Int
ern
at
i
onal
Journ
al of Inf
orm
at
ic
s
and
Co
m
munic
at
i
on
Tec
hn
olog
y (IJ
-
I
CT)
Vo
l.
6
,
No.
3
,
D
ece
m
ber
201
7
, pp.
146
~
154
IS
S
N:
22
52
-
8776
,
DOI: 10
.11
591/ijict
.
v6
i
3
.
pp
14
6
-
154
146
Journ
al h
om
e
page
:
http:
//
ia
esj
ou
r
nal.co
m/
on
li
ne/in
dex
.php
/
IJ
ICT
Custom
ers’ Pe
rcep
tion Towards S
ervi
ce
s
of
Telec
om
mu
nicati
ons Ope
rators
Driss
Ait Om
ar
*
1
, Mo
ha
me
d Ba
sl
am
2
,
M
ou
r
ad
N
achaoui
3
, Mohamed
Faki
r
4
1,2,4
Sulta
n
Moul
a
y
Sl
imane
Univ
e
rsit
y
,
Fa
cul
t
y
of
Scie
nc
es
and
Techni
cs,
Inform
ation
Proce
ss
ing a
nd
Dec
ision
Support
La
bora
tor
y
,
Ben
i´
Mell
al,
Moroc
co.
3
Sulta
n
Moul
a
y
Slim
ane
Univer
s
ity
,
Facult
y
of
Scie
n
ce
s
and
T
echnic
s,
Ma
the
m
atics
and
Appli
ca
t
i
on
La
bor
at
or
y
,
Beni
´
Mell
al,
Moro
cc
o
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
ug
1
5
th
,
20
1
7
Re
vised
Oct
2
0
th
, 201
7
Accepte
d
Nov
4
th
, 201
7
Curre
ntly
th
e
op
era
tors
in
th
e
telec
om
m
unic
atio
ns
m
ark
et
pre
sent
offe
rs
of
subs
cri
pti
on
to
t
he
consum
ers,
a
nd
give
n
that
c
om
pet
it
ion
is
st
rong
in
thi
s
are
a
,
m
ost
of
the
se
adve
r
ti
sing
offe
rs
are
pre
p
a
re
d
to
attra
c
t
an
d
/
or
kee
p
customers.
For
thi
s
re
ason,
customers
fa
ce
proble
m
s
in
choosing
oper
at
or
s
tha
t
m
eet
the
ir
ne
eds
in
te
r
m
s of
pric
e,
qua
l
ity
of
serv
ic
e
(Q
oS),
et
c
.
.
.
,
while
ta
king
int
o
ac
coun
t
the
m
arg
in
bet
wee
n
wh
at
is
adve
rt
ising
and
what
is
re
al.
The
re
fore
,
we
are
le
d
to
solve
a
proble
m
of
dec
ision
support
.
Mathe
m
atical
m
odel
ing
of
thi
s
proble
m
l
e
d
to
th
e
solut
io
n
of
an
inve
rse
proble
m
.
Spe
cifi
-
call
y
,
the
inve
rse
proble
m
is
to
find
the
re
al
Quali
t
y
o
f
Servic
e
(QoS
)
func
ti
on
knowing
the
theoret
i
ca
l
QoS
.
To
s
olve
thi
s
probl
em
we
hav
e
re
fo
rm
ula
te
d
i
n
an
opti
m
iz
a
ti
on
proble
m
of
mi
nimizi
ng
th
e
d
iffe
re
n
ce
be
twe
en
the
re
al
qual
ity
of
servi
ce
(QoS
)
and
the
ore
ti
c
al
(QoS
).
Thi
s
m
odel
will
hel
p
customers
who
see
k
to
know
the
degr
e
e
of
sinc
eri
t
y
of
Th
ei
r
o
per
at
ors,
as
w
el
l as i
t
is
an
o
pportuni
t
y
fo
r
o
per
at
ors who wa
nt
to
m
ai
n
tain
th
ei
r
r
esourc
es
so t
hat
they
gai
n
the
trust
of
cust
om
ers.
The
re
sul
ti
ng
opt
imizatio
n
proble
m
is
solved
using
evol
uti
onar
y
a
lgor
it
hm
s.
The
num
eri
ca
l
re
sul
ts
show
ed
the
re
liabilit
y
and
c
re
dibi
l
it
y
of
our
inve
rse
m
odel
and
the
p
erf
or
m
anc
e
and
eff
ective
n
ess of our a
pproa
ch
Ke
yw
or
d:
Inverse
prob
le
m
QoS
Ra
ti
on
al
it
y Opt
i
m
iz
at
ion
Gen
et
ic
Algori
thm
Ser
vice Pr
ovid
er (SP)
Copyright
©
201
7
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Dr
iss
A
it
O
m
ar
Inform
at
ion
Processin
g
a
nd
D
eci
sion
Sup
por
t
Lab
or
at
ory
Su
lt
an
M
oula
y Sl
i
m
ane Univ
ersit
y, Faculty
of Sciences
and Tec
hnic
s,Be
ni´
Mellal
, Mo
ro
cc
o.
Lotissem
ent M
enzeh Al
Atla
s
2
,
N1
351 , Be
ni´
Mellal
, Mo
ro
cc
o.
E
-
m
ail: ai
to
m
a
rd@g
m
ai
l.com
1.
