Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 4
,
A
ugu
st
2015
, pp
. 76
5
~
77
1
I
S
SN
: 208
8-8
7
0
8
7
65
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Time Series
P
r
ediction Using
Radial Basis Function Neural
Network
Haviluddin
*
, Imam
T
a
h
y
u
d
i
n**
* Dept. of Comp
uter Science, Facult
y
of Mathematic and
Natur
a
l
Scienc
e, Mulaw
a
rman University
, Indonesia
** Dept. of
Infor
m
ation S
y
stem,
ST
MIK AMIKOM Purwokerto, I
ndonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 18, 2014
Rev
i
sed
Ap
r
23
, 20
15
Accepted
May 16, 2015
This paper presents an approach for
predicting
dail
y
n
e
twork traffic usin
g
artif
icial neur
al networks (ANN), na
me
ly
radi
a
l
ba
si
s function neural
network (RBFNN) method. The data is
gained f
r
om 21-24
June 2013 (192
sa
mple
s se
rie
s
da
ta
) in ICT Unit of Mula
wa
rma
n
Unive
r
sity
,
Ea
st
Kalim
antan
,
Ind
ones
i
a.
The res
u
lts
of m
eas
urem
ent are us
ing
s
t
atis
ti
cal
analy
s
is, e.g. su
m of
square error (SSE
), mean o
f
square error (MSE), mean
of abs
o
lute p
e
r
cent
a
ge e
rror (
M
AP
E)
, and mean of absolu
te deviation
(M
AD). The res
u
lts
s
how that values
ar
e the sa
m
e
, with differ
e
nt goals tha
t
have b
een s
e
t
ar
e 0.001
, 0
.
002, and 0.
003, and
spread 200
.
The s
m
allest MSE
value indicates
a good method
for accu
racy
. Th
erefore, the
RB
FNN
model
illustrates
the pr
oposed best m
o
d
e
l
to
pr
edict d
a
il
y
network
traff
i
c.
Keyword:
MA
D
MA
PE
MSE
Net
w
or
k t
r
a
ffi
c
RBFNN
SSE
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Hav
iludd
in
,
Dept
.
o
f
C
o
m
put
er
Sci
e
nce,
Facu
lty of Math
em
at
ics an
d
Natural Scien
c
e,
Mu
lawarm
an
Un
i
v
ersity, East Kalim
an
tan
,
Indo
n
e
sia.
Em
a
il: h
a
v
ilu
dd
in@un
m
u
l
.ac.id
1.
INTRODUCTION
The m
a
nagem
e
nt
o
f
t
r
af
fi
c
qu
ot
a i
s
a
n
i
m
port
a
nt
pa
rt
,
especi
al
l
y
f
o
r
t
h
e
or
ga
ni
zat
i
ons
t
h
at
use
in
fo
rm
atio
n
tech
no
log
y
.
Subsequ
e
n
tly, for
th
e lead
ersh
i
p
, m
a
n
a
g
e
m
e
n
t
traffic
qu
o
t
a
will h
e
lp
i
n
mak
i
n
g
d
ecision
s th
at
will b
e
n
e
fit th
e efficiency and e
ffective for
org
a
n
i
zatio
n
s
inclu
d
i
ng
un
iv
ersities.
