ANALYTIC HIERARCHY PROCESS AND ITS APPLICATION

TO GRADE OF TRAFFIC SERVICE FOR CELLULAR

NETWORK

Kentaro Hoshi, Sadahiko Kano

Graduate School of Global Information and Telecommunication Studies, Waseda University, Shinjuku, Tokyo, Japan

Yoshitaka Takahashi

Faculty of Commerce, Waseda University, Shinjuku, Tokyo, Japan

Shigeru Kaneda, Noriteru Shinagawa

Network Laboratories, NTT DoCoMo, Inc., 3-5, Hikarinooka, Yokosuka, Kanagawa, Japan

Keywords: Analytic Hierarchy Process, Consistency index, Threshold, Grade of traffic service, Group decision making.

Abstract: In a cellular network, several tra

ffic control services are previously provided. Above all, when the network

becomes congested e.g. world-cup ticket-reservation, THREE traffic control scenarios are proposed. In this

paper, applying an AHP (Analytic Hierarchy Process) approach enables us to obtain a solution which

scenario is best/worst among these traffic control scenarios, from user’s view point. Firstly, we construct a

web site on which cellular network users can simply answer a questionnaire regarding grade of traffic

services via internet. We then formulate a pair-wise comparison matrix (p.c.m.) through this questionnaire

result for an individual respondent. We next calculate the maximum eigenvalue of the p.c.m., which leads to

CI (consistency index). Via this CI value, we can see how well the respondent answers logically. Through

this process, we obtain all CI values for all questionnaire respondents. We propose a decision making

technique for questionnaire respondents group through these individual CI values. Taking the geometric

mean of p.c.m. elements we obtain the weighted eigenvector for the maximum eigenvalue of this geometric

mean p.c.m., namely priority (users’ dissatisfaction) vector. From the priority vector, we can see how

well/badly these traffic control scenarios operate.

1 INTRODUCTION

In a Cellular Network, several traffic control

services are previously provided. Above all, when

the network becomes congested e.g. world-cup

ticket-reservation, THREE traffic control scenarios

are proposed and becoming important (Akinaga,

Kaneda, 2005); spatial distribution, time

distribution, and traffic reduction. By spatial

distribution, we mean that users are recommended to

move in an area where communication channels are

not so busy. Traffic can be spatially distributed. By

time distribution we mean that users are

recommended to wait for a while so that users can

access the network with a higher probability. Traffic

can be distributed over a period of time. By traffic

reduction we mean that users are recommended to

change from voice service into data (e-mail or web)

service. Traffic can be reduced since data service

(channel holding) time is much shorter than voice

service time (channel holding). The main purpose of

this paper is to evaluate these traffic control

scenarios by using an AHP (Analytic Hierarchy

Process) approach.

The AHP approach is applied to obtain a solution

ich scenario is best/worst among these traffic

control scenarios, from user’s view point. Firstly, we

construct a web site on which cellular network users

can simply answer a questionnaire (a set of

questions) regarding grade of traffic control

scenarios via internet. There are very few literatures

on AHP questionnaires systems at web site in Japan.

114

Hoshi K., Kano S., Takahashi Y., Kaneda S. and Shinagawa N. (2006).

ANALYTIC HIERARCHY PROCESS AND ITS APPLICATION TO GRADE OF TRAFFIC SERVICE FOR CELLULAR NETWORK.

In Proceedings of the International Conference on Wireless Information Networks and Systems, pages 114-120

 SciTePress

The secondary purpose this paper is to provide an

idea and philosophy for making a web-site AHP

questionnaire system. At the beginning of our AHP

analysis, we formulate a pair-wise comparison

matrix (p.c.m.) through this questionnaire result for

an individual respondent. We next calculate the

maximum eigenvalue of the p.c.m., which leads to

CI (consistency index). Via this CI value, we can see

how well the respondent answers logically. When CI

value is smaller, the more the questionnaire

respondent answers consistently (The questionnaire

answer result with a high CI value is not reliable).

Figure 1: Analytic hierarchy process.