INTROD
U
CTION
Pr
ivati
zat
ion
and
li
ber
at
i
on
ser
vices
i
n
te
le
com
m
un
i
cat
ion
s
i
n
m
any
c
ountries
le
ad
t
o
a
div
e
rsificat
ion
of
ope
rato
rs;
f
or
ex
am
ple
in
Mor
occo,
after
the
validat
ion
of
the
la
w
24
-
96
in
1997,
a
num
ber
of
op
e
rato
rs
wer
e
a
ble
to
ta
ke
their
plac
e
in
the
Mor
oc
can
m
ark
et
as
Or
a
nge
TEL
ECOM,
MOR
OCCO
TELEC
O
M
a
nd
I
N
WI
.
This di
ver
sit
y
le
ads
t
o
str
ong
c
om
petit
ion
betwee
n
them
,
each
of
w
hich
t
ries
to
at
tract
and
/
or
retai
n
custom
ers.
Si
nce
S
P
s
do
not
gi
ve
tr
ue
in
form
ation
a
bout
their
syst
em
s
(cli
ent
confu
si
on)
,
custom
ers
do
no
t
ha
ve
c
om
plete
inform
at
io
n
to
m
ak
e
a
good
de
ci
sion.
T
his
c
onf
us
io
n
pr
ese
nt
a
n
obst
acl
e
t
o
custom
ers
to
ha
ve
al
l
the
inform
ation
on
the
op
e
rato
r’
s
offe
r.
So
c
us
tom
er
cho
ic
e
is
of
te
n
un
ce
rtai
n
(
bounde
d
rati
on
al
it
y).
The
pro
blem
s
relat
ed
to
the
c
ho
ic
e
of
a
n
operator
is
on
se
ver
al
par
am
et
ers
incl
ud
i
ng
:
re
al
qu
al
it
y
of
serv
ic
e,
the
or
et
ic
a
ser
vice
qua
li
ty
,
bandw
i
dth,
pri
ce,
...
Op
e
r
at
or
s
deci
de
a
pr
ic
e
a
nd
Q
oS
for
se
rv
ic
es
off
ered
to it
s cu
st
om
ers
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
ICT
IS
S
N:
22
52
-
8776
Custo
mers’ Pe
rcepti
on T
owards
Services
of
Tele
comm
un
ic
ation
s
…
(
Driss
Ait
Oma
r
)
147
QoS
pr
opos
e
d
rem
ai
ns
a
par
a
m
et
er
that
depends
on
oth
e
r
var
ia
bles
nam
el
y
bandw
i
dth
,
t
he
s
har
e
of
th
is
m
ark
et
op
erat
or
.
In
th
ese
ci
rcu
m
stan
ces
an
ope
ra
tor
can
ne
ve
r
gu
ara
ntee
the
qu
al
it
y
of
serv
ic
e
it
prom
ise
s
to
custom
ers.
W
e
c
al
l
i
t
then
theo
reti
cal
Qo
S,
w
hile
the
Qo
S
pe
rceive
d
by
cu
stom
ers
is
the
act
ual
QoS.
In
the
te
le
com
m
un
ic
at
ion
s
m
ark
et
,
the
cre
di
bili
ty
of
each
op
erat
or
is
m
easur
e
d
by
the
diff
ere
nce
betwee
n
it
s
th
eor
et
ic
al
Q
oS
and
t
he
real
Q
oS
.
A
c
us
tom
er
is
interest
e
d
in
the
re
co
gnit
ion
of
SP
with
good
cred
i
bili
ty
(w
hi
ch
has
a
real
QoS
cl
os
e
to
t
he
the
or
et
ic
al
QoS).
A
nd
as
t
her
e
is
no
real
QoS
to
operat
or
s
can
no
t sol
ve
this p
roblem
in a d
irect
w
ay
. H
enc
e this k
ind
of problem
can
be
m
od
el
le
d
within the
m
eaning
o
f
the
inv
e
rse pr
oble
m
.
The
i
nv
e
rse
prob
le
m
is
gen
e
r
al
ly
ill
-
po
se
d
pro
blem
,
on
t
he
con
t
rar
y
li
ve
w
it
h
the
direct
pro
blem
that
the
so
l
ution
e
xists,
is
uniq
ue
and
de
pends
on
data.
F
or
exam
ple,
if
it
is
to
reconstr
uc
t
the
past
sta
te
of
a
syst
e
m
kn
owin
g
it
s
current
st
at
e,
we
are
dea
li
ng
with
a
n
in
ver
se
pro
blem
;
bu
t
the
fact
of
pr
e
dicti
ng
t
he
fu
t
ur
e
sta
te
giv
e
n
the
curre
nt
sta
te
is
a
di
rect
pro
bl
e
m
.
Si
m
i
la
rly
,
in
the
case
of
a
determ
inati
on
of
pa
ram
et
er
s
of
a
syst
e
m
kn
ow
i
ng
a
pa
rt
of
t
he
sta
ge
(a
par
t
of
the
set
of
par
am
et
ers)
;
w
e
sp
eak
of
pa
r
a
m
et
er
identific
at
ion
pro
blem
s.
To
m
y
kn
ow
l
edg
e
,
the
re
ar
e
no
pr
e
vi
ou
s
stud
ie
s
on
t
hi
s
prob
le
m
of
rati
on
al
c
ho
i
ce
of
se
rv
ic
e
pro
vid
er
s
(S
P
s)
in
the
te
le
com
m
un
ic
at
ion
s
m
ark
et
.
