Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
8
,
No.
6
,
D
ece
m
ber
201
8
, pp.
4391
~
43
97
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v8
i
6
.
pp
4391
-
43
97
4391
Journ
al h
om
e
page
:
http:
//
ia
es
core
.c
om/
journa
ls
/i
ndex.
ph
p/IJECE
Analysis
Model i
n t
he Cloud
Opti
mizati
on
Consum
ption in
Pricin
g the
Inter
net Band
width
Indra
w
at
i
,
Fit
ri
M
ay
a
P
uspi
ta
,
Sri E
rl
it
a
,
Ino
se
nsius
N
adeak
Depa
rt
m
ent
o
f
Mathe
m
at
i
cs,
Fa
cul
t
y
of
Ma
the
m
at
i
cs
and
Natur
a
l
Scie
n
ce
s,
Sriwij
a
y
a
Univ
ersity
,
I
ndonesia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Ma
y
2
, 2
01
8
Re
vised
Ju
l
2
,
201
8
Accepte
d
J
ul
21
, 2
01
8
The
probl
em
of
int
ern
et
pri
ci
ng
i
s
a
proble
m
tha
t
is
ofte
n
a
m
aj
or
proble
m
in
opti
m
iz
ation.
In
thi
s
stud
y
,
the
in
te
rne
t
pri
ci
ng
sc
heme
foc
uses
on
opti
m
iz
ing
the
use
of
band
width
consum
pti
on.
T
h
is
rese
ar
ch
utilizes
m
odifi
cation
o
f
cl
oud
m
odel
in
findi
ng
opti
m
a
l
soluti
on
in
n
e
twork.
Cloud
c
om
puti
ng
is
computat
ion
al
m
odel
which
is
li
ke
n
et
work,
se
rve
r,
stor
age
an
d
service
th
at
is
uti
lizing
in
te
r
net
conn
ec
t
ion.
As
IS
P'
s
Inte
rne
t
service
provid
er
req
uir
es
appr
opriate
pri
c
ing
sche
m
es
in
orde
r
to
m
axim
iz
e
rev
enu
e
a
nd
provide
qual
ity
of
servi
c
e
(Qual
i
t
y
o
n
Se
rvic
e)
or
QoS
so
a
s
to
sati
sf
y
in
t
ern
et
users
or
u
sers.
The
m
odel
used
wil
l
be complet
ed
wi
th
t
he
hel
p
of LING
O software
progra
m
to
get
opti
m
al
solut
ion
and
a
cc
ur
at
e
re
sult.
Based
on
t
he
opti
m
al
soluti
on
obtaine
d
from
the
m
odifi
cation
of
the
c
loud
m
odel
ca
n
be
uti
l
iz
ed
ISP
to
m
axi
m
iz
e
rev
enu
e
and
pr
ovide
serv
ices
in
accorda
n
ce
wit
h
nee
ds
and
req
uests.
Ke
yw
or
d:
Cl
oud
c
om
pu
ti
ng
In
te
r
net
pr
ic
in
g
LING
O
Copyright
©
201
8
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
:
Fit
ri May
a Pu
s
pita,
Dep
a
rtm
ent o
f M
at
hem
a
ti
cs, F
acult
y o
f
Ma
them
atics and
Natu
ral Scie
nc
es
,
S
riwij
ay
a
U
niv
e
rsity
,
Jln.
Ra
ya
Pale
m
ban
g
-
P
rabu
m
u
l
ih K
M
32 Ind
e
ralay
a,
Og
a
n Ili
r
,
Indon
esia
.
Em
a
il
: fit
ri
m
a
yap
uspit
a@
unsr
i.ac.i
d
1.
INTROD
U
CTION
I
nter
net
m
od
er
nizat
ion
ta
ke
s
an
act
ive
r
ole
in
hum
an
act
ivit
ie
s
and
li
fe.
F
or
s
om
e
peo
pl
e,
intern
et
is
al
read
y
a
pa
rt
of
thei
r
li
ves.
The
I
nter
net
is
a
colle
ct
ion
of
com
pu
te
r
networks
that
are
connecte
d
t
o
eac
h
oth
e
r.
I
n
the
i
nt
ern
et
acce
ss
it
is
require
d
a
sta
nd
a
r
d
prot
ocol
su
ch
as
(TCP
)
Protoc
ol
Tra
ns
m
issi
on
Cont
ro
l
or
(I
P
)
I
nter
net
P
ro
t
oco
l
duty
to
prov
i
de
ad
dr
e
sses
an
d
ide
ntit
ie
s
on
each
c
om
pu
te
r
in
ord
er
to
av
oid
e
rror
s
i
n
sen
ding
data
[
1]
.
I
n
to
day'
s
m
od
ern
era
,
in
te
rn
et
us
e
rs
ha
ve
m
et
a
ll
the
l
ow,
m
idd
le
,
an
d
up
per
cl
ass
.
In
te
r
net
us
a
ge
al
so
do
no
t
ca
re
the
a
ge,
from
young
to
old.
T
he
grow
t
h
of
us
e
r
s
involvi
ng
al
l
ci
rcles
an
d
a
ges
is
in
flue
nce
d
by
the
li
fe
sty
le
t
hat
fo
ll
ow
s
t
he
dev
el
op
m
ent
of
the
e
ra
tha
t
i
m
pact
on
th
e
patte
rn
of
li
fe.
I
n
tod
ay
'
s
te
r
m
s,
t
he
I
nter
net
can
be
sai
d
to
be
a
li
br
ary
in
w
hich
there
a
re
ki
nd
s o
f
i
nfor
m
at
ion
el
em
ents
s
uch
as
te
xt,
vi
deo,
gr
a
ph
ic
s
, a
nd sou
nd,
wil
l
hav
e
a
lot o
f very c
omplet
e inform
at
i
on
[
2]
.
The
m
or
e
In
te
rn
et
us
e
rs,
the
gr
eat
er
the
de
m
and
f
or
qual
it
y.