Th
e pred
icting
activ
ities
are a
p
a
rt o
f
org
a
n
i
zatio
n m
a
n
a
g
e
m
e
n
t
. Sub
s
eq
u
e
n
tly, th
e daily n
e
twork
t
r
affi
c
pre
d
i
c
t
i
on i
s
al
s
o
a p
r
ocess
of a
n
al
y
z
i
ng a
nd
det
e
r
m
i
n
i
ng t
h
e
qu
ot
a o
f
ba
nd
wi
d
t
h i
n
a net
w
o
r
k i
n
t
h
e
fut
u
re, i
n
whic
h a technical analysis approa
ch usa
g
e
da
t
a
t
r
af
fi
c. Fu
rt
he
r
m
ore, t
h
e pre
d
i
c
t
i
ng t
ech
ni
q
u
e
s use
d
in
th
e literatu
re can
b
e
classified
in
t
o
two
categ
o
ries: stati
s
tical an
d
so
ft-co
m
p
u
tin
g
m
o
d
e
ls. Th
e statistical
m
odel
s
i
n
cl
ud
es si
m
p
l
e
regr
essi
on
l
i
n
ear
(
S
R
L
), e
x
po
ne
n
t
i
a
l
sm
oot
hi
n
g
,
t
h
e aut
o
re
g
r
es
si
ve m
ovi
ng
a
v
era
g
e
(AR
M
A
)
,
aut
o
reg
r
essi
ve
i
n
t
e
grat
e
d
m
ovi
n
g
ave
r
age
(
A
R
I
M
A
) a
n
d
gene
ral
i
zed a
u
t
o
reg
r
essi
ve
co
n
d
i
t
i
onal
h
e
tero
sk
ed
asti
city (GARCH)
m
o
d
e
ls. Nev
e
rth
e
less, th
es
e m
odels are foc
u
se
d around
the su
ppo
sitio
n
t
h
at th
e
several
of tim
e
series
data linearly correlate
and
p
r
ovi
de
po
or
p
r
edi
c
t
i
o
n
p
e
rf
orm
a
nce [
1
-
5
]
.
Mean
wh
ile, the d
a
ily n
e
twork
traffic
d
a
ta are
n
o
n
lin
ear an
d non
-stationary in
n
a
ture.
To
ov
erco
m
e
t
h
i
s
l
i
m
i
t
a
t
i
on, t
h
e secon
d
m
odel
i
s
so
ft
-c
o
m
put
i
ng m
e
t
hods
ha
ve bee
n
sug
g
est
e
d
.
F
u
rt
herm
ore, m
odel
i
n
g
u
s
ing
th
e artifi
c
ial n
e
ural n
e
t
w
ork (A
NN)
m
o
d
e
l can
prov
id
e
b
e
tter an
alytical resu
lts, an
d it is effect
iv
e fo
r
forecasting, i
n
whic
h this
m
e
thod is
able t
o
work
well
on t
h
e
non-linear ti
me-series
data
[3, 6-8].
Th
erefo
r
e, th
is p
a
p
e
r will stud
y on
e
of th
e
ANN
m
o
d
e
ls,
n
a
m
e
l
y
th
e Rad
i
al Basis Fu
nctio
n
Neural
Net
w
or
k (R
B
F
N
N
),
i
n
or
de
r t
o
a
d
dress t
h
e i
ssu
e o
f
ne
t
w
o
r
k t
r
af
fi
c t
i
m
e
seri
es dat
a
t
h
at
has
n
o
n
-
l
i
n
ea
r
ch
aracteristics. Th
is
p
a
p
e
r con
s
ists of fou
r
sectio
n
s
.
In
trodu
ctio
n sectio
n is th
e m
o
tiv
atio
n
to
do
th
e
writ
in
g
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
76
5
–
77
1
76
6
th
e article.
Nex
t
, th
e m
e
th
o
d
o
l
og
y is
d
e
scri
b
e
s
o
f
m
o
d
e
l.
Th
ird
section
i
s
th
e an
alysis
an
d d
i
scu
ssi
o
n
resu
lts,
and fi
nally conclusion section is resea
r
ch s
u
mmaries.
2.
R
E
SEARC
H M
ETHOD
The R
B
F
NN i
s
t
h
e a
b
b
r
evi
a
t
i
on
of
radi
al
basi
s f
u
nct
i
o
n
ne
ural
net
w
o
r
k
w
h
i
c
h i
s
b
a
sed
on t
h
e
fu
nct
i
o
n ap
pr
o
x
i
m
at
i
on t
h
eo
r
y
or su
pe
rvi
s
e
d
an
d
uns
u
p
er
vi
sed m
a
nner
were
use
d
t
o
g
e
t
h
er. S
u
bse
q
u
e
nt
l
y
, i
t
has a
u
n
i
q
ue t
r
ai
ni
n
g
al
go
ri
t
h
m
cal
l
e
d hy
b
r
i
d
m
e
t
hod
t
h
at e
m
erg
e
d as
a v
a
rian
t
o
f
NN in late 80
’s. Th
is
m
o
d
e
l is a k
i
nd
o
f
f
eed-
f
or
war
d
n
e
u
r
al
n
e
t
w
or
k (
F
FNN)
in
wh
ich
in
cludes an
i
n
pu
t layer
,
a
h
i
dd
en
layer
,
and
an
out
put
l
a
y
e
r
[
9
,
1
0
]
as see
n
i
n
Fi
gu
re
1.