Stu
di
es
that
hav
e
been
c
onduct
e
d
on
the
relat
ion
s
hi
p
betwee
n
c
us
to
m
ers
an
d
SP
S.
Our
wor
k
is
pa
rt
of
the
relat
ion
s
hi
p
bet
wee
n
c
us
tom
ers
an
d
SP
s,
it
is
ba
sed
on
the
pa
per
[
3]
whose
a
utho
rs
us
e
d
the
t
heor
y
of
gam
es
to
analy
ze
the
c
om
pet
it
ion
betw
een
the
SP
s
.
Seve
ral
stud
ie
s
hav
e
be
en
car
ried
out
,
by
way
of
ex
a
m
ple
([
9],
[
4]
),
w
hich
m
od
el
ed
the
be
ha
vior
of
c
us
t
om
ers
in
the
current
com
petit
ion
be
twee
n
t
he
S
P
s
in
t
he
te
le
com
m
un
ic
a
ti
on
s
m
ark
et
.
The
m
igrati
on
of
cust
om
ers
in
this
m
ark
et
is
m
od
el
ed
as
a
Ma
r
kov
chai
n.
T
he
s
tud
ie
s w
ere b
a
sed
on
t
he
(the
or
et
ic
al
)
a
dv
e
rt
isi
ng
strat
e
gies
of
SP
s,
w
hic
h
le
aves
cons
um
ers
co
nfuse
d
si
nce the
y hav
e
no i
de
a ab
ou
t t
he real
strategie
s
of S
P s.
The
rest
of
the
pap
e
r
is
or
ga
ni
zed
as
fo
ll
ows
.
In
Sect
io
n
2.,
we
pr
ese
nt
m
od
el
in
g
pr
ob
le
m
at
ic
in
the
sense
of
in
verse
pro
blem
s.
In
Sect
io
n
3.,
We
pr
ese
nt
th
e
al
gorithm
that
we
use
d
to
so
lve
t
he
op
ti
m
iz
at
ion
m
od
el
s
propos
ed
in
this
st
udy.
In
Sect
io
n
4.,
we
pr
ese
nt
t
he
dif
fe
re
nt
nu
m
erical
resu
lt
s
obta
ined
.
In
S
ect
ion
5.
,
w
e
conclu
de
the
pap
e
r.
2.
FOR
M
ULAT
ION
A
ND M
ODELIN
G
O
F THE P
ROB
LE
M
In
t
his
sect
io
n,
we
m
od
el
the
pro
fit
of
a
c
ust
om
er
if
he
c
hoose
s
to
subsc
ribe
i
n
the
SPi
an
d
we
use
the
Luce
m
odel
to
m
at
he
m
a
ti
se
the
discre
t
e
cho
ic
e
of
c
li
ents
by
exp
l
oiti
ng
the
s
of
t
m
ax
functi
on
or
the
norm
al
iz
ed
exp
one
ntial
f
unct
ion
[
12
]
, a
s in
the a
rtic
le
[
11]
.
2.1.
Model
of
Ut
il
ity
C
u
st
omers
The
be
nef
it
of
a
con
su
m
er
is
of
te
n
cal
culat
ed
base
d
on
th
e
strat
egies
of
it
s
op
erato
r,
w
hich
are
the
QoS
an
d
the
pr
ic
e
it
offe
rs.
The
prof
it
ui
of
a
c
ons
um
e
r
re
gisters
with
the
operato
r
’s
ser
vices
S
P
i
is
as
fo
ll
ows:
W
it
h
q
i
is a
cli
ent’s re
venue i
f he c
hoos
es
th
e SP
i
a
nd
> 0
.
2.2.
The L
uce
Model
The
L
uce
m
od
el
is
a
first
pr
obabili
sti
c
cho
ic
e
m
od
el
that
inco
r
porates
bo
unde
dly
rati
onal
cho
ic
e
of
custom
ers[
1]
-
[
2].
W
it
h
t
his
m
od
el
,
c
us
t
om
er
s
can
ch
oose
t
he
ope
rator
t
ha
t
will
m
axi
m
ize
prof
it
s
by
c
hoos
i
ng
on
e
t
hat
has
th
e
m
ax
-
i
m
um
pr
oba
bili
ty
;
bu
t
forcin
g
this
ch
oice
is
inade
quat
e
in
this
area
giv
e
n
the
exis
te
nc
e
of
hidde
n
in
form
ation
that
ha
s
not
bee
n
re
pr
ese
nted
in
t
his
m
od
el
.
T
he
fo
ll
owin
g
e
quat
ion
re
pr
es
e
nts
the
pro
bab
il
it
y t
hat the c
us
tom
er c
hoos
es
SP
i
:
with
2
[
0;
1]
is
the
degree
of
custom
er
irrati
on
al
it
y,
N
is
the
nu
m
ber
of
S
P
s
and
p
a
nd
q
are
res
pecti
ve
ly
the
vecto
r of
pri
ce
and QoS
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2252
-
8776
IJECE
V
ol.
6
,
No.
3
,
Decem
ber
20
1
7
:
146
–
154
148
Wh
e
n
te
nd
s
t
o
0,
m
eans
that
custom
er
be
ha
vior
is
rati
on
al
,
i.e.,
they
ha
ve
al
l
the
in
f
or
m
at
ion
an
d
ru
le
s t
hat all
ow them
to
m
axi
m
iz
e their p
r
ofi
t, whil
e cust
om
ers
are ir
rati
onal
whe
n
a
ppr
oach
e
s
1.