As
an
In
te
rn
et
ser
vice
prov
i
der
,
the
In
te
r
net
Se
rv
i
ce
Prov
i
der
(ISP)
s
houl
d
prov
i
de
bette
r
qu
al
it
y
and
bette
r
qual
it
y
of
serv
ic
e
t
o
use
rs
i
n
achievin
g
t
he
best
qual
it
y
of
inf
or
m
at
ion
a
t
a
cost
that
is
eff
ic
ie
nt.
The
refor
e
ISPs
ar
e
require
d
t
o
pro
vid
e
pro
per
I
ntern
et
co
st
plan
ning
m
echan
ism
s to
be
nef
it
ISPs
a
s servic
e
prov
i
der
s
and
us
e
rs as i
nter
ne
t u
ser
s
[
3]
.
In
c
reasin
g
t
he
num
ber
of
i
nt
ern
et
us
ers
is
certai
nly
di
re
ct
ly
pr
op
or
ti
onal
to
the
i
nc
rease
in
the
a
m
ou
nt
of
ba
ndwi
dth
c
onsum
pt
ion
.
T
he
a
m
ou
nt
of
ba
ndwidth
c
ons
umpti
on
is
ce
rtai
nly
relat
ed
to
t
he
co
st
.
Ba
ndwidt
h
is
a
qu
a
ntit
y
that
sh
ows
the
a
m
ou
nt
of
data
that
can
pass
in
a
netwo
r
k
connecti
on.
C
omm
o
n
internet
pri
ci
ng
schem
es
are
flat
rate,
us
ag
e
-
base
d
an
d
two
-
pa
rt
ta
riff.
Ba
sed
on
pr
e
vi
ou
s
rese
arc
h
on
non
-
li
near
wi
reless
internet
pr
ic
in
g
sc
hem
es
com
pi
le
d
by
[
4]
,
internet
pr
ic
in
g
sc
hem
es
on
m
ul
ti
ple
Qo
S
f
or
si
ngle
li
nk
[
5]
,
wirele
ss
inter
net
pri
ci
ng
sc
hem
es
are
usual
ly
assoc
ia
te
d
with
QoS
band
widt
h
at
tr
ibu
te
s,
bit
er
ror
rate
(BER),
en
d
-
to
-
end
delay
[6]
.
Op
ti
m
al
intern
et
pr
ic
ing
is
re
qu
i
red
by
co
nsi
der
in
g
net
wor
k
ser
vices.
I
ntern
et
pr
ic
in
g
sc
hem
es arethe
pr
ob
le
m
s
and
r
e
qu
i
re
the
rig
ht so
l
ution
s
to
b
e
nef
it
I
SPs
a
nd users
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
20
88
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
4391
-
4397
4392
Re
search
c
onduct
ed
by
[
7]
sta
te
d
that
o
ne
of
the
strat
e
gies
that
the
I
SP
ca
n
do
t
o
m
ini
m
i
ze
costs
a
nd
m
axi
m
iz
e
pr
ofi
ts
is
bund
le
pri
ci
ng.
B
un
dle
pr
ic
in
g
ca
n
be
interp
r
et
ed
as
a
m
ark
et
ing
pract
ic
e
w
her
e
t
wo
or
m
or
e
diff
ere
nt
pr
od
ucts
are
pu
t
to
gethe
r
in
on
e
pac
ka
ge.
In
ad
diti
on
to
bund
le
pri
ci
ng,
Acc
ordi
ng
t
o
[8]
,
util
it
y
fu
nctio
ns
relat
e
to
the
l
evel
of
sat
isfac
ti
on
co
ns
um
ers
get
fo
r
the
co
ns
u
m
ption
of
inf
or
m
at
ion
ser
vices
that ca
n
m
axim
iz
e p
rofit
s to a
chieve
certai
n g
oals
.
In
pre
vious
re
search
done
by
[9
]
,
[
10]
t
he
pri
ci
ng
sc
he
m
e
to
al
locat
e
Q
oS
an
d
m
axim
iz
e
IS
P
rev
e
nue
ha
de
been
al
s
o
dis
cusse
d.
T
he
pr
ic
in
g
schem
e
is
do
ne
to
m
ake
reso
ur
ce
eff
ic
ie
ncy
to
fin
d
op
ti
m
iz
ation
pro
blem
so
luti
ons
us
i
ng
bott
le
necks
[3]
al
so
cond
uct
resear
ch
on
QoS
al
locat
ions
invol
ving
a
sing
le
route
fro
m
the sour
ce
dest
inati
on
.
Ever
y
I
ntern
et
us
e
r
m
us
t
ha
ve
a
c
ollec
ti
on
of
file
s
sto
r
ed
in
el
ect
roni
c
-
file
s.
S
om
e
file
s
m
a
y
be
ob
ta
ine
d
from
e
-
m
ail,
at
ta
chm
ents,
dow
nloa
ds
,
a
nd
m
or
e
.
In
ge
ner
al
,
do
c
um
ents
stored
in
va
rio
us
hard
m
edia,
su
c
h
a
s
hard
disk
,
fl
ash
disk
,
PC
and
la
ptop
f
or
instance,
Staa
S
[11]
.
I
n
file
stora
ge
,
it
ha
s
so
m
e
const
raints
su
c
h
as
file
loss,
lost
stora
ge
m
e
dia,
ex
posed
viru
ses
a
nd
so
on.
T
her
e
fore
,
it
would
be
nice
if
the
stora
ge
of
data
or
file
s
buil
t
and
sto
red
in
on
e
place
t
hat
is
el
ect
ro
nic
file
s.
I
n
a
ddit
ion
t
o
pro
vid
e
easy
a
ccess
that ca
n be
do
ne
an
yt
i
m
e and
anyw
her
e
, elec
tro
nic f
il
e sto
ra
ge
al
s
o helps i
n
te
rm
s o
f
d
at
a
loss.
Pr
oble
m
s ab
out t
he
networ
k
m
uch
d
isc
us
se
d
in the wo
rld of
c
om
pu
te
rs
a
nd
business
w
orl
d.
Netw
ork
pro
blem
is
m
o
stl
y
do
ne
in
int
ern
et
pri
ci
ng
optim
iz
at
ion
prob
le
m
.