Through this process, we obtain all CI values for all

questionnaire respondents. Taking the geometric

mean of p.c.m. elements we obtain the weighted

eigenvector for the maximum eigenvalue of this

geometric mean p.c.m., namely priority (users’

dissatisfaction) vector. From the priority vector, we

can see how well/badly the traffic control scenarios

operate.

The rest of this paper is organized as follows.

Section 2 describes our hierarchy structure and the

necessary linear algebra mechanism. Section 3

constructs our web-site AHP questionnaire engine,

enabling one to obtain our solution. Here, we

propose a decision making technique for

questionnaire respondents group through individual

CI values. Section 4 summarizes our result and

mentions reaming our research topics.

2 AHP APPROACH

2.1 Hierarchical Structure and

Analytic Procedure

AHP is a mathematical approach for multicriteria

decision making (Saaty, 1980). In the AHP approach,

we have to start expressing a hierarchical structure

by dividing our problem into the several layers. Each

layer is assumed to consist of some elements. Here,

the number of layers and that of elements are not

constant, in other words, we have to decide how

many layers there are in the hierarchical structure

and elements in the individual layers. AHP is a very

flexible approach.

Though, the top layer of the hierarchical structure is

assumed to consist of only one element called a goal

(problem target). The bottom layer is called the

solution layer that may consist of some elements

where each element corresponds to a solution to the

goal. The middle layer(s) are (is) called the criteria

layer(s). Each element in the criteria layer will be

also called as criteria element; See Figure 1.

We have to subsequently compute the weights

between a pair of the elements in an individual layer.

If we denote by n the number of pair-wise

comparisons, we have to compare

2)1( −nn

times, since our pair-wise comparison should have a

special reciprocal form, i.e.

jiij

.We finally

calculates the weights of the overall layers. Based on

the calculated weights, we can evaluate priority to

the goal of an individual solution. For our analytical

process see Figure 1. We will describe the details of

CI (as seen in the figure) in the next section.

1=× a



2.2 Linear Algebra Structure

We calculate weight

on the

element layer

n21

. At this time,

if we assume importance occasion to of

that

, element

p.c.m.

becomes

www ,,,



AAA ,,,

][

. When provided

is well-known,

www ,

][

A becomes (1)

Note that, for any i, j and k holds

jkij

. The

evaluation illustrates completely consistent.

aa =×

To multiply a weight column vector w by this p.c.m.

111 12 1

221 22 1

,1,2

// /

/, 1/,

nn n nn

ij i j ij ji

ij n

AA A

ww ww ww

awwa a w

⎡

⎤

⎢

⎥

⎢

⎥

⎡⎤

⎣⎦

⎢

⎥

⎢

⎥

⎣

⎦

⎡⎤

⎢⎥

== =

⎢⎥

⎣⎦



  





(1)

Aw nw

A give a vector nw.

This expression is able to change an eigenvalue.

(1)An w 0

−

(2)

ANALYTIC HIERARCHY PROCESS AND ITS APPLICATION TO GRADE OF TRAFFIC SERVICE FOR

CELLULAR NETWORK

115

I is an identity matrix. The following (2), if w ≠ 0 is

hold, n must become the eigenvalue A. Then w

becomes the eigenvalue vector A. Because rank A is

1, the eigenvalue

),2,1( ni

=

becomes

one is non-zero, others are zero. Moreover, when the

sum total of the main opposite angle element A is

n, and λ

max

is λ

which is not zero,

max max

0, ( )

λλλ

==≠ (3)

Therefore, a weight vector w to

becomes a eigenvalue vector in

normalized to the maximum eigenvalue λ

AAA ,,,



∑

= )1( w

max

of A.

When it is actually applied to the questionnaire

analysis,

ｗ

is unknown, we then must calculate

′

We can evaluate

from the p.c.m.

′

given

questionnaire answer.

'' ' '

max

′

is the maximum eigenvalue of

. It gives

unknown . As conditions become more

complicated, it is in the tendency the results of the

questionnaire answer are not consistent more. We

know as does not become consistent, λ

′

max

grows bigger than n (Saaty, 1984).

max

()

jij i

iji

ijij

wa w

ww a n

==+

−

∑∑

(4)

Following (4), always hold λ

max

≧ n. If λ

max

= n,

provided satisfy consistency. We can denote

consistency index by (5).

max

−

(5)

CI (Consistency Index) denotes whether pair

comparison is properly. Saaty who is the advocate of

AHP is proposed from experience when CI is less

than 0.15 or 0.1, we should do pair comparison

again because pair comparison can not be done

properly. When CI is 0, called perfect consistency,

and effective is value less than 0.15 or 0.1.