2.3.
Dem
an
d
mo
d
el
D
i
We
c
on
si
der
a
m
ark
et
siz
e
n
(the
t
otal
num
ber
of
c
us
tom
e
rs)
,
the
f
un
ct
io
n
of
t
he
a
pp
li
c
at
ion
to
the
op
e
rato
r’
s
ser
vi
ces
i,
Di
is
t
he
pro
ba
bili
ty
that
a
cust
om
er
sel
ect
s
the
ope
r
at
or
m
ulti
plied
by
the
siz
e,
n,
of
the
m
ark
et
. I
t i
s
express
ed
b
y:
2.4.
Theoretic
al Q
ua
li
t
y of
Servi
ce
We c
onsider
Del
ay
u
the ti
m
e
require
d for
da
ta
tran
sm
issi
on
to
a
SPi
us
er
u. i
This ti
m
e is exp
ress
ed
in
That
m
eans
m
or
e
dem
and
is
gr
eat
er
tha
n
the
tim
e
increases,
an
d
vice
ver
sa
,
over
th
e
bandw
i
dth
increases
the ti
m
e b
ecom
es less i
m
po
rtant. T
his
propo
rtion
a
li
ty
is log
ic
al
since:
a.
More
as
dem
a
nd
i
ncr
ease
s,
t
he
num
ber
of
custom
ers
co
nnect
ed
to
t
he
SPi
bec
om
es
l
arg
e
a
nd
th
us
the tim
e b
eco
m
es
m
or
e im
po
rta
nt.
b.
More
t
han
t
he
band
width
incr
eases,
the
SP
l
arg
el
y
ha
s
cap
aci
ty
to
cov
e
r
al
l
custom
ers
and
there
f
ore
the tim
e b
ecam
e sm
aller.
In
the
m
od
el
of
L.
Klei
nr
oc
k
[8
]
with
que
ues,
Q
ualit
y
of
serv
ic
e
Q
oS
is
the
inv
erse
of
the
total
respo
ns
e ti
m
e
wh
e
n
the
us
e
r wants t
o
acce
s
s the service. L
et
ci the d
eadli
nes
f
or
t
ransm
i
ssion
of
data
be
tween
the
serv
ic
e
pr
ovide
r
an
d
the
pro
vid
er
se
rv
ic
es
l’SPi,
the
to
ta
l
t
i
m
e
of
the
answ
e
r
is
accum
ulate
s
between
ci
and D
el
ay
iu.
T
hu
s
the
quali
ty
o
f
servic
e is e
xpress
ed
b
y t
he follo
wing e
qua
ti
on
:
Fr
om
the
tw
o
equ
at
io
ns
(
4)
e
t
(5),
we
s
how
the
e
xistence
of
the
relat
ions
hip
bet
ween
th
e
qual
it
y
of
serv
ic
e,
d
em
an
d
Di(
p; q) = n i
(p;
q
)
and
ba
ndw
idth
i by the
f
ollow
i
ng equati
on
[3
]
:
or b
y t
he
f
ollo
wing e
qu
at
io
n:
Fr
om
the
e
qu
at
ion
s
(
6)
,
we
can
de
duce
t
hat
w
he
n
de
m
and
of
SPi
appr
oach
co
ve
rin
g
al
l
the
band
width
;
Q
oS bec
om
es less.
2.5.
Pro
blem
Formul
at
i
on
Fr
om
equati
on
(1),
we fi
nd t
ha
t t
he
the
or
et
ic
al
b
ene
fit o
f
a
us
er
is:
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mers’ Pe
rcepti
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owards
Services
of
Tele
comm
un
ic
ation
s
…
(
Driss
Ait
Oma
r
)
149
then
t
he real
b
e
nifit i
s:
with
qiR is a
re
al
Q
oS a
nd p
Ri
is a r
eal
pri
ce.
Assum
ption
1
I
n
te
le
com
m
un
ic
at
io
ns
,
the
re
is
no
gen
e
r
al
diff
e
re
nce
betwee
n
prom
otion
al
pri
ce
(the
or
et
ic
al
)
a
nd
the
real
pr
ic
e
that
the
us
e
r
pa
id
w
he
n
the
invoice
set
tl
em
ent.
Howe
ver,
as
in
al
l
areas
,
there
are
hidden
p
e
na
lt
ie
s r
el
at
ed
to
VAT,
t
he
i
nvoi
ce paym
ent tim
e ..
. B
ut in o
ur stu
dy w
e
ass
um
e that pi =
pR
i.
Takin
g
int
o
c
onside
rati
on
thi
s
assum
ption
1,
the
diff
e
re
nc
e
betwee
n
the
real
an
d
the
or
e
ti
cal
ben
efit
beco
m
es:
2.5.1.
Res
ou
rc
e M
anag
e
men
t Mo
del
Used
to
hel
p
op
e
rato
rs
i
n
t
he
te
le
com
m
un
ic
at
ion
s
fiel
d
to
m
ai
ntain
their
res
ources
so
that
t
he
diff
e
re
nce
bet
ween
thei
r
off
ers
an
d
ad
ver
ti
sing
that
be
ne
f
it
the
custom
e
r
act
ually
is
op
tim
al
.