Cl
ou
d
com
pu
ti
ng
pro
blem
s
beco
m
e
on
e
of
the
pro
blem
s
in
the
netw
or
k
that
is
warm
ly
discuss
ed
tod
ay
[
12
]
.
Cl
oud
com
pu
ti
ng
[
13]
is
one
of
the
com
pu
ti
ng
m
od
el
that
can
be
acce
ssed
a
ny
wh
e
re
an
d
a
ny
tim
e.
Cl
ou
d
com
pu
ti
ng
is
an
on
-
dem
and
serv
ic
e
acce
ss
to
a
c
ol
le
ct
ion
of
c
ompu
ti
ng
res
ourc
es
su
c
h
as
net
works,
se
r
ver
s
,
stora
ge,
ap
plica
ti
on
s
s
uc
h
as
secu
re
vo
ti
ng
syst
em
u
sin
g
c
ript
ogra
ph
y
[
14
]
a
nd
s
erv
ic
es.
T
he
m
ai
n
co
nce
rn
ab
ou
t
cl
oud
com
pu
ti
ng
is
reli
a
bili
ty
issues
i
n
pro
vid
in
g
c
om
pu
ti
ng
nee
ds
as
re
quire
d
by
us
ers
su
c
h
as
pe
rform
ing
the
pr
oc
ess
to
gethe
r,
s
end
i
ng
and
receivin
g
file
s
tog
et
he
r.
This
is
becau
s
e
the
cl
ou
d
sy
stem
will
serve
as
a
ph
ysi
cal
serv
e
r
that
will
dr
ive
m
ul
ti
ple
virtu
al
serv
ers
.
The
l
ast
few
ye
ars
,
the
de
velo
pm
ent
of
cl
oud
com
pu
ti
ng
wa
s
on
c
e
discuss
e
d
by
[15]
con
ce
r
ning
use
fu
l
par
al
le
l
c
om
pu
ti
ng
.
T
o
div
i
de
the
ta
sk
int
o
se
ver
a
l
m
or
e
com
puti
ng
a
nd
/
or
stora
ge
resou
rces,
w
hi
ch
creat
e
a
la
rg
e
scal
e
syst
em
and
sen
d
ba
ck
the
res
ults
to
the
us
e
r.
P
roblem
s
abo
ut
scheduli
ng
ta
sk
s
in
the
e
nvir
on
m
ent
of
c
loud
com
pu
ti
ng
ha
ve
al
so
be
en
disc
us
se
d
by
[16
]
,
[
17]
.
Re
search
by
[
18]
and
[19]
ha
ve
al
s
o
form
ulate
d
ta
sk
sc
hedulin
g
pro
blem
s
that
are
run
us
in
g
m
ulti
pr
ocess
syst
em
s
so
that
the
le
ng
t
h
of
t
he
sc
hedul
e
can
be
m
ini
m
iz
ed,
an
d
em
plo
yi
ng
gen
et
i
c
al
gorithm
s
fo
r
optim
iz
at
io
n
ot
her
t
ha
n
that
[
20
]
discusse
s
hem
orrh
a
ge
pa
rtic
le
opti
m
iz
at
ion
(PSO
)
base
d
on
cl
oud
re
sou
rce
a
pp
li
cat
ion
sche
dule
s
that
ta
ke
into acc
ount
both c
om
pu
ta
ti
onal
cost
s and
da
ta
tran
sm
issi
on
c
os
ts
.
This
stu
dy
ai
m
s
to
stud
y
an
d
analy
ze
sc
he
m
es
fo
r
cl
ou
d
netw
orks
a
nd
t
o
f
or
m
ulate
new
dy
nam
ic
m
od
el
plans
a
nd
can
w
ork
unde
r
wi
reless
netw
ork
cl
ouds
.
This
st
ud
y
fo
c
us
es
on
optim
iz
ing
the
us
e
of
band
width
i
n
wh
ic
h
the
m
odel
of
the
cl
ou
d
will
be
com
pl
et
ed
u
sin
g
the
op
ti
m
iz
ation
m
et
ho
d.
Cl
oud
m
od
el
it
sel
f
will
be
sim
pl
ifie
d
into
the
m
at
he
m
a
ti
c
al
m
od
el
first
by
determ
ining
the
pu
rpose
functi
on
an
d
f
un
ct
i
on
const
raints.
T
he
adv
a
ntage
s
of
this
resea
rc
h
include
resea
rc
h
on
the
cl
oud
m
od
el
is
still
new
an
d
has
not
been
m
uch
discuss
e
d.
B
esi
des
that
,
this
researc
h
can
be
ap
preci
at
ed
and
us
ef
ul
fo
r
inter
net
serv
ic
e
pro
vide
r
(I
S
P
)
who
ca
n
a
pply
this
m
et
ho
d
s
o
as
t
o
ben
e
fit
businessm
an.
T
his
st
ud
y
al
so
has
a
dvanta
ges
wh
ic
h
the
case
raised
from
thi
s
stud
y
fo
c
us
es
on
the
c
onsu
m
ption
of
ba
nd
w
idth
wh
ic
h
is
the
thi
ng
t
hat
re
m
ai
ns
a
hot
issue
i
n
the
net
wor
k
w
or
l
d.
W
it
h
t
his
resea
rch
,
the
e
xp
e
xtati
on
to
use
the
data
bandw
i
dth
ca
n
be
op
ti
m
iz
ed.
R
esearc
h
on
optim
iz
ation
of
cl
oud
c
om
pu
ti
ng
m
od
el
has
al
so
ra
rely
been
ex
plore
d
so
t
h
is
resea
rch
beco
m
es
the
m
ai
n
con
t
rib
ution o
f
this r
e
searc
h.
2.
RESEA
R
CH MET
HO
D
In
this
researc
h,
t
he
cal
c
ulati
on
will
be
c
omplet
ed
by
us
in
g
the
opti
m
iz
a
t
ion
so
l
ution
in
the
form
of
Mi
xed
In
te
ger
Linear
P
rogr
a
m
m
ing
(MILP
)
by
sim
ulatin
g
the
f
or
m
of
op
ti
m
iz
ation
m
od
el
us
in
g
L
I
N
G
O
so
ft
war
e
.