Fi
gu
re 1.
R
B
F
neu
r
al
net
w
or
k
st
ruct
ure
[
11]
In
ge
neral
,
R
B
FN
N p
r
ocess t
h
e fi
rst
p
h
ase i
s
u
n
su
pe
rvi
s
e
d
l
earni
n
g
bet
w
een i
n
p
u
t
l
a
y
e
r an
d hi
dd
e
n
layer
th
at non-
lin
ear
r
a
d
i
al-b
ased
activ
atio
n fu
nctio
n
s
,
co
mm
o
n
l
y G
a
u
ssian fu
nction
.
Second
p
h
ase is
sup
e
r
v
i
s
ed
l
ear
ni
n
g
bet
w
ee
n
h
i
dde
n l
a
y
e
r a
n
d
out
put
l
a
y
e
r
wi
t
h
a l
i
n
e
a
r.
‖
1
‖
1
w
h
er
e
‖
1
‖
is the E
u
clidea
n
distance,
c
is
th
e cen
ter
o
f
Gau
ssian fun
c
tion
1
,
2
,…,
,…
,
is th
e
qt
h
inp
u
t d
a
ta.
Hen
c
e, in th
is t
h
is stud
y th
e arch
itectu
r
e
of
R
B
FNN
as s
h
ow
n i
n
Fi
g
u
r
e
2, a
n
d
t
h
e e
q
uat
i
o
n i
s
.
whe
r
e:
Y = ou
tpu
t
va
lu
e;
φ
=
hi
dde
n
val
u
e
;
W
=
w
e
i
ght
s (
0
-
1
)
The al
gorithm
of RBFNN to a
n
alyze withi
n
t
i
m
e
series d
a
ta ch
aracteristics is:
1.
In
itializatio
n
of th
e n
e
t
w
ork.
2.
Determ
in
in
g
the in
pu
t si
g
n
a
l t
o
h
i
dd
en layer, and
find
is a
distance
data
to
wh
er
e
,
1
,
2
,
…
,
3.
Find
1
is a resu
l
t
activ
atio
n
from
d
i
stan
ce d
a
ta m
u
lt
ip
ly b
i
as.
1
∗
x
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ti
me
Seri
es Pr
edi
c
t
i
on
Usi
n
g
Ra
di
al
B
a
si
s F
unct
i
o
n N
e
ur
al
N
e
t
w
ork
(
H
avi
l
ud
di
n)
76
7
4.
Fi
nd
wei
ght
a
n
d
bi
as l
a
y
e
rs,
2
and
2
, in eac
h
1
,
2
,
…
,
Determi
n
ing
tra
i
n
i
ng
samp
les an
d test samp
les
Th
e n
e
t
w
ork
traffic d
a
ta no
rm
ally sh
o
w
s n
e
t
w
ork
activ
ities is wh
ich
in
d
i
cate th
e p
e
riod
s o
f
tim
e
[1
2
]
. In
th
is stud
y, th
e d
a
ta
were collected
fro
m
ICT serv
er
of
Un
i
v
ersitas M
u
lawarm
an
. Th
en, th
e d
a
ta
were
collected from
21-24 J
une
2013
(192 sam
p
les series
data) as s
h
ow
n
in Table 1.
T
h
e
n
,
each network traffi
c
dat
a
was
capt
u
re
d
by
t
h
e C
A
C
T
I s
o
ft
wa
r
e
. The
dai
l
y
network t
r
affic data was
anal
yzed usi
n
g MATL
AB
R2
013
b.