It
is
a
too
l
to
custom
ers
w
ho
w
a
nt to re
gister w
it
h
the
oper
at
or
t
hat m
eet
s
their
need
s
.
unde
r
the
const
raints:
The
first
co
ns
t
raint
is
relat
ed
t
o
custom
er
pu
rc
hasin
g
po
w
er.
the
seco
nd
const
raint
is
a
form
ulati
on
in
te
rm
s
of
cu
stom
er
need
s
in
real
Q
oS.
it
m
us
t
m
eet
a
m
ini
m
u
m
thre
sh
ol
d
an
d
it
sh
ould
not
exc
eed
the
theo
reti
cal
Q
oS.
2.5.2.
Discrete
C
h
oice
Mode
l Cus
to
me
rs
L
et
s
cust
om
ers
know
t
he
weigh
t
(since
rity
)
of
al
l
operato
r
s
in
the
te
le
co
m
m
un
ic
at
ion
s
m
ark
et
.
T
his
pro
blem
is fo
r
m
ula
te
d
as a t
hi
s m
ult
i
-
obj
ect
ive m
od
el
:
unde
r
the
const
raints:
To
s
ol
ve
the
m
ul
ti
-
obj
ect
ive
pro
blem
(MOP)
,
we
m
us
t
transfo
rm
it
into
a
sin
gle
-
obj
ec
ti
ve
pro
blem
weig
hted. F
or this,
we
a
ppli
ed
the a
ggre
gatio
n
m
et
ho
d
a
nd t
he result
of the
tran
s
f
or
m
at
ion
is:
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ber
20
1
7
:
146
–
154
150
unde
r
the
const
raints:
To
s
ol
ve
the
m
ul
ti
-
obj
ect
ive
pro
blem
(MOP)
,
we
m
us
t
transfo
rm
it
into
a
sin
gle
-
obj
ec
ti
ve
pro
blem
weig
hted. F
or this,
we
a
ppli
ed
the a
ggre
gatio
n
m
et
ho
d
a
nd t
he result
of the
tran
s
f
or
m
at
ion
is:
w
ith
is c
onside
red vect
or
wei
gh
t
of the
oper
at
or
s i
n
the
tel
ecom
m
un
ic
at
ion
s m
ark
et
.
3.
GENET
IC
AL
GOR
IT
HM
Gen
et
ic
Algori
thm
s
(G
As
),
de
velo
ped
by
H
olland
[
9]
a
nd
his
stu
de
nt
G
ol
db
e
r
g
[
6],
a
re
base
d
on
the
m
echan
-
ic
s
of
natu
ral
ev
olu
t
ion
a
nd
nat
ur
a
l
gen
et
ic
s.
G
A
s
dif
fer
from
us
ua
l
inv
e
rsion
al
gorithm
s
be
cause
they
do
not
re
qu
i
re
a
sta
rting
value
.
The
GA
s
us
e
a
sur
viv
al
-
of
-
the
-
fit
te
st
sche
m
e
wi
th
a
rando
m
or
gan
iz
e
d
search
t
o
fin
d
the b
est
s
olu
ti
o
n
to a problem
.
So
lve a
n
opti
m
iz
at
ion
p
r
ob
l
e
m
is fin
d
the o
ptim
u
m
o
f
a fu
nct
i
on
from
a
finite
nu
m
ber
of
c
hoic
es,
oft
en
ver
y
la
rg
e.
T
he
pract
ic
al
app
li
cat
ion
s
a
re
num
e
rous,
w
hethe
r
in
the
fiel
d
of
indust
rial
producti
on
,
trans
port
or
econom
ic
s
-
wh
e
re
ver
the
re
is
need
to
m
i
nim
iz
e
or
m
ax
i
m
iz
e
dig
it
al
functi
ons
in
syst
em
s
si
m
ultaneou
sly
op
e
rate
a
la
r
ge
nu
m
ber
of
pa
ram
et
ers.
Algorithm
(1
)
repr
esents
the g
e
netic
alg
or
it
hm
u
sed
to op
ti
m
iz
e the
m
od
el
s
prop
os
e
d i
n
this
work.
4.
NUMER
IC
A
L RES
ULTS
In
t
his
sect
io
n,
we
present
t
he
num
erical
resu
lt
s
obta
ine
d
by
ass
um
ing
that
we
ha
ve
S
P
s
in
this
te
le
com
m
u
-
nic
at
ion
s
m
ark
et
.
We
us
e
the
ge
netic
al
go
rith
m
with
the
para
m
et
ers
that
will
a
ll
ow
us
to
ob
ta
in
the opti
m
al
so
l
ution f
or ou
r propose
d
m
od
el
s
.
4.1.
T
he
Real
Qua
li
t
y of t
h
e Func
tion S
t
udy
4.1.1.
St
u
dy o
f
a
Li
mi
te
d
Case
In
the
te
le
com
m
un
ic
at
ion
s
m
ark
et
,
the
real
qu
al
it
y
of
ser
vice
is
a
fu
nc
ti
on
that
depe
nd
s
on
th
e
band
width
i
a
nd
th
e
dem
and
Di
of
SPi.