The
stud
y
use
s
sec
onda
ry
data
of
internet
ba
nd
width
c
onsu
m
ption
w
hich
is
the
traff
ic
m
a
il
data
ob
ta
ine
d
from
the
local
se
r
ve
r
in
Pale
m
ba
ng
w
hich
t
he
n
the
da
ta
will
be
s
ubsti
tuted
into
the
ap
pro
pr
ia
te
par
am
at
er on
t
h
e e
xisti
ng m
od
el
.
3.
RESU
LT
S
A
ND AN
ALYSIS
In this st
ud
y t
he
optim
iz
at
ion
m
od
el
u
sed
is
base
dar
e a
s fol
lows
∑
∑
.
+
(
−
)
.
∈
∈
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
& C
om
p
Eng
IS
S
N: 20
88
-
8708
An
alysis Mo
de
l i
n
the Cl
oud
Op
ti
miz
atio
n
C
on
s
umpti
on in Pri
ci
ng
….
(
Fit
ri May
a
P
.
)
4393
∑
.
≤
.
∀
∈
,
∀
∈
∈
(2)
∑
∑
=
1
∀
∈
∈
∈
(3)
∑
≤
1
∀
∈
∈
(4)
≤
∀
∋
,
∀
∈
∈
{
0
,
1
}
,
∈
{
0
,
1
}
,
∈
[
0
,
1
]
(5)
The object
ive
f
un
ct
io
n
is s
ho
wn
i
n (1) a
nd
t
he
c
on
st
raint fun
ct
io
n
s a
re
s
how
n
i
n
(
2), (3
), (4),
a
nd (5
).
Con
st
raint
(
2)
is
us
ed
to
a
vo
i
d
the
possibil
it
y
of
a
s
olu
ti
on
that
will
exce
ed
the
ca
pacit
y
set
.
Con
st
raint
(
3)
ens
ur
e
s
that
th
e
ser
ver
assig
ns
the
us
a
ge
pro
per
ly
.
C
onstrai
nt
(
4)
s
hows
t
ha
t
on
ly
one
f
re
qu
e
ncy
on
wi
ll
be
sel
ect
ed.
C
ons
trai
nt
(
5)
is
use
d
t
o
bind
t
he
decisi
on
va
ri
able
with
to
the
obj
ect
ive
f
un
ct
io
n
.
Af
te
r
def
i
ning
the
e
xisti
ng
m
od
el
,
the
ne
xt
de
finiti
on
of
eac
h
pa
ram
et
er
and
the
va
riables
us
e
d
i
n
the
m
od
el
in
T
able
1
a
nd 2
will
b
e e
xp
la
i
ne
d.
Table
1.
Param
et
ers
f
or Eac
h M
od
el
Para
m
eter
Def
in
itio
n
Bu
sy
b
an
d
wid
th
to
r
u
n
server
at f
req
u
en
cy
Activ
e
-
id
le ban
d
w
id
th
to run
server
at f
requ
en
cy
W
o
rklo
ad
de
m
an
d
o
f
app
licatio
n
Max p
erfo
r
m
an
ce
o
r
capacit
y
Table
2
.
Var
ia
bles fo
r
Eac
h M
od
el
Variable
Def
in
itio
n
Utilizatio
n
of
server
run
n
in
g
at
f
requ
en
cy
Bin
ary
vari
ab
le
Bin
ary
vari
ab
le
Af
te
r
def
i
ning
each
pa
ram
et
e
r
an
d
var
ia
ble
us
e
d,
in
Table
3
we
will
sh
ow
the
data
us
e
d.
T
he
dat
a
us
e
d
in this
res
earch
is sec
onda
ry d
at
a obtai
ne
d
f
ro
m
o
ne of
the local ser
ve
r.
T
he
data
us
e
d
is data t
ra
ff
ic
m
ai
l
that
is
div
i
ded
into
tw
o
sessi
ons,
nam
el
y
wh
e
n
the
us
e
of
the
ser
ve
r
in
bu
sy
tim
es
and
th
e
us
e
of
i
dle
se
rv
e
rs
bu
t
rem
ai
n
act
i
ve.
In
this
stu
dy
there
a
re
two
di
ff
ere
nt
cases
base
d
on
the
us
ef
uln
e
ss
of
each
m
od
el
.
I
n
case
I
is
a
gen
e
ral
m
od
el
work
i
ng
on
the
serv
e
r
wh
il
e
in
case
II
is
us
e
d
to
balance
t
he
us
e
of
the
se
r
ver
s
o
it
can
be
us
e
d
wh
e
n
the
w
orkloa
d
excee
ds
the
capaci
ty
because
in
cas
e
I
can
no
t
be
us
e
d
f
or
c
ondi
ti
on
s
w
he
n
w
orkl
oad
exceed
s ca
pacit
y, ie
a.
Ca
se I
In
case
I
the
m
od
el
f
or
m
will
fo
ll
ow
t
he
m
ain
m
od
el
f
orm
,
so
t
her
e
is
no
s
ign
ific
a
nt
di
f
fe
ren
ce
.
I
n
ot
her
words,
the
obje
ct
ive
functi
on
in
case
I
with
the
m
a
in
m
odel
will
be
the
sa
m
e
so
the
co
ns
trai
nt
functi
on
will
r
em
ai
n
the sam
e.
b.
Ca
se I
I
In case
II
t
hat
disti
nguish i
s i
n
case
II this c
onditi
on used
will
b
e
diff
e
re
nt that is
∈
[
0
,
1
]
In
a
dd
it
io
n,
th
e
functi
on
c
on
strai
nts
(
2)
,
a
nd
(
3)
to
be
cha
ng
e
d
wit
h
the
functi
on
co
ns
tr
ai
nts
(6),
an
d
(
7)
as foll
ows
∑
∑
.
≥
∀
∈
∈
∈
(6)
∑
≤
∀
∈
,
∀
∈
∈
(7)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
20
88
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
4391
-
4397
4394
In
this
st
ud
y
,
there
are
al
so
s
ever
al
c
onditi
ons
t
hat
f
ollo
w
t
wo
pre
vious
ca
ses.
T
her
e
are
4
c
onditi
ons
for
eac
h
case.