Tabl
e
1. T
h
e
re
al
of
dai
l
y
net
w
o
r
k
d
a
t
a
Date Time
Inbound+Outbound
6/21/2013
1
0:00:00
6293000
2 0:30:00
5185000
…
…
…
48 23:30:00
11661000
6/22/2013
49
0:00:00
8390000
50 0:30:00
7307000
…
…
…
96 23:30:00
14530000
6/23/2013
97
0:00:00
10517000
98
0:30:00
6715000
…
…
…
144
23:30:00
5236000
6/24/2013
145
0:00:00
4528000
146
0:30:00
3603000
…
…
…
192
23:30:00
5969000
Sin
ce the im
p
l
icit fu
n
c
tion
of RBFNN is
Gau
s
sian
fu
n
c
t
i
o
n
,
in wh
ich
g
e
n
e
ral
requ
ires fo
r inp
u
t
val
u
e bet
w
e
e
n
0
a
n
d 1. The
dai
l
y
net
w
or
k t
r
affi
c dat
a
n
e
ed
n
o
rm
alized
u
s
ing
statistical d
a
ta norm
a
l
i
zatio
n
,
whi
c
h i
s
us
ual
l
y
exp
r
esse
d as:
whe
r
e:
X
is th
e actu
a
l v
a
lu
e
of sam
p
le;
takes a large
value, and
tak
e
s a sam
p
les o
f
d
a
ta is less th
an
th
e min
i
m
u
m
v
a
lu
e to
en
su
re n
o
rm
alized
v
a
lu
e is n
o
t
cl
ose to
0
.
Later,
p
r
o
cess inv
e
rse tran
sform
to
g
e
t th
e
act
ual
val
u
e i
s
obt
ai
ne
d.
Furt
herm
ore,
i
n
t
h
i
s
e
x
peri
m
e
nt
we
used
t
h
e s
u
m
of s
qua
re e
r
r
o
r
(S
SE),
m
ean of
squ
a
re e
r
r
o
r
(M
SE)
,
m
ean
of a
b
sol
u
t
e
pe
rcent
a
ge err
o
r (M
APE
)
, a
nd
m
ean of abs
o
l
u
t
e
devi
at
i
o
n (
M
AD
) were e
nga
ge
d
t
h
e p
r
e
d
i
c
t
e
d
o
u
t
p
ut
wi
t
h
t
h
e
desi
re
d
out
put
.
3.
R
E
SU
LTS AN
D ANA
LY
SIS
In t
h
i
s
ex
pe
ri
m
e
nt
, t
h
e i
npu
t
l
a
y
e
rs were eval
uat
e
d
base
d
on a pre
d
e
f
i
n
ed fu
nct
i
o
n:
P = [
p(
t
-
2)
,p(
t
-
1)
], an
d
th
e ou
tpu
t
layer was on
e (
t
), whe
r
e
the values for
t-2
,
t-
1
, a
n
d
t
were t
a
ke
n f
r
o
m
Tabl
e 2. T
h
e
architecture of RBFNN as s
h
own in Figu
r
e
2. I
n
o
r
de
r t
o
t
e
st
and
val
i
d
at
e the different er
ro
r
go
als,
f
our
statistical
; SSE, MSE, MAPE, an
d MAD test were carr
ied
o
u
t
. Fro
m
th
e sim
u
latio
n
s
carried ou
t, it was
created a precise neural network by
new
r
b (
P
,T,err
or_
g
o
a
l
,spre
ad)
funct
i
on,
whi
c
h i
s
t
h
i
s
fu
nct
i
o
n cr
eat
es
RBFNN stru
ct
u
r
e, au
to
m
a
tic
ally selec
t
ed
th
e n
u
m
b
e
r o
f
h
i
d
d
e
n
layer and
m
a
d
e
th
e error to
0
.
In
th
is test, fo
r
t
h
e er
ro
r
goal
val
u
es
we
re 0
.
00
1,
0
.
0
0
2
, a
n
d 0
.
0
0
3
, a
n
d t
h
e
spre
ad
val
u
e
of
2
0
0
.
T
h
e
pl
ot
res
u
l
t
s
t
r
ai
ni
ng
an
d
t
e
st
i
ng
obt
ai
ne
d a
r
e s
h
o
w
n i
n
Fi
gu
re
3 a
n
d
4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
76
5
–
77
1
76
8
Tab
l
e
2
.