3 WEB AHP QUESTIONNAIRE

ENGINE

3.1 Quality Evaluation

THREE traffic control scenarios are proposed and

becoming important (Akinaga, Kaneda, 2005);

spatial distribution, time distribution, and traffic

reduction. By spatial distribution, we mean that

users are recommended to move in an area where

communication channels are not so busy. Traffic can

be spatially distributed. By time distribution we

mean that users are recommended to wait for a while

so that users can access the network with a higher

probability. Traffic can be distributed over a period

of time. By traffic reduction we mean that users are

recommended to change from voice service into data

(e-mail or web) service. Traffic can be reduced since

data service (channel holding) time is much

shorter than voice service time (channel holding).

Let evaluate a quantity about user dissatisfaction by

using an AHP.

Define,

z Goal: selection

z Criteria: usability, preference, reliability

z Solution: spatial distribution, time distribution,

traffic reduction (Figure 1).

A terrible earthquake: Situation in which user calls

terrible earthquake to know safety of important

person.

A large fireworks: Situation in which user who gets

lost to friend in a large fireworks calls.

Ticketing reservation: Situation in which user calls

for ticketing early reservation of event

We construct hierarchical structure (Figure1).When

among solution is taken in criteria layer, element

‘usability’ imply whether to take much time,

element ‘preference’ implies whether to be poor,

element ‘reliability’ implies whether a worry is left.

Elements of Solution layer, ‘spatial distribution’

imply user movement. ‘time distribution’ implies

time shift. ‘traffic reduction’ implies other media

recommendation.

We must decide a number of layers with AHP,

however if one layer is increased, pair comparative

items increase by the element, and so questionnaire

despondence takes labour too much. In this paper,

criteria layer is only three, because avoid the AHP

questionnaire being repeated concerning.

3.2 Questionnaire Engine Construct

As for the questionnaire, although there are various

things of the paper base, exit polls, telephone

surveys and mailing investigations in principle, it is

the most suitable for the questionnaire via an

internet how to collect it to count data economically

in a short time.

Here, we construct Questionnaire Engine on web

presumed questionnaire answer via the internet for

questionnaire survey, collective and analysis.

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As a preparation for set up on Web, we rent the free

server which can use CGI, and registers for DDNS

(Dynamic Domain Name Server) for reducing URL

because improve access easily (URL, 2006).

As a preparation for questionnaire counting, we

construct the engine that is able to input to the

spreadsheet software automatically by programming

it in HTML, and able to analyze by preparing a

calculation program. Moreover, we presume the

problem which is not input to the spreadsheet

software properly in the un answer and so on, take

measure to prepare dummy answer.

Importance measure for generate p.c.m. define as

follow Table 1.

Table 1: Intensity of the dissatisfaction and definition.

When an answer clicks on ‘absolute reliability’ on

the ‘spatial distribution’ side, input “7” to

spreadsheet software, and when clicks on ‘strong

reliability’ on the ‘traffic reduction’ side, input it

“1/5” (Figure 2).

We putted the engine to the test which included

movement confirmation before the questionnaire

survey actual take. Consequently, a wrong point did

not occur in the counting processing of the data

which it was afraid of, though respondent to a

questionnaire did not recognize hardly the difference

in valuation item which server constructing side

intends, rather than their contents of answer got

confusion (Consistency index was strangely high)．

Therefore, we use much visual information in the

part of the question so that a respondent can

understand obvious (Figure 3). We made Waseda

university students as well as Fukagawa high school

'''

'' '

123

,( 1,2,3)

wwwi

vvv

⎛⎞

⎜⎟

⎝⎠

(6)

students reply to the questionnaire from December,

2005 to February, 2006 via the Internet. They can

fully utilize cellular communication system and used

to internet. We received a response rate of 95%

(valid response).