Condit
ions
ar
e
disti
nguis
he
d
by
dif
fer
e
nc
es
in
the
sel
e
ct
ion
of
fr
e
qu
ency
val
ues
f
or
eac
h
serv
e
r.
S
om
e
o
f
these
co
nd
it
ion
s
a
re
m
ade
i
n
orde
r
to
ad
j
ust
to
any
po
ssi
bili
ti
es
that
exi
st
so
that
the
m
od
el
can stil
l
be use
d.
a.
Condit
ion 1
In co
ndit
ion
1
,
sel
ect
ed
f
reque
ncy as
fo
ll
ows
=
{
{
1
,
2
}
,
f
or
=
1
{
3
,
4
}
,
f
or
=
2
b.
Condit
ion 2
In co
ndit
ion
2 sel
ect
ed
f
reque
ncy f
or each
se
rv
e
r
i i
s t
he
sa
m
e, that
is
=
{
1
,
2
}
,
for
=
1
,
2
c.
Condit
ion 3
In co
ndit
ion
3
,
sel
ect
ed
f
reque
ncy as
fo
ll
ows
=
{
{
1
,
2
}
,
for
=
1
{
3
,
4
,
5
}
,
for
=
2
d.
Condit
ion 4
In co
ndit
ion
4
,
sel
ect
ed
f
reque
ncy as
fo
ll
ows
=
{
{
1
,
2
,
3
}
,
for
=
1
{
3
,
4
}
,
f
or
=
2
Table
3
.
Value
of
Eac
h
Pa
ram
et
er
Para
m
eter
s
Valu
e
11
5
3
3
4
.9
2
8
1
7
8
12
9
9
4
4
.3
3
2
1
2
7
13
8
8
0
2
.4
5
0
7
21
9
3
2
0
.4
9
5
2
2
8
22
1
0
8
3
7
.64
8
7
5
23
1
0
3
0
9
.12
0
8
4
24
1
0
6
0
4
.62
5
1
2
25
9
0
9
3
.0
6
0
1
6
1
11
7
8
8
2
.6
2
5
1
2
1
12
1
1
6
3
0
.88
4
8
6
13
1
2
5
6
3
.42
0
7
6
21
1
2
9
0
4
.85
2
8
5
Para
m
eters
Valu
e
22
1
1
1
7
5
.84
8
5
2
23
1
3
1
9
3
.51
5
9
7
24
1
2
6
4
5
.80
8
0
3
25
1
1
9
2
9
.06
4
1
1
1149
2
1290
11
1553
12
1607
13
1068
21
1724
22
1811
23
1766
24
1819
25
1937
Af
te
r
determ
ining
t
he
existi
ng
case
a
nd
the
var
i
ou
s
co
ndit
ion
s
us
e
d,
the
n
the
m
od
el
is
sol
ved
by
us
i
ng
LING
O
as
an
app
li
cat
io
n
to
so
lve
the
opti
m
iz
at
ion
pro
ble
m
.
Table
4
a
nd
Ta
ble
5
s
how
the
res
ults
of
th
e
LING
O
s
olu
ti
on
for
eac
h of t
he
existi
ng case
s,
as
fo
ll
ow
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
& C
om
p
Eng
IS
S
N: 20
88
-
8708
An
alysis Mo
de
l i
n
the Cl
oud
Op
ti
miz
atio
n
C
on
s
umpti
on in Pri
ci
ng
….
(
Fit
ri May
a
P
.
)
4395
Table
4
.
So
l
ver Stat
us
for
Ca
s
e 1
on Eac
h
C
onditi
on
So
lv
er
Statu
s
Cas
e I
Co
n
d
itio
n
I
Cin
d
itio
n
I
I
Co
n
d
itio
n
I
II
Co
n
d
itio
n
I
V
Mod
el Class
MI
L
P
MI
L
P
MI
L
P
MI
L
P
State
Glo
b
al Opti
m
al
Glo
b
al Opti
m
al
Glo
b
al Opti
m
al
Glo
b
al
Op
ti
m
al
Ob
jectiv
e
1
5
6
4
4
.05
1
4
6
5
5
.42
1
4
4
2
7
.99
5
3
3
4
.9
2
8
Inf
easib
ility
0
0
0
0
Iter
atio
n
0
0
0
0
Exten
d
ed
Solv
er
Statu
s
So
lv
er
T
y
p
e
Bran
ch
and
Bo
u
n
d
Bran
ch
and
Bo
u
n
d
Bran
ch
and
Bo
u
n
d
Bran
ch
and
Bo
u
n
d
Bes
t Objectiv
e
1
5
6
4
4
.05
1
4
6
5
5
.42
1
4
4
2
7
.99
5
3
3
4
.9
2
8
Step
s
0
0
0
0
Up
d
ate
Interval
2
2
2
2
GMU
(K
)
28
28
31
31
ER (
Se
c)
1
0
0
0
In
the
cas
e
I
f
or
the
f
our
c
ondi
ti
on
s,
the
gr
ea
te
st
ob
j
e
ct
ive
s
olu
ti
on
was
found
in
c
onditi
on
I
with
the
op
ti
m
al
so
luti
on
obta
ine
d
w
as
15
644.0
5
obta
ined
th
rou
gh
21
it
erati
on
s
with
no
in
f
easi
bili
ty
.
Generat
ed
Mem
or
y
Use
d
(G
M
U)
s
how
s
the
am
ou
nt
of
m
e
m
or
y
al
l
ocati
on
us
e
d
i
s
28K
a
nd
Ela
ps
e
d
Ru
nti
m
e
(ER)
descr
i
bes
t
he
t
otal t
i
m
e sp
ent
to g
e
ne
rate an
d com
plete
the
m
od
el
. ER for
conditi
on I i
s 0 seco
nds
.
Table
5
.
