Lecture#11

Forecasting in the telecommunications

The Bonch-Bruevich Saint-Petersburg State University of Telecommunications

Series of lectures “Telecommunication networks”

Instructor: Prof. Nikolay Sokolov, e-mail: sokolov@niits.ru

Forecasting: foreword

Forecasting is the process of making statements about events whose actual outcomes (typically) have not yet been observed. A commonplace example might be estimation of the expected value for some variable of interest at some specified future date. Prediction is a similar, but more general term. An important, albeit often ignored aspect of forecasting, is the relationship it holds with planning. Forecasting can be described as predicting what the future will look like, whereas planning predicts what the future should look like. There is no single right forecasting method to use. Selection of a method should be based on your objectives and your conditions (data, etc.).

Source: http://en.wikipedia.org/

Forecast (XV century)

“The time will come when people from the most distant countries will speak to one another and answer one another”.

Leonardo da Vinci

“Inaccurate” Predictions

“This ‘telephone’ has too many shortcomings to be seriously considered as a means of communication. The device is inherently of no value to us”

Western Union internal memo, 1876

“I think there is a world market for maybe 5 computers” Thomas Watson, Chairman of IBM, 1943

“There is no reason anyone would want a computer in their home ”

Ken Olson, President, Chairman & Founder Digital Equipment Corporation, 1977

“640K ought to be enough memory for anybody” Bill Gates, Microsoft, 1981

Conclusion: “Prediction is very difficult, especially if it's about the future“. (Niels Bohr, Nobel Prize in Physics in 1922.).

Main considerations One of the reasons of qualitative network development is the interest of the group of subscribers which brings in a good return to Operator in new kinds of services. A number of requirements of this subscriber's group stimulate radical changes in different components of telecommunications network. At present time, the most essential changes take place in access networks. It is desirable that qualitative changes were recognized during the development of forecasts. These results are necessary for the choice of rational principles of further telecommunication system development. Different methods are being applied during the process of telecommunications networks planning. Method selection is carried out taking into consideration problem put by, character of the considered process, and available statistic information.

Unexpected surprise

Time

Number of PSTN subscribers

T1 T2T0

F(t)

F3(t)

F2(t)

F1(t)

100%

Formalized forecasting methods Formalized forecasting methods are effective in the cases when prehistory of studied process is known well. At present time, majority of forecasts is carried out with the help of methods of extrapolation and expert judgments. Each of these two methods is realized in different ways. Selection of the method depends on the studied process and the problem put by. Example of forecasting of two processes represented with functions 1( )F t and 2 ( )F t is shown on the figure. It is assumed that statistical data cumulated during period of time 0[ , ]rt t allow determining of analytic expressions for the functions 1( )F t and 2 ( )F t . Statistical data are

depicted by squares on the segment 0[ , ]rt t .

Problem put by comes to the calculation of values of these functions for the forecasting period – 0[ , ]ft t . Corresponding trends are depicted by dotted lines. Besides, it is expedient to

estimate confidence intervals. On the figure they are shown for the function 2 ( )F t by dash-dot lines. Complication of the forecasting development, in addition to problems with reliability of necessary statistical information, is explained by the circumstances of this kind:

Some kinds of new services are so specific, that it is very hard to select adequate analogues for their forecasting;

To a number of infocommunication market segments (mobile network is a typical example) development processes which essentially differ from the tendencies, thoroughly studied by Operators of other countries, are peculiar.

Two examples of trend extrapolations

Time

Extrapolation of Trends

tr t0 tf

F2(t)

F1(t)

Trends for functions F1(t), F2(t)

Economic indicators For the forecasting of some values it is expedient to use method based on taking into account one of the most important economic indices – gross domestic product (GDP) per capita. In a number of publications there is a substantiation of the estimate of infocommunication services demand – ( )D t which can be represented in following form:

0

( ) ( )b

tj

GD t F t

G

. (11.1)

Quantities tG and 0G are the values of the GDP per capita for the predictable time t and initial point on the axis "Time". Factor b determines extent of the influence of GDP growth on the level of solvent demand for the estimated service. Function ( )jF t is

one of the prognosis curves. Mostly these curves belong to S -shaped models. Such models are good for reflection of the process development, which passes three main stages: slow start, intensive growth, saturation stage. Typical example of the S -shaped model is the logistic curve frequently used for solution of the forecasting problems. A set of functions ( )jF t included in formula (11.1) is quite extensive. In particular, in

the technical literature following dependencies are considered:

Set of functions: 1( )F t a bt .