Th
e daily n
e
twork data after
no
rm
a
lized
Gro
u
p
Input ne
urons
P=[p(
t-2
)
,
p(
t-1
)]
Outp
ut
neuron
T
Gro
u
p
Input ne
urons
P=[p(
t-2
)
,
p(
t-1
)]
Outp
ut
neuron
T
t-2
t-1
t
t-2
t-1
t
Group Train
1 0.
20
0.
16
0.
17
Group Tes
t
142
0.
27
0.
23
0.
16
2
0.
16
0.
17
0.
12
143
0.
14
0.
11
0.
19
3
0.
17
0.
12
0.
07
144
0.
11
0.
19
0.
18
4
0.
12
0.
07
0.
05
145
0.
19
0.
18
0.
14
5
0.
07
0.
05
0.
08
146
0.
18
0.
14
0.
08
…
… …
…
…
… …
…
…
… …
…
…
… …
…
…
… …
…
…
… …
…
…
… …
…
…
… …
…
…
… …
…
…
… …
…
137
0.
41
0.
42
0.
45
184
0.
22
0.
32
0.
31
138
0.
42
0.
45
0.
48
185
0.
32
0.
31
0.
27
139
0.
45
0.
48
0.
43
186
0.
31
0.
27
0.
32
140
0.
48
0.
43
0.
27
187
0.
27
0.
32
0.
20
141
0.
43
0.
27
0.
23
188
0.
32
0.
20
0.
19
Fi
gu
re
2.
A
t
y
p
i
cal
of R
B
F
N
N
by
usi
n
g
2-
1
-
1
arc
h
i
t
ect
ure
B
a
sed o
n
expe
ri
m
e
nt
,
t
h
e M
S
E val
u
e of R
B
FN
N t
e
st
i
ng w
a
s 0.0
0
0
9
9
8
4
1
.
It
m
eans t
h
at
the R
B
F
N
N
settin
g
with
erro
r_
goa
l
0.
0
0
1
and
spre
ad
2
0
0
ha
s bee
n
a
b
l
e
t
o
achi
e
ve t
h
e per
f
o
r
m
a
nce goal
,
a
n
d al
so
has
a
g
ood
MSE
v
a
lu
e.
Th
e resu
lts ob
tain
ed
are su
mmarized
in
Table
3. The
n
, the c
o
m
p
ar
i
n
g of
er
ro
r g
o
al
wi
t
h
real data are
summarized in Table 4 a
n
d also plot
of
forecas
t com
p
aring
with
differe
n
t error
goal as shown
i
n
Fi
gu
re 5.
Tabl
e
3. T
h
e
R
B
F
NN
t
r
ai
ni
ng
an
d t
e
st
i
n
g r
e
s
u
l
t
s
RBFNN
Spr
e
a
d
200
Tr
aining Te
sting
S
S
E
MS
E
MAPE
MAD
S
S
E
MS
E
MAPE
MAD
E
r
r
o
r
0.
001
0.
6935
642
4
0.
0048
164
2
0.
0170
039
7
0.
0508
708
9
0.
0479
237
6
0.
0009
984
1
0.
0037
066
4
0.
0238
334
3
E
r
r
o
r
0.
002
0.
6935
642
4
0.
0048
164
2
0.
0170
039
7
0.
0508
708
9
0.
0926
976
0
0.
0019
312
0
0.
0071
687
0
0.
0319
922
4
E
r
r
o
r
0.
003
0.
6935
642
4
0.
0048
164
2
0.
0170
039
7
0.
0508
708
9
0.
1413
658
2
0.
0029
451
2
0.
0109
372
2
0.
0373
576
2
t-2
Input
s
Layer
(2)
Hidden
Layer
(1)
Output
Layer
(1)
…
t-1
y
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
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:
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8-8
7
0
8
Ti
me
Seri
es Pr
edi
c
t
i
on
Usi
n
g
Ra
di
al
B
a
si
s F
unct
i
o
n N
e
ur
al
N
e
t
w
ork
(
H
avi
l
ud
di
n)
76
9
(a)
e
r
r
o
r goal 0
.
0
0
1
(
b
)
er
ro
r go
al
0.00
2
(c)
e
r
r
o
r goal 0
.
0
0
3
Fi
gu
re
3.