So
l
ver Stat
us
for
C
as
e 2
on Eac
h
C
onditi
on
So
lv
er
Statu
s
Cas
e I
I
Co
n
d
itio
n
I
Co
n
d
itio
n
I
I
Co
n
d
itio
n
I
II
Co
n
d
itio
n
I
V
Mod
el Class
MI
L
P
MI
L
P
MI
L
P
MI
L
P
State
Glo
b
al Opti
m
al
Glo
b
al Opti
m
al
Glo
b
al Opti
m
al
Glo
b
al Opti
m
al
Ob
jectiv
e
1
5
6
4
4
.05
1
4
6
5
5
.42
1
4
4
2
7
.99
1
7
2
6
4
.99
Inf
easib
ility
0
0
0
0
Iter
atio
n
21
22
26
24
Exten
d
ed
Solv
er
Statu
s
So
lv
er
T
y
p
e
Bran
ch
and
Bo
u
n
d
Bran
ch
and
Bo
u
n
d
Bran
ch
and
Bo
u
n
d
Bran
ch
and
Bo
u
n
d
Bes
t Objectiv
e
1
5
6
4
4
.05
1
4
6
5
5
.42
1
4
4
2
7
.99
1
7
2
6
4
.99
Step
s
0
0
0
0
Up
d
ate
Interval
2
2
2
2
GMU
(K
)
30
30
33
33
ER (
Se
c)
0
0
0
0
In
t
he
sec
ond
case
f
or
al
l
fou
r
c
onditi
on
s
,
the
great
est
obj
ect
ive
so
luti
on
was
ob
ta
ine
d
i
n
conditi
on
I
V
with
the
opti
m
al
so
luti
on
ob
ta
ine
d
was
17264.9
9
obta
ined
t
hro
ugh
24
it
erati
on
s
with
no
infeasibil
it
y.
G
ener
at
e
d
Me
m
or
y
Use
d
(
GM
U)
s
hows
the
a
m
ou
nt
of
m
e
m
or
y
allocati
on
us
e
d
f
or
33
K
an
d
Ela
ps
ed
Ru
nti
m
e
(ER)
descr
i
bes
the
total
tim
e
us
ed
to
generate
and
com
plete
the
m
od
el
.
ER
fo
r
co
nd
i
ti
on
IV
is
0
seco
nd
s
.
Fo
r
t
he
so
l
utio
n
of
each
var
i
able
us
e
d
in
the
m
od
el
fo
r
each
case
an
d
fo
r
eac
h
c
ondi
ti
on
is
sh
ow
n
in
T
a
ble 6
.
Table
6.
So
l
ution f
or Eac
h Va
riables
Variables
Cas
e 1
Cas
e 2
Co
n
.
I
Co
n
.
II
Co
n
.
II
I
Co
n
.
IV
Co
n
.
I
Co
n
.
II
Co
n
.
II
I
Co
n
.
IV
11
1
1
1
0
0
1
0
0
12
0
0
0
0
0
0
0
0
13
0
0
21
1
1
22
0
0
23
1
0
1
0
24
0
0
0
0
0
0
25
1
0
1
0
11
1
1
1
1
1
1
1
1
12
0
0
0
0
0
0
0
0
13
0
0
21
1
1
22
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
20
88
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
4391
-
4397
4396
Table
6.
So
l
ution f
or Eac
h Va
riables
Variables
Cas
e 1
Cas
e 2
Co
n
.
I
Co
n
.
II
Co
n
.
II
I
Co
n
.
IV
Co
n
.
I
Co
n
.
II
Co
n
.
II
I
Co
n
.
IV
23
1
0
1
0
24
0
0
0
0
0
0
25
1
0
1
1
111
1
1
1
1
0
.93
3
0
3
2
8
0
.93
3
0
3
2
8
0
.93
3
0
3
2
8
0
.51
6
4
1
9
8
112
0
0
0
0
0
.06
6
9
6
7
1
6
0
.06
6
9
6
7
1
6
0
.06
6
9
6
7
1
6
0
121
0
0
0
0
0
0
0
0
122
0
0
0
0
0
0
0
0
131
0
0
132
0
0
211
0
0
212
1
0
.68
7
9
3
5
0
221
0
0
222
0
0
231
0
0
0
0
232
1
0
0
.67
1
5
7
4
2
0
241
0
0
0
0
0
0
242
0
0
0
0
0
0
251
0
0
0
0
.33
4
0
2
1
7
252
1
1
0
.61
2
2
8
7
0
0
The
va
riable
s
olu
ti
ons
sho
w
us
that
for
s
om
e
par
ts,
the
values
are
0s
or
1s
dep
e
nd
ing
on
the
conditi
ons
as
form
s
of
m
ixed
intege
r
li
nea
r
pro
gr
am
m
in
g
pro
blem
.
The
so
luti
ons
on
ly
wo
r
k
f
or
C
ase
1
pro
blem
on
ly
.
Since
f
or
Ca
se
2,
s
om
e
var
ia
ble
val
ues
vio
l
at
e
th
e
intege
r
const
raints.
So,
the
Ca
se
1
w
he
re
the
m
od
el
fo
rm
will
fo
ll
ow
t
he
m
ai
n
m
od
el
form
will
be
the
best
so
l
ution
t
hat
IS
P
ca
n
c
onside
r
in
gaini
ng
t
he
prof
it
by u
ti
li
zi
ng the cl
oud o
pti
m
iz
at
ion
-
pri
ci
ng
schem
e.
4.
CONCL
US
I
O
N
In
t
his
re
searc
h,
t
her
e
are
2
diff
e
re
nt
cases
that
ha
ve
4
c
onditi
ons
re
spe
ct
ively
.
From
the
s
olu
ti
on
us
in
g
L
ING
O
it
was
f
ound
th
at
the
res
ults
f
or
eac
h
c
onditi
on
dif
fer
from
each
ot
her
but
al
l
are
in
the
f
or
m
of
Mix
ed
In
te
ger
Linear
Pro
gr
a
m
m
ing
(
MILP
)
w
it
h glo
bal s
ol
ution
.
ACKN
OWLE
DG
E
MENTS
The
researc
h
l
eadin
g
to
this
stud
y
was
fina
ncial
ly
su
pp
or
t
ed
by
Sr
i
wij
ay
a
U
niv
e
rsity
f
or
sup
port
thr
ough
Com
petit
ive Leadin
g Gra
nt i
n 201
7
.
REFERE
NCE
S
[1]
Y.