I
n
reali
ty
,
we
know
that
w
he
n
the
ba
ndwi
dth
inc
reases,
the
real
qua
li
ty
of
se
r
vice
(
QoS)
inc
re
ases
a
nd
vice
ve
rsa;
al
so
wh
e
n
dem
and
inc
r
eases,
real
se
rvi
ce
qual
it
y
dec
reases
and
incre
ases wh
e
n
dem
and
d
ecrease
s.
In
t
his
co
ntext,
we
obser
ve
d
that t
he
real qu
al
it
y
can b
e
e
xpress
ed
as a
po
ly
nom
ia
l of
degree
2, the
va
riable
xi
is t
he
r
at
io
betwee
n i
an
d Di,
as
fo
l
lowing:
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Custo
mers’ Pe
rcepti
on T
owards
Services
of
Tele
comm
un
ic
ation
s
…
(
Driss
Ait
Oma
r
)
151
We
us
e
d
the
gen
et
ic
al
gorithm
(w
it
h
the
t
able
set
ti
ng
s
1)
to
fin
d
these
coef
fici
ents
f
or
di
ff
e
rent
values
of
band
width
i
an
d
of
dem
and
Di.
T
he
Fi
gure
s
1
et
2
s
how
the
i
nfl
ue
nce
of
res
pe
ct
ively
i
and
Di
on
Q
oS (t
he
or
ic
al
and real)
.
Table
1.
Ge
netic
A
lg
or
it
hm
Par
am
et
ers
to th
e
Fig
ur
e
s
of t
he
Result
s
1
et
2
Po
p
u
latio
n
size N
16
Ty
p
e sel
ectio
n
rou
lette
Ty
p
e of
cr
o
ss
o
v
er
Sin
g
le
-
p
o
in
ts
Prob
ab
ility
o
f
cr
o
ss
o
v
er
Pc
0
.7
Ty
p
e of
m
u
tatio
n
u
n
ifor
m
e
Prob
ab
ility
o
f
m
u
t
atio
n
0
.05
Maxi
m
u
m
nu
m
b
er
of
gen
eration
s
100
Fr
om
figs
(
1
e
t
2)
we
no
te
t
hat
with
the
c
hange
of
band
width
i
an
d
th
e
dem
and
Di,
the
ge
netic
al
gorithm
was
able
t
o
fin
d
t
he
good
c
oe
ff
i
ci
ents
of
t
he
poly
no
m
ia
l
to
m
ini
m
iz
e
the
gap
betwee
n
wh
at
is
theo
reti
cal
and
wh
at
is real.
I
n
the n
e
xt
pa
rt,
we
will
not
re
stric
t
ourselves
to
the
case p
re
sented
a
bove
, b
ut w
e
are
ex
pandin
g
the
stud
y
of
th
e
var
ia
ti
on
of
t
he
act
ual
qual
it
y
us
ing
the
te
chn
i
qu
e
of
dis
creti
zat
ion
do
m
inates
def
i
niti
on
of
th
eor
et
ic
al
qu
al
it
y
seeking
at
each
point
the
va
lue
of
the
act
ua
l
qu
al
it
y
by
s
olv
in
g
the
m
od
el
for
m
anag
in
g resources
.
4.1.2.
St
u
dy o
f
a
Gener
al Ca
se by Discre
ti
z
at
ion
The
qual
it
y
theor
et
ic
al
of
a
SPi
m
ay
var
y
within
a
ra
ng
e
delim
it
ed
by
a
m
ini
m
u
m
and
m
axi
m
u
m
value
qit
2
[qm
in;
q
m
ax].
To
m
ake
a
dig
it
al
reso
luti
on,
we
will
discret
iz
e
the
interval
3,
that
is
to
say
,
turn
it
into
a
n
a
ppr
oxim
a
te
prob
le
m
(d
isc
rete)
t
o
fin
d
the
val
ues
of
the
act
ual
qual
it
y
qi
R
at
each
poi
nt
of
t
he
discrete
do
m
ai
n.
Figure
3. Disc
r
et
iz
at
ion
of a
n i
nterv
al
or h i
s a
posit
ive
regular
pitc
h.
Stud
y
T
he
I
m
pact
of
Ba
ndwi
dth
on
qt
an
d
qr
We
la
un
c
hed
the
gen
et
ic
al
go
rithm
;
Ma
t
la
b
pro
gr
am
m
ed
with
the
par
a
m
et
ers
li
ste
d
i
n
Table
2;
on
the
m
od
el
of
reso
urce
m
anag
em
ent
with
var
ia
ti
on
of
band
width
i, a
nd w
e
obtai
n
t
he res
ults s
ho
wn in
Fig
ur
e
s
4,
5
a
nd
T
a
ble
3.
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V
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,
No.
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,
Decem
ber
20
1
7
:
146
–
154
152
Table
2.
Ge
netic
A
lg
or
it
hm
Par
am
et
ers
to th
e
Fig
ur
e
s
of t
he
r
es
ults 4
and
5
Po
p
u
latio
n
size N
20
Ty
p
e sel
ectio
n
at r
o
u
lette
Ty
p
e of
cr
o
ss
o
v
er
Multi
-
p
o
in
t
Prob
ab
ility
o
f
cr
o
ss
o
v
er
Pc
0
.65
Ty
p
e of
m
u
tatio
n
n
o
n
un
i
f
o
r
m
e
Prob
ab
ility
o
f
m
u
t
atio
n
0
.05
Maxi
m
al
Nu
m
b
e
r
o
f
gen
eration
300
The
Fi
gure
4
sh
ows
t
he
dec
rease
of
the
f
un
ct
io
n
F
it
ne
ss
relat
ive
to
i
te
rati
on
s
(g
e
ne
rati
on
s
)
the
gen
et
ic
al
-
go
rithm
. Th
e o
bject
ive f
unct
io
n
va
lue b
egi
ns
10
3, in the f
irst ge
ne
rati
on, to
r
eac
h
the v
al
ue
10 4
, in
the 2
53m
e g
en
erati
on.Th
is
re
su
lt
sh
ows that
the d
ecrease is
I
gue (r
em
ark
a
ble).