The
R
B
F
NN
t
r
ai
ni
ng
res
u
l
t
s
c
u
r
v
es
(a)
e
r
r
o
r goal 0
.
0
0
1
(
b
)
er
ro
r go
al
0.00
2
(c)
e
r
r
o
r goal 0
.
0
0
3
Fig
u
re 4
.
Th
e RBFNN
testing
resu
lts
cu
rv
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
76
5
–
77
1
77
0
Fig
u
r
e
5
.
Fo
r
e
cast co
m
p
ar
ing
o
f
RBFNN
w
ith
d
i
f
f
e
r
e
n
t
err
o
r
s
0
.
0
0
1
,
0.002, and
0
.
00
3
Tab
l
e
4
.
C
o
m
p
ar
ing
RBFN
N
w
ith
er
ro
r go
al
0
.
00
1,
0
.
0
0
2
,
an
d 0.003
Real
Erro
r
Go
al
Real
Erro
r
Go
al
0.
001
0.
002
0.
003
0.
001
0.
002
0.
003
0.
0664
8
0.
0057
6
0.
0233
9
-
0
.
01052
0.
7508
1
-
0
.
04932
0.
0271
7
0.
0023
7
0.
0682
1
-
0
.
00802
-
0
.
02441
0.
0137
5
0.
7038
6
-
0
.
01774
-
0
.
10069
-
0
.
09002
0.
0929
6
0.
0292
6
0.
0247
4
0.
0033
9
0.
8414
3
0.
1025
2
0.
1127
1
0.
1659
8
0.
0471
2
-
0
.
02022
-
0
.
01998
0.
0032
1
0.
7623
5
0.
0151
7
0.
0113
8
-
0
.
01479
0.
0352
2
0.
0383
0
0.
0200
5
0.
0381
4
0.
5362
2
-
0
.
03948
-
0
.
08967
-
0
.
14309
0.
0283
0
-
0
.
01737
-
0
.
03236
0.
0092
2
0.
6976
8
0.
0457
5
0.
1062
4
0.
1317
5
0.
0088
1
0.
0364
1
0.
0586
1
-
0
.
01996
0.
6515
5
-
0
.
00928
-
0
.
01080
0.
0184
0
0.
0129
3
-
0
.
03549
-
0
.
03112
0.
0280
4
0.
4835
0
-
0
.
04717
-
0
.
04191
-
0
.
04722
0.
0262
8
-
0
.
00942
-
0
.
00502
-
0
.
01180
0.
4719
7
-
0
.
01007
-
0
.
05560
-
0
.
06083
0.
0000
0
-
0
.
03957
-
0
.
02515
-
0
.
06509
0.
2928
0
-
0
.
02275
-
0
.
03760
-
0
.
04238
0.
1182
5
0.
0274
0
0.
0237
9
0.
0176
2
0.
4114
3
-
0
.
01146
0.
0026
3
0.
0236
9
0.
1311
8
0.
0209
1
0.
0064
1
0.
0362
9
0.
3508
8
0.
0002
4
-
0
.
00034
-
0
.
06424
0.
3241
1
-
0
.
00742
-
0
.
00781
0.
0004
7
0.
2392
6
0.
0600
8
0.
0506
6
0.
0054
6
0.
4509
7
-
0
.
00468
0.
0003
1
-
0
.
02004
0.
3574
7
0.
0039
4
0.
0120
9
0.
0414
1
0.
8006
5
0.
0028
1
0.
0007
3
0.
0087
5
0.
3488
2
0.
0732
1
0.
0847
6
0.
1072
2
0.
7207
5
-
0
.
00024
-
0
.
00223
-
0
.
00458
0.
3047
5
-
0
.
04591
-
0
.
04076
0.
0343
2
0.
7096
3
0.
0005
2
0.
0038
8
0.
0029
5
0.
3595
3
0.
0098
6
0.
0287
5
0.
0431
8
0.
7747
0
-
0
.
00014
-
0
.
00278
-
0
.
00464
0.
2100
2
-
0
.
03086
-
0
.
05778
-
0
.
07835
0.
9699
3
-
0
.
00063
0.
0035
2
-
0
.
00526
0.
2009
1
0.
0088
8
0.
0117
8
-
0
.
01676
1.