Mar
y
ono
and
B.
P.
Istia
n
a, "T
eknol
ogi
Inform
asi
dan
Kom
unika
si",
A.
B.
Dar
m
adi
,
Ed
.
,
2008.
[2]
L.
Sidh
arta, "Int
ern
et Informasi
Beba
s Ham
batan
”,
Jak
arta, E
l
ex M
edi
a
Kom
putindo
,
1996
.
[3]
J.
B
y
un
and
S.
C
hat
t
erj
e
e,
"A
stra
te
gi
c
pricing
for quali
t
y
of
servi
c
e
(QoS
)
net
work
business
"
,
in
Pr
oce
ed
ings o
f
th
e
Tenth
Ame
ri
cas
Confe
renc
e
on
I
nformation
Syst
e
ms
,
New
York,
2
004.
[4]
E.
W
allen
ius
an
d
T.
Häm
äl
ä
ine
n
,
"P
ric
ing
Model
for
3G/4G
Net
works
"
,
in
13th
IEE
E
Inte
rnat
io
nal
Symposium
on
Pe
rs
onal,
Indoo
r,
and
Mob
il
e
R
adio
Comm
unications
,
2002
.
[5]
F.M.
Pus
pit
a,
K
.
Sem
an,
B.
M.
Ta
ib
,
and
Z
.
Sh
afi
i
,
"Im
prove
d
Models
of
Int
er
net
Ch
arg
ing
S
c
heme
of
Singl
e
Bott
le
n
ec
k
Li
nk
in
Multi
QoS
Ne
tworks
"
,
Journal
of Appl
i
ed
S
ci
en
ce
s,
vo
l. 13, pp.
572
-
579,
2013
.
[6]
Indra
wati,
Irm
eil
y
ana,
F.M.
Pus
pit
a
,
and
O.
Sa
njay
a
,
"Int
ern
et
pric
ing
on
band
width
func
t
ion
diminished
with
inc
re
asing
b
and
width
ut
i
li
t
y
fun
ct
ion"
,
TEL
KOMNIKA,
vo
l. 13, pp. 299
-
304,
20
15.
[7]
S.
Visw
ana
th
an and
G.
Ananda
l
i
ngam,
"P
ric
ing
strategie
s fo
r
info
rm
at
ion
goods"
,
pp.
257
-
274
,
20
05.
[8]
X.
W
ang
and
H.
Schulz
rinn
e,
"P
ric
ing
net
work
resourc
es
for
ada
pti
v
e
applic
at
ions
in
a
diff
e
ren
tiate
d
servi
ces
net
work
"
,
in
Pro
ce
ed
ings o
f
IEEE
INFOCOM 20
01
,
2001
.
[9]
W
.
Yang,
H
.
L.
Ow
en,
and
D.M.
Blough,
"A
Com
par
ison
of
A
uct
ion
and
Fla
t
Prici
ng
for
Diffe
ren
t
ia
t
ed
Servi
ce
Networks
"
,
in
P
roce
edi
ngs o
f th
e
IE
EE Int
ernat
i
onal
Conf
ere
nce on
Comm
unic
at
ions
,
2004.
[10]
W
.
Yang,
H.
L.
Ow
en,
and
D.M.
Blough
,
"
Dete
rm
ini
ng
Di
ffe
ren
t
ia
t
ed
Ser
vic
es
N
e
twork
Prici
ng
Throug
h
Aucti
ons
"
,
in
Ne
tworki
ng
-
ICN
20
05,
4th
Int
ernational
Conf
ere
nce on
Ne
tworki
ng
April
2005
,
2005
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
& C
om
p
Eng
IS
S
N: 20
88
-
8708
An
alysis Mo
de
l i
n
the Cl
oud
Op
ti
miz
atio
n
C
on
s
umpti
on in Pri
ci
ng
….
(
Fit
ri May
a
P
.
)
4397
[11]
S.
Ro
y
,
P.K.
Pa
t
tna
ik
,
and
R
.
M
al
l
,
"A
cogni
t
ive
Approac
h
for
E
val
ua
ti
ng
th
e
Us
abi
lit
y
of
Stor
ag
e
as
a
Serv
ice
in
Cloud
Com
puti
n
g
Envi
ronm
ent
"
,
Inte
rnationa
l
J
ournal
of
E
le
c
tric
al
and
Computer
Engi
n
ee
ring
(
IJE
CE)
,
vol.
6
,
pp.
759
-
769
,
20
16.
[12]
K.K.
Chenna
m
and
M.A.
La
kshm
i,
"Cloud
Secur
ity
in
Cr
y
pt
Dat
aba
se
Serve
r
Us
in
g
Fine
Grain
ed
Acc
ess
Control
"
,
Inte
rnational
Jo
urnal
of El
e
ct
ri
c
al
and
Comput
er
Engi
n
ee
ring
(
IJE
CE)
,
vol
.
6
,
pp
.
915
-
924,
2016.
[13]
T.
Sasidh
ar,
V.
Havisha
,
S
.
Kou
shik,
M.
Dee
p
,
a
nd
V.K.
R
edd
y
,
"Loa
d
Ba
la
n
ci
ng
Techni
ques
for
Eff
icient
Tr
aff
i
c
Mana
gement
in
Cloud
Envi
ronm
ent
"
,
Inte
rnat
ion
al
Journal
of
Elec
tri
cal
and
Computer
Engi
nee
r
ing
(
IJE
CE)
,
vol.
6,
pp
.
963
-
973
,
2016.
[14]
M.
Ranj
an
,
A.H.
Mondal,
a
nd
M.
Saikia,
"A
Clo
ud
Based
Secur
e
Voting
S
y
stem
using
Hom
o
m
or
phic
En
cr
y
pti
o
n
for
Android
Plat
form
"
,
Inte
rnational
Journal
of
El
e
ct
rica
l
and
Computer
Engi
ne
ering
(
IJE
CE)
,
vol.
6,
pp.
2994
-
3000,
2016
.
[15]
V.
Kum
ar,
A.
Gr
ama,
A.
Gupta
,
a
nd
G.
Kar
y
p
is,
"
Introduc
t
ion
to
p
ara
l
le
l
computin
g"
,
vol
.