F
ro
m
Figu
re
5,
w
e
no
te
that t
o
achieve t
he
sa
m
e
m
ini
m
u
m
v
al
ue,
the
alg
or
i
thm
n
eed
s to
go to t
he 2
53 g
e
ner
at
io
n.
Table
3.
C
onve
rg
e
nce Res
ults
of the
Ge
netic
A
lg
or
it
hm
(
va
r
ia
ti
on
of
i)
Nu
m
b
e
r
o
f
gen
erat
io
n
253
m
in
i
m
u
m
cos
t
2
:
517
*10
-
4
step
of
dis
critization
h
Im
pact
on
De
m
and
St
ud
y
qt
and
qr
We
la
unche
d
t
he
ge
ne
ti
c
al
go
rithm
;
with
th
e
par
am
et
ers
li
ste
d
i
n
Table
4;on
the
m
od
el
of
res
ource
m
anag
em
ent
with
va
riat
ion
of
the
dem
and
Di,
an
d
w
e
obta
in
the
re
su
lt
s
sh
ow
n
in
the
foll
ow
i
ng
Fig
ur
e
s 6,
7
a
nd tabl
e 5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
ICT
IS
S
N:
22
52
-
8776
Custo
mers’ Pe
rcepti
on T
owards
Services
of
Tele
comm
un
ic
ation
s
…
(
Driss
Ait
Oma
r
)
153
Table
4.
ge
netic
algorit
hm
p
ar
a
m
et
e
rs
to the
Figure
s
of the
re
su
lt
s 6 an
d 7
Po
p
u
latio
n
size N
10
Ty
p
e of
selectio
n
at r
o
u
lette
Ty
p
e of
cr
o
ss
o
v
er
Multi
-
p
o
in
t
Prob
ab
ility
o
f
cr
o
ss
o
v
er
Pc
0
.60
Ty
p
e of
m
u
tatio
n
n
o
t un
i
f
o
r
m
e
Prob
ab
ility
o
f
m
u
t
atio
n
0
.05
Maxi
m
u
m
nu
m
b
er
of
gen
eration
200
The
Fi
gure
6
sh
ows
t
he
dec
rease
of
the
f
un
ct
io
n
F
it
ne
ss
relat
ive
to
i
te
rati
on
s
(g
e
ne
rati
on
s
)
the
gen
et
ic
al
go
-
rithm
.
the
obj
ect
ive
f
un
ct
i
on
val
ue
be
gins
with
102
in
t
he
first
gen
e
rati
on,
re
achin
g
the
valu
es
5;
694
10
4,
in
th
e
167th
gen
e
ra
ti
on
.
T
his
res
ul
t
sh
ows
that
th
e
decr
ease
is
I
gu
e
(r
em
ark
abl
e).
From
the
Figure
7,
We
note
that
to
ac
hieve
the
sam
e
m
ini
m
u
m
v
al
ue,
the al
gorithm
n
eeds
to go
t
o
the
16
7 gen
e
rati
on.
Table
5
. C
onve
rg
e
nce Res
ults
of the
Ge
netic
A
lg
or
it
hm
(v
a
r
ia
ti
on
of
Di)
Nu
m
b
e
r
o
f
g
en
erat
io
n
167
m
in
i
m
u
m
cos
t
5
:6
9
4
*10
-
4
step
of
dis
critization
h
4.2.
M
od
el
Re
so
luti
on
of the
Weigh
t C
alcu
lation
In
this
par
t,
w
e
con
si
der
t
hat
we
ha
ve
a
te
le
com
m
un
ic
at
i
on
s
m
ark
et
tw
o
operat
or
s
.
We
will
us
e
the
m
od
el
of
discr
et
e
cho
ic
e
of
custom
ers
to
fin
d
their w
ei
ght
in
this
m
ark
et
ran
gi
ng
phii
and
Di
an
op
e
rat
or.
Th
e
cal
culat
ion
of
these
wei
gh
ts
i
s
a
kin
d
of
dec
is
ion
sup
port
f
or
c
us
tom
ers
seekin
g
to
re
gis
te
r
with
the
se
rv
ic
es
of the m
os
t si
nc
ere
op
e
rato
r (
who has m
or
e
confide
nce i
n
t
he
se
ns
e
of the
d
if
fer
e
nce
bet
ween qt a
nd
qR
).
4.2.1.
I
mp
act
of Ban
dwi
dt
h
on
The
Wei
ght
of
Oper
ators
We
var
y
the
band
width
of
the
ope
rat
or
1
an
d
obse
rv
e
the
infl
ue
nce
on
wei
gh
t
a
nd
that
of
the
adv
e
rsa
ry.
