie
ne WxchangeRate
Se Earnigs
Minutes Revenueln
ap aciorbnice
Alfa— cVv>
<Beta> CostMinutes
FracChangeOfPrice CostTrafficMinute <CMM
TimeToPerceivePrice
NewPrice
Figure 2. Prices, Minutes From To, Revenues and Costs
Customers enter into the system either from the population or from the pool of former
customers of any of the operators. Customers leaving one operator may switch to another
one or return to the original, depending upon actual sales effort. (Barron 1998). New
customers consume less than old ones; so, per capita average consumption MOUi for any
operator i goes down as penetration increases. Prices from_to affects the monthly
consumption Mi for any operator i. Minutes and prices make revenues, minutes and clients
make costs, profits measure the consequences of decisions.
Four mobile and two fixed operators are considered, but the model can be extended to
almost any number of operators. Elasticity fits real data using non linear parameter
calibration. The model has been used to design interconnection contracts, to study business
cases, to design prices for calls and to assist players in the telecommunication game.
Policy Design
Managers set prices for From_To calls, and control growth in fixed and mobile services.
The more desired growth, the higher the advertising and customer acquisition cost. But
new customers consume less; so, there is a profit trade off, to what point more people is
better. Lower prices from_to, encourages outgoing calls to and increase incoming calls
from; but, decrease outgoing revenues and increase costs. Lower fixed to mobile prices
increase fixed to mobile traffic; but, it substitutes mobile to mobile calls.
Low mobile to fix price is surprisingly found to be a powerful lever to increase profits. It
improves fixed penetration, because mobile behaves like a fixed phone when calling to fix.
So, mobile phone satisfies for new fixed lines and saves money on the last miles
(Vogelsang 1997); in addition, call back from fixed networks increases revenues.
One of the mobile competitors charges a 30% premium to call other operators to
compensate for the interconnection charge when calls terminate elsewhere. As a result,
outgoing calls went down, incoming calls from other operators also went down. Thus,
revenues decrease 17%. Model shows that this strategy is wrong, because it closes the
stable door with the horses outside.
Economy applies optimization, which is quite powerful when used as a part of a SD model.
Otherwise, it does not go beyond sub optimization: better part and worse whole.
Jay Forrester enhances the scope of System Dynamics, when he calls a system to solve a
problem and challenges the clouds to make room for improvements.
References
Arthur, W. Increasing Returns and Path Dependence in the Economy. Ann Arbor MI:
University of Michigan Press. 1994
Baumol, William J. Toward Competition in Local Telephony. The MIT Press, 1994
Evans, Philip Blown to Bits; How the New Economics of Information Transforms
Strategy. Harvard B. S. Press, 2000
Barron, Antonio. “The Wireless Marketing”. Telefonica de Espafia, Madrid. 1998
Eberlein, Robert “Vensim 5.1 Reference Manual”. Ventana Systems 2003
Lyneis, James. Corporate Plannig and Policy Design: A System Dynamics Approach.
The MIT Press, 1980
Sterman John, Paich Mark, Langley Paul “Explaining Capacity Overshoot and Price War:
Misperceprion of Feedback in Competitive Growth Markets”. International System
Dynamics Conference 1998
Jean Jacques Competition in Telecommunications. The MIT Press, 2000
Salanie, Bernard The Economics of Contracts. The MIT Press, 1999
Vogelsang, Ingo Telecommunications Competition -The Last Ten Miles- The MIT
Press, 1997
Back to the Top