22 ( )F t a bt ct .

3( ) btF t a ce .

4 ( )1 bt

aF t

ce

.

5 ( ) .btceF t ae

2

2

( )

26 2

0

1( )

2

yt

F t a e dy

.

2

2

(ln( ) )

27 2

0

1( )

2

yt

F t a e dyy

.

18

2

( )1

bt

bt

a c eF t

c e

.

9

9

( )ln

1 ( )

F tc bt

F t

.

Least-squares method Least-squares method originates from the works of prominent mathematicians C. Gauss and A. Legendre. It suggests select function ( )f x for which condition of the following kind is valid:

2

1( )

N

i ii

f x y min

.

Least-squares method is frequently used for the substitution of prognosis curve by the function similar to 1( )F t . It is implied, that available statistics is represented by N meanings of values iX and iY . Factors a and b are defined by following formulas:

1 1 12

2

1 1

N N N

i i i ii i i

N N

i ii i

N X Y X Yb

N X X

, 1 1

N N

i ii i

Y b Xa

N

.

If prognosis function essentially differs from linear one, these formulas can not be applied. Then parameters of prognosis function are determined by means of numerical methods. In these cases least-squares method is also useful.

Forecasting of the future and the past

Year

Behavior of the investigated process for three ensembles

0 1 2 3 4 5 6 7 8 9 10 11 12 13

{X1} {X2} {X3}

F(t)

Revenue generated by PSTN

Portion of revenues generated by the telephone traffic

Year

90%

85%

80%

75%

70%2002 2003 2004 2005 2006 2007 2008 2009 2010

Future revenue structure

Internet21 €

New Services26 € (+124%)

Interactive games – 16,4%

Video services – 23,0%

Change of the bandwidth requirements in access network

Year

1995 2000 2005 2010 2015 2020 2025

Households, %100

80

60

40

20 1.5 Mb/s

6 Mb/s

24 Mb/s

100 Mb/sSources: Alcatel Telecommunications Review, 2nd Quarter 2003, Telektronikk, Volume 100, No. 4, 2004.

Forecasting related to access networks

Narrow band lines

Only mobile

Only broadband

Number of households, millions

40,0

30,0

20,0

10,0

0,0

2002 2007 2012

60%

20%

Year

PC markets (1)

PC markets (2)

PC markets (3)

Internet access

Internet in Europe

Mobile traffic (types of terminals)

Laptops and Internet

Statistics of disasters

Generalization (1)Forecasting can be broadly considered as a method or a technique for estimating many future aspects of a business or other operation. There are numerous techniques that can be used to accomplish the goal of forecasting. For example, a retailing firm that has been in business for 25 years can forecast its volume of sales in the coming year based on its experience over the 25-year period—such a forecasting technique bases the future forecast on the past data. While the term "forecasting" may appear to be rather technical, planning for the future is a critical aspect of managing any organization—business, nonprofit, or other. In fact, the long-term success of any organization is closely tied to how well the management of the organization is able to foresee its future and to develop appropriate strategies to deal with likely future scenarios. Intuition, good judgment, and an awareness of how well the economy is doing may give the manager of a business firm a rough idea (or "feeling") of what is likely to happen in the future. Nevertheless, it is not easy to convert a feeling about the future into a precise and useful number, such as next year's sales volume or the raw material cost per unit of output. Forecasting methods can help estimate many such future aspects of a business operation.

Source: Reference for Business. Encyclopedia of Small Business, 2nd edition.

Generalization (2)

Source: Reference for Business. Encyclopedia of Small Business, 2nd edition.

Suppose that a forecast expert has been asked to provide estimates of the sales volume for a particular product for the next four quarters. One can easily see that a number of other decisions will be affected by the forecasts or estimates of sales volumes provided by the forecaster. Clearly, production schedules, raw material purchasing plans, policies regarding inventories, and sales quotas will be affected by such forecasts. As a result, poor forecasts or estimates may lead to poor planning and thus result in increased costs to the business. How should one go about preparing the quarterly sales volume forecasts? One will certainly want to review the actual sales data for the product in question for past periods. Suppose that the forecaster has access to actual sales data for each quarter over the 25year period the firm has been in business. Using these historical data, the forecaster can identify the general level of sales. He or she can also determine whether there is a pattern or trend, such as an increase or decrease in sales volume over time. A further review of the data may reveal some type of seasonal pattern, such as peak sales occurring before a holiday.

Instructor: Prof. Nikolay Sokolov, e-mail: sokolov@niits.ru

Questions?

Forecasting in the telecommunications