T
he
Fig
ur
e
8
s
how
that
the
weig
ht
of
the
operat
or
is
a
n
inc
reasin
g
f
un
ct
io
n
c
om
par
ed
t
o
band
width
1
,
then
the
weig
ht
of
it
s
ad
ver
sa
ry
is
a
decr
eas
ing
f
unct
io
n
w
it
h
resp
ect
to
1.
This
r
e
su
lt
is
real
,
since
the
inc
re
ase
in
ba
ndwi
dt
h
1
ca
us
es
the
i
m
pr
ovem
ent
of
th
e
real
Q
oS
q1R
an
d
the
refor
e
t
he
oper
at
or
1
m
us
t hav
e a
go
od r
e
puta
ti
on
a
nd a
good
weig
ht for his
adver
sary.
4.2.2.
I
mp
act
of D
em
and
D on
The
Wei
ght
of
Oper
ators
We
will
var
y
the
re
quest
of
the
operato
r
1
a
nd
ob
se
r
ve
the
i
nf
lue
nce
on
weig
ht
a
nd
that
of
t
he
adv
e
rsa
ry.
The
Figu
re
9
show
s
that
the
wight
of
op
e
rato
r
1
is
decr
easi
ng
f
un
ct
io
n
com
par
ed
to
dem
and
D1
,
then
the
wight
of
it
s
a
dversa
ry
is
a
i
ncr
ea
s
ing
f
un
ct
io
n
c
om
par
ed
t
o
D
1
.
This
res
ult
is
real,
beca
use
the
increase
in
de
m
and
D
1
caus
es
degrad
at
io
n
of
the
real
Q
oS
q1
R
a
nd
the
r
efore
the
opera
tor
1
m
us
t
no
t
hav
e
a
good
reputat
io
n
a
nd a
good
w
ei
gh
t
for his a
dversa
ry.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2252
-
8776
IJECE
V
ol.
6
,
No.
3
,
Decem
ber
20
1
7
:
146
–
154
154
5.
CONCL
US
I
O
N
we
us
e
d
the
I
nv
e
rse
P
roble
m
Theo
ry
in
the
te
le
co
m
mu
nicat
io
ns
fiel
d
to
so
l
ve
the
prob
le
m
of
m
ini
m
iz
ing
the
dif
fer
e
nce
bet
ween
the
t
heor
et
ic
al
qu
al
it
y
and
the
act
ual
qual
it
y
wh
ic
h
th
e
operat
or
offe
rs
to
us
ers
,
w
hich
is
a
pr
oble
m
of
decisi
on
suppo
rt.
W
e
ha
ve
of
fer
e
d
cust
om
ers
a
too
l
for
de
ci
sion
by
cal
cu
la
ti
ng
the w
ei
gh
t
of t
he op
e
rato
rs
i
n t
he
te
le
com
m
un
ic
at
io
ns
m
ark
et
.
Fo
r
the
num
er
ic
al
so
luti
on
of
in
ver
se
pro
bl
e
m
s
fo
rm
ulate
d
as
optim
izati
on
prob
le
m
s,
we
us
e
d
gen
et
ic
al
go
-
rit
hm
s
that
hav
e
sh
ow
n
t
heir
power
s
in
t
he
fiel
d
of
opti
m
iz
at
i
on.
T
he
first
m
od
el
,
ha
s
al
lo
w
ed
us
to
stud
y
the
s
ha
pe
of
the
real
qu
al
it
y.
The
s
econd
m
od
el
,
al
lowed
us
to
cal
culat
e
the
weigh
t
of
the
op
erators
in
the
te
le
com
m
un
ic
at
ion
s
m
ark
et
as
a
decisi
on
s
upport
t
oo
l
that
al
lo
w
s
us
er
s
to
stre
a
m
li
ne
their
operat
or
cho
ic
e.
In this
wor
k,
t
h
e num
erical
r
esults sh
ow the
e
ff
ect
ive
ness o
f t
he
ap
proac
h f
ollow
e
d.
REFERE
NCE
S
[1]
H.S.
Kim
;
C.
H.
Yoon,
“
Dete
rm
ina
nts
of
subs
criber
chur
n
and
c
ustom
er
lo
y
alt
y
in
the
Korea
n
m
obil
e
t
el
epho
n
y
m
ark
et
”
,
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ec
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mm
unic
ati
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J.
Qi,
Y.
Zha
n
g,
Y.
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ng
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Shi,
“
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ti
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”
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AP
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m
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h
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h
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ket
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e
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rs
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ral
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a
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ral
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ine
tt
i
and
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y
lva
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Tuff
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rna
ti
on
al
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er
en
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es,
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ti
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iz
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n,
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m
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h
abbi
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ir,
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n
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ce
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ke
t
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e
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e
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h
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ersar
ial
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e
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ers and
migrating customers
.
”
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c.
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eNe
ts,
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China,
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il 2011.
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Michalewi
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ti
c
al
gor
ithm
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dat
a
struct
ure
s
=
evol
ut
io
n
progra
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”
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.
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it
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uta
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te
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i
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an
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si
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li
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at
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bio
lo
g
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cont
r
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and
a
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re
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l
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Naldi
and
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ng
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”
17th
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ti
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E
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at
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ul
at
ion
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om
pute
r
and
Te
l
ec
om
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unic
at
io
n
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y
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EE
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r
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ber
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[11]
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edi
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e
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v
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l
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her
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Evaluation Warning : The document was created with Spire.PDF for Python.