3.3 Individual User Analysis

It is noted if λ´

max

of preceding section 2.2 is n=3,

we are able to get λ´

max

to evaluate geometry mean

of element constituent A´ (Oguchi, 2006).A result of

a questionnaire applies in the Table 2.

Table 2: Respondent to a questionnaire example.

Criteria Usability Preference Reliability

Usability 1 7 3

Preference 1/7 1 1/3

Reliability 1/3 3 1

Usability Spatial Time Traffic

Spatial distribution 1 1/5 1/3

Time distribution 5 1 3

Traffic reduction 3 1/3 1

Preference Spatial Time Traffic

Spatial distribution 1 1/3 1/3

Time distribution 3 1 3

Traffic reduction 3 1/3 1

Reliability Spatial Time Traffic

Spatial distribution 1 1/3 3

Time distribution 3 1 5

Traffic reduction 1/3 1/5 1

Intensity of

relative importance

Definition

1 Equal dissatisfaction

3 Weak dissatisfaction

5 Strong dissatisfaction

7 Absolute dissatisfaction

Figure 3: Visual information.

Figure 2: Spreadsheet software input screen.

ANALYTIC HIERARCHY PROCESS AND ITS APPLICATION TO GRADE OF TRAFFIC SERVICE FOR

CELLULAR NETWORK

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We calculated weight for solution of each

criteria.We applies weights of other criteria was

evaluated in the same way (Table 3).

Table 3: Result of evaluated each weight.

As in Table 3, this respondent to a questionnaire

feels weight with ‘usability’ in solutions, and feels

weight with ‘time distribution’ in each criteria. At

this time, maximum eigenvalue λ´

max

is given (4),

and CI is given (5). Result of evaluated CI illustrate

Table 4, regard this answer is consistency because

CI in each pair comparison is less than 0.1,Multiply

weight in the whole by in the weight to each criteria,

we find the priority of the solution finally. Multiply

0.105 which is weight of ‘usability’ for ‘spatial

distribution’ by 0.669 which is weight of criteria, we

find that 0.105 x 0.669=0.07. Result of evaluated all

elements, we find that upper 4 rows (Table 4). The

priority of the solution is given sum cols.

Consequently, we find this user feels most

dissatisfaction to waiting for the time.

Table 4: Priority.

3.4 Group Users Analysis

This section, we evaluate priority vector whole of

the user group in terms of result of an analysis user

individual. We use Gm. We consider about the

priority of the individual solution as follow

preceding section. It knows result of an analysis user

individual is selected by the CI with an AHP

analysis technique. Though, the group analysis

algorithm is not set up with AHP. Here, a CI is taken

with the threshold, and we propose in accordance

with the computational algorithm of the Figure 6.

Here that a change in that threshold, how influences

a priority vector.

Criteria Solution Spatial Time Reductio

Usability 0.669 0.105 0.637 0.258 0.019

Preference 0.088 0.135 0.584 0.281 0.068

Reliabilit

0.243 0.258 0.637 0.105 0.019

Figure 4: Group decision making algorithm.

Step1: If it is not consistent with the questionnaire,

this CI is used as a threshold (T) though an

adjustment occasion CI grows big. In other words,

evaluate CI from the p.c.m. of the respondent to a

questionnaire, and when CI exceeds (T), reject that

data. If CI is less than (T), save that pair

comparative matrix data.

Spatial distribution Time distribution Traffic reduction

Usability

0.070 0.426 0.173

Prefer ence

0.012 0.051 0.025

Reliability

0.063 0.155 0.026

Priorit y

0.145 0.632 0.223

Step2: The entire respondents to questionnaires

members do a step 1.

Step3: element of the representing p.c.m. to

CI and priority vector in conges tion assumption

under ticket reservation situation

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0 0,05 0, 1 0,15 0,25 0, 3 1

Priority vector (%)

Spatial distribution

Time distribution

Traffic reduction

Figure 5: CI and priority vector in congestion assumption

under a ticket reservation situation.

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express the will of the group is given to it in the Gm

of the p.c.m.

element of (is not reject) save in

the step 1-2. For example, when there are forty

people are not rejected, it is the Gm which consists

of forty elements.