0000
0
-
0
.
00723
0.
0957
1
0.
1084
5
0.
2142
6
-
0
.
03785
-
0
.
03213
-
0
.
02329
0.
9794
1
0.
0299
9
-
0
.
03414
0.
0078
7
0.
1686
2
-
0
.
04646
-
0
.
02968
-
0
.
01739
0.
9415
1
-
0
.
02249
-
0
.
00014
-
0
.
00534
0.
1776
4
0.
0197
9
-
0
.
02188
-
0
.
03695
0.
9192
7
0.
0272
3
0.
0373
8
0.
0311
0
0.
1236
9
-
0
.
01743
-
0
.
00511
0.
0135
8
0.
7401
0
-
0
.
01334
-
0
.
05879
-
0
.
07801
0.
0544
5
0.
0139
5
0.
0210
8
-
0
.
03606
4.
CO
NCL
USI
O
N
In t
h
i
s
pa
pe
r,
t
h
e anal
y
s
i
s
u
s
i
ng R
B
F
NN
t
echni
que
t
o
ac
h
i
eve t
h
e m
odel
of
dai
l
y
net
w
or
k t
r
a
ffi
c
activ
ities h
a
v
e
b
een condu
cted
in th
e ICT Un
it, Un
iversitas Mu
law
a
rm
an
. A
c
cord
i
n
g to Figu
re 3 and
4
,
t
h
e
r
e
su
lts
o
f
RBFN
N
t
r
ain
i
ng
sho
w
s th
at fo
r
err
o
r
go
al valu
e i
s
0
.
00
1
t
h
en
SSE v
a
l
u
e is 0.69
356
424
, MSE v
a
lu
e
is 0
.
004
816
42
, MAPE
v
a
lue is 0
.
017
003
97
, an
d
M
A
D
valu
e is 0
.
0
5087
089
.
A
f
terw
ar
d, th
e v
a
l
u
es
o
f
the
RBFN
N
testing
ar
e
SSE
v
a
lu
e is 0.047
9237
6, MSE
v
a
lu
e is 0
.
0
009
9841
, MAPE
v
a
lue is 0
.
0
037
0664
, an
d
M
AD
val
u
e i
s
0.
02
3
8
3
3
4
3
.
B
a
sed o
n
res
u
l
t
s
, R
B
F
N
N
wi
t
h
pa
ram
e
t
e
r err
o
r
g
o
al
0.
0
0
1
an
d s
p
read
2
00
ha
s
been
abl
e
a
go
od
M
S
E
val
u
e
.
I
n
ot
her
w
o
rds
,
t
h
e R
B
F
N
N
a
r
e c
onsi
d
ere
d
c
l
oser t
o
t
h
e
act
ual
val
u
e.
Accord
ing
to i
n
d
i
cator test
resu
lt of
d
a
ta is t
h
e sm
allest error val
u
e, where
val
u
e indicat
ing
an error
testin
g
is th
e
best
m
o
d
e
l [1
1
]
. Th
erefore, t
h
e d
e
term
in
atio
n
o
f
t
h
e b
e
st
m
o
d
e
l is d
e
termin
ed
b
y
selectin
g
th
e
sm
a
llest
v
a
lu
e o
f
testin
g
erro
r. In
o
t
h
e
r words, th
e RBFNN
m
o
d
e
l with
d
i
fferen
t
erro
r goal v
a
lu
es illu
strates
th
e propo
sed best
m
o
d
e
l to
p
r
ed
ict d
a
ily n
e
twork traffic
activ
ities. Th
erefo
r
e, on
e
o
f
t
h
e
p
l
ann
e
d fu
ture
works
i
s
t
o
com
b
i
n
e
t
h
e R
B
F
N
N
m
e
t
hod
wi
t
h
a ge
net
i
c
al
go
ri
t
h
m
(GA)
i
n
or
de
r t
o
o
p
t
i
m
i
ze t
h
e pre
d
i
c
t
i
o
n
accuracy.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ti
me
Seri
es Pr
edi
c
t
i
on
Usi
n
g
Ra
di
al
B
a
si
s F
unct
i
o
n N
e
ur
al
N
e
t
w
ork
(
H
avi
l
ud
di
n)
77
1
ACKNOWLE
DGE
M
ENTS
Thi
s
st
u
d
y
has
been c
o
m
p
l
e
ted t
h
a
n
k
s
t
o
t
h
e hel
p
an
d s
u
pp
o
r
t
fr
om
vari
ous
part
i
e
s t
h
at
cann
o
t
b
e
m
e
nt
i
oned
one
by
o
n
e.