110
,
199
4.
[16]
D.
Agrawal
,
S.
Das,
and
A.
E.
A
bbadi
,
"Big
data
and
c
loud
computing:
cur
ren
t
state
and
fu
ture
o
pportuni
ties
"
,
i
n
14th
Int
ernati
on
al
Conf
ere
nce o
n
Exten
ding
Dat
abase
Technol
og
y
,
ACM
,
2011.
[17]
V.
Petruc
ci,
O.
Loque
s,
and
D.
Mos
se,
"A
Dy
n
a
m
ic
Optimiza
ti
o
n
Model
for
Po
wer
and
Perform
anc
e
Mana
g
eme
nt
of
Virtua
l
ized
C
luste
rs"
,
in
Proc
ee
ding
e
-
En
ergy
'10
Proceedi
ng
s
of
the
1st
In
ter
nati
onal
Conf
e
renc
e
on
Ene
rgy
-
Ef
fici
ent
Comput
ing
and
N
et
work
ing
Pass
au, Ge
r
m
an
y
,
2010.
[18]
E.
S.H.
Hou,
N.
Ans
ari
,
and
H
.
Ren,
"A
gen
et
i
c
al
gori
thm
for
m
ult
iproc
essor
sche
dul
ing,
Par
allel
and
Distribu
t
ed
S
y
stems
,
"
Int
ernati
onal Journal of
Gr
id
and
Dist
ribute
d
Comput
i
ng,
vol
.
7
,
2014
.
[19]
P.
Vara
l
akshm
i,
A.
R
amasw
am
y
,
A.
Balasubram
ani
an,
and
P.
Vij
a
y
kum
ar,
"A
n
Optimal
W
orkflow
Based
Schedul
ing
and
Resourc
e
Al
loca
ti
on
in
Cloud"
,
i
n
Computing
an
d
Comm
unic
ati
o
ns
,
2011,
pp.
41
1
-
420.
[20]
S.
Pande
y
,
L
.
W
u,
S.
Guru,
a
nd
R.
Bu
yy
a
,
"
A
Parti
cle
Sw
ar
m
Optimiza
ti
on
-
Based
Heuri
st
i
c
for
Sch
edul
in
g
W
orkflow
Applic
ations i
n
C
loud
"
.
BIOGR
AP
H
I
ES
OF
A
UTH
ORS
Indra
wati
h
er
S.Si
degr
ee
in
Math
emati
cs
from
Sriwijay
a
Univer
si
t
y
,
South
Sum
at
e
ra,
Indone
sia
in
1996.
The
n
s
he
recei
ved
h
er
M.Si
in
Actua
ri
a
l
Scie
nc
e
in
200
4.
She
has
bee
n
a
Mathe
m
at
i
cs
Depa
rtment
m
e
m
ber
at
Fa
cul
t
y
m
at
hematics
an
d
Natur
a
l
Sci
en
ce
s
Sriwij
a
y
a
U
nive
rsit
y
South
Sum
at
era
Indon
esia
sinc
e
1998
.
Her
rese
arc
h
i
nte
rests
in
cl
ud
e
opti
m
iz
a
ti
on
,
a
ct
uar
ia
l
scie
n
ce
and
insuran
ce pr
oble
m
s.
Fitri
Ma
y
a
Pus
pit
a
re
ce
iv
ed
her
S.Si
degr
ee
in
Mathe
m
at
i
cs
from
Sriwijay
a
Univer
sit
y
,
South
Sum
at
era
,
Indo
nesia
in
1997.
The
n
she
recei
ved
he
r
M.Sc
in
Mathe
m
at
i
c
s
from
Curti
n
Univer
sit
y
of
Technol
og
y
(CUT)
W
este
rn
Aus
tralia
in
2004.
She
rev
ei
v
ed
h
is
Ph.D
in
Sci
ence
and
Technol
og
y
in
2015
from
Univer
siti
Sains
Islam
Malay
s
ia.
She
has
be
en
a
Mathe
m
atics
Depa
rtment
m
e
m
ber
at
Fa
cul
t
y
m
at
hematics
an
d
Natur
a
l
Sci
en
ce
s
Sriwij
a
y
a
U
nive
rsit
y
South
Sum
at
era
Indon
esia
sinc
e
1998.
Her
rese
ar
ch
in
te
rests
in
cl
ude
o
pti
m
iz
ation
and
it
s
appl
i
cations
such
as
v
ehi
c
le r
outi
ng
prob
le
m
s a
nd
QoS
pri
ci
ng
and
ch
arg
ing
in
t
hird
gen
erati
on
i
nte
rne
t
.
Sri
Erl
ita
cur
r
e
ntly
is
an
und
erg
rad
ua
te
stud
ent
a
t
Mathe
m
at
i
cs
Depa
rtme
nt,
Facu
lty
of
Mathe
m
at
i
cs
an
d
Natur
al
Sci
en
ce
s,
Sriwij
a
y
a
U
nive
rsit
y
.
She
is
cur
ren
t
l
y
on
fin
al
stag
e
of
her
the
sis
subm
issio
n.
Her
topic
intere
st
in
cl
udes
Optimiza
ti
o
n
an
d
it
s
appl
i
ca
t
ion
on
pric
ing
of
informati
on
serv
ic
e
in
cl
oud
e
nv
i
ronm
ent
.
Inosensius
Nade
ak
cur
ren
tly
is
a
n
under
gra
dua
te
student
a
t
Mathem
at
ic
s
Depa
rtm
ent
,
Fa
cul
t
y
of
Mathe
m
at
i
cs
an
d
Natur
al
Sc
ie
n
ce
s,
Sriwij
a
y
a
Univer
sit
y
.
He
i
s
cur
ren
tly
on
fi
nal
stag
e
of
her
the
sis
subm
is
sion.
His
topi
c
int
ere
st
inc
lud
es
Optimiza
ti
o
n
and
it
s
appl
ic
a
ti
on
on
pr
ic
ing
of
informati
on
serv
ic
e
e
in cl
oud
en
vironment.
Evaluation Warning : The document was created with Spire.PDF for Python.