Step4: Eigenvalue and a weight vector are evaluated

to the representing p.c.m. which it could get in the

step 3; we evaluate a priority vector as well as CI.

Here, CI of the horizontal shaft of each figure

illustrates a threshold. In other words, data exceed

threshold are rejected (We restrict group to the user

of under the threshold).

When an approximate straight line by the regression

line of the least squares was calculated, Y-intercept

became a minus at the case of this questionnaire

(Figure 7). In other words, when the threshold of CI

is made very small, it devotes that the population

which satisfies disappears. CI had better be big from

the viewpoint of the group. On the other hand, CI

had better be low from individual viewpoint (The

existence of the trade-off). From the above, we

propose that CI what took the priority of 0.1～0.15

(about 50% of the whole) is effective in group

decision making. When it tried how to control traffic

by the spatial distribution (spatial movement), time

distribution (time shift), and traffic reduction (other

media recommendation), many students feel

dissatisfaction with the spatial movement most, and

feel dissatisfaction few with the changing other

media recommendation traffic control, in this case.

4 CONCLUSION

We have set up a problem how a user thinks of

traffic control scenarios in cellular networks. We

have solved this problem applying the AHP

approach. We have firstly presented a visual

questionnaire on the web site by using the hyper text

mark-up language (HTML) so that the respondents

can answer easily and quickly. We have then

formulated a pair-wise comparison matrix (p.c.m.)

through this questionnaire result for an individual

respondent. We have subsequently calculated the

maximum eigenvalue of the p.c.m.. Through this

process, we have obtained all CI (consistency index)

values for all questionnaire respondents. We have

proposed a decision making technique for

questionnaire respondents group through these

individual CI values. Taking the geometric mean

of p.c.m. elements we have obtained the weighted

eigenvector for the maximum eigenvalue of this

geometric mean p.c.m., namely priority (user’s

dissatisfaction) vector. From the priority vector, we

have been able to see how well/badly these traffic

control scenarios operate. It is left as a future

research topic to analyze not only our traffic control

scenarios (spatial distribution, time distribution and

traffic reduction) but also other control scenarios in

cellular networks. It is also left as a future research

topic to investigate another decision making

technique since group decision is not yet unique in

the AHP approach (We have adapted the geometric

mean of p.c.m. elements for the questionnaire

respondents whose CI values are less than our

threshold).

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Akinaga, Y., Kaneda, S., Shinagawa, N., and Miura, A.,

2005. A proposal of mobile communication traffic

forecasting method using call characteristics and

environmental information. IEICE Technical Report,

vol. 105, no. 12, NS2005-6, pp. 21-24.

Ferguson, P., and Huston, G., 1998. Quality of Service.

John Willy & Sons, New York.

Hoshi, K. Web AHP questionnaire engine, 2006.

http://roo.to/question/ (2006/03/24) (in Japanese)

Kaneda, S., Akinaga, Y., Shinagawa, N., and Miura, A.,

2005. The 19

International Teletraffic Congress, in

Proc. 6a, pp.583-592, Traffic Control by Influencing

Users’ Behaviour in Mobile Networks.

CI (Thr prior it y vect or in congest ion assumpt ion

t icket reservat ion sit uation

100

05 0.1 0.15 0.25 0.3 1

Priority vector (%)

eshold) and

under

0 0.

Figure 6: CI ( and priority vector in congestion

assumption under a ticket reservation situation.

Figure 7: CI ity vector in congestion assumption

under ticket re situation.

Threshold)

and prior

servation

y = 19.267

9808

-20

100

120

012345678

16.447x -

= 0.

ANALYTIC HIERARCHY PROCESS AND ITS APPLICATION TO GRADE OF TRAFFIC SERVICE FOR

CELLULAR NETWORK

119

Oguchi, K., Takahashi, Y., Hoshi, K., Kaneda, S., and

Akinaga, Y., 2006. User’s dissatisfaction performance

for mobile communication network: an AHP

approach.

Saaty, T.L., 1980. The Analytic Hierarchy Process.

McGraw-Hill, New York.

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