Espec
i
al
l
y
t
h
ank y
o
u t
o
ou
r
fam
i
ly, children a
n
d
wife. Researchers
say a
bi
g thank
y
ou
t
o
fam
i
l
y
of
M
u
l
a
warm
an Uni
v
ersi
t
y
and
STM
I
K AM
I
KOM
Pu
r
w
o
k
e
r
t
o
wh
o has gi
ve
n
s
u
p
p
o
r
t
t
o
co
m
p
lete th
is stu
d
y
.
Ho
p
e
fu
lly th
is research
can
b
e
u
s
efu
l
.
REFERE
NC
ES
[1]
Haviluddin
,
and
R. Alfred, “
F
orecast
i
ng
Netwo
r
k Activit
ies Using ARIMA Method”
,
Journal of Advances in
Computer Netwo
r
ks,
vol. 2
,
no
. 3
,
September
2014
, pp
. 173-179
, 2
014.
[2]
B. Majhi, M. Ro
ut, and V. Bagh
el,
“On the development and per
f
ormance
evalu
a
tion of a m
u
ltiobjec
tive GA-bas
e
d
RBF
adaptive
m
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BIOGRAP
HI
ES OF
AUTH
ORS
Haviluddin
was born in Loa Tebu, East Kalimant
an
, Indonesia. He gr
aduated from STMI
K
WCD Sa
marinda in th
e field
of
Management Information,
a
nd he com
p
let
e
d a M
a
s
t
er
at
Univers
itas
Gadj
ah M
a
da, Yog
y
a
k
arta in th
e field
of Com
puter S
c
ienc
e. He is
als
o
a Lectur
er in
the Depar
t
ment of Computer Scie
nce
,
F
acul
t
y
of
M
a
them
ati
c
s
and Natural S
c
i
e
nc
e, Univers
i
tas
Mulawarman, East Kalimantan, I
ndonesia. Cur
r
ently
,
he is pu
rs
uing his PhD in the field of
Com
puter S
c
ien
ce a
t
th
e F
acu
lt
y of
Com
puting
and Inform
ati
c
s, Universiti
Mala
ysi
a
Sabah
,
Mala
y
s
ia
. He is a m
e
m
b
er of the Institute of E
l
e
c
t
r
ica
l
and El
ectro
nic Engin
eers (I
EEE)
, Institut
e
of Advanced
Engineering
an
d Science (IA
ES
), and Indo
nesian Computer,
Electronics,
Instrumentation
Support Society (IndoCEISS), and
Association
of Computing and Informatics
Institutions
Indo
nesia (APTIKOM) societ
ies.
Imam Tahy
udin
was born in Indramay
u
,
West Java,
Indon
esia. He gradu
a
ted
from Jenderal
Soedirman University
, Purwoker
t
o in 2006 in
the
field of Mathematics,
and h
e
completed
a
Master at Jend
eral Soedirman
University
in
2010 in the field of Management. Th
en, he
graduated a master degree at
STMIK AMIKOM Yogy
akar
ta in 2013 in field
of Information
Techno
log
y
. H
e
is also
a Lectur
er in STMIK A
M
IKOM Pur
w
o
k
erto, Centr
a
l J
a
va, Indon
esia.
Currentl
y
,
he
is
a Head
of LP
P
M
of S
T
M
I
K AM
IKOM
P
u
rwokerto.
He is
a m
e
m
b
er of Ins
t
i
t
ut
e
of Advanced
Engineer
ing and
Science (IAES), Association
of
Computing an
d Informatics
Institutions Indo
nesia (APTIKOM), Indonesian
Com
puter, El
ect
ronics, Instrum
e
ntation Support
Society
(IndoCEISS), Association of Information
Sy
stem (AIS) and Association of Information
S
y
stem for Indonesia (AISINDO).
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