Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 2
,
A
p
r
il
201
5, p
p
.
33
3
~
33
9
I
S
SN
: 208
8-8
7
0
8
3
33
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
Bus Arri
val
Pred
iction – t
o
Ensu
re Use
r
s no
t to
Miss the
Bus
Lutfi F
a
n
a
ni
*
#
, Ach
m
ad Basuki*,
De
ron
Liang
#
* Depart
em
ent o
f
El
ectr
i
c
a
l
Engi
neering
,
Univ
ers
i
t
y
of
Brawij
a
y
a
#
Department of
Computer Scien
ce
and Informat
ion Engin
eering
,
National Cen
t
ral University
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 19, 2014
Rev
i
sed
Feb 9, 20
15
Accepted
Feb 20, 2015
Predicting
arriv
a
l tim
es of buses is a ke
y
cha
lleng
e in the
contex
t of building
intel
ligen
t publ
i
c
tr
ansportat
i
on
s
y
stem
s. Th
e bu
s arriva
l t
i
m
e
is
the prim
a
r
y
inform
ation for providing pas
s
e
ngers
with an accura
te inform
at
ion s
y
s
t
em
that
can
reduce
passenger waitin
g times.
In this paper,
we
used the
normal
distribution
method to the rando
m of trav
el
times data
in a bus line number
243 in
Taip
ei
area. In d
e
velop
i
ng th
e models, data wer
e
co
llected from
Taip
ei Bus Compan
y
.
A normal
distri
bution method used for predicting
the
bus arrival
time
in bus stop to en
sure
users not to
miss the bus, and compare
the res
u
l
t
with
t
h
e exis
t
i
ng appl
i
cat
ion.
The r
e
sult of our exp
e
riment showed
that our proposed method has
a better
p
r
edictio
n than
existing
application
,
with the
probab
ilit
y
user not
to
m
i
ss
the bus i
n
peak
tim
e
is 93% and i
n
norm
a
l tim
e is 85%, great
er than
from
the existing applic
ation wi
th the 65%
probability
in p
e
ak time,
and 70
% in normal time.
Keyword:
Bu
s arriv
a
l
pred
ictio
n
B
u
s r
o
ut
e
pl
an
ni
n
g
No
rm
al distribution
Waitin
g
tim
e
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
:
Lu
tfi Fan
a
n
i
,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Uni
v
ersity of
Brawijaya,
Jl
. Vet
e
ra
n,
M
a
l
a
ng
6
5
1
4
5
,
E
a
st
Java,
I
n
do
n
e
si
a.
Depa
rt
m
e
nt
of
C
o
m
put
er Sci
e
nce a
n
d
I
n
f
o
rm
at
i
on E
n
gi
nee
r
i
n
g
,
Natio
n
a
l Cen
t
ral Un
i
v
ersity,
N
o
.
3
0
0
,
Jhon
gd
a R
d
., Jhon
g
l
i
City, Tao
y
u
a
n Cou
n
t
y
3
200
1, Taiw
an
, RO
C
.
Em
a
il: lu
tfifan
an
i@yahoo
.com
1.
INTRODUCTION
A goo
d pub
lic tran
sp
ort is of in
creasing
l
y to
m
a
in
tain
an
d
im
p
r
o
v
e
qu
ality o
f
life b
y
p
r
ov
id
i
ng
m
obili
ty and accessibility. Any traveler
who wa
nts to tra
v
el between t
w
o places
will have to take a
num
b
er
of decisions
such as
m
ode of t
r
ans
p
ortatio
n,
r
out
e,
t
r
a
v
el
t
i
m
e
an
d s
o
o
n
[
4
]
.
Wh
en
trav
elling
with
bu
ses, t
h
e tr
av
elers
u
s
u
a
lly wan
t
t
o
kn
ow t
h
e accu
r
ate trav
el tim
es
o
f
t
h
e
b
u
s
.
Excessi
ve l
o
n
g
wai
t
i
ng t
i
m
e
s
at
t
h
e bus st
op
s
m
a
y dri
v
e
away the anxi
ous travele
r
s
and m
a
ke the
m
reluctant
t
o
use t
h
e b
u
s.
No
wa
day
s
, m
o
st
bus o
p
e
r
at
i
n
g com
p
ani
e
s
hav
e
b
e
en
pr
ov
i
d
ing
th
eir
tim
e
table for t
h
e travelers
[3]
.
To estim
ate the bus ar
riv
a
l tim
e
s at stops is a ch
allenging task
, beca
us
e bus tra
v
el tim
e
s (from
a real-tim
e
obs
er
vat
i
o
n
p
o
s
i
t
i
on) t
o
a
spe
c
i
f
i
e
d st
o
p
de
p
e
nd
o
n
a
num
ber
o
f
fact
o
r
s
(e.
g
.,
del
a
y
s
of
i
n
t
e
rsect
i
o
ns,
dwel
l
ti
m
e
s at sto
p
s
,
trav
el tim
es o
n
lin
k
s
, etc.), and
flu
c
tu
ate sp
at
ially an
d
tem
p
o
r
ally [1
].
Travel
t
i
m
e i
n
fo
rm
ati
on i
s
t
h
e m
o
st
prefe
r
red i
n
f
o
rm
at
i
on by
t
r
a
v
el
ers
[1
4]
, [
1
5]
. H
o
we
ve
r, t
h
i
s
i
n
f
o
rm
at
i
on can n
o
t
be m
e
asure
d
di
rect
l
y
. As has
been
expl
ai
ne
d o
n
[1
6]
, t
h
e p
r
o
v
i
s
i
o
n o
f
t
i
m
e
l
y
an
d
accurate tra
n
sit travel ti
m
e
inform
a
tion is i
m
portant
because it attracts a
dditional ri
dership and inc
r
ease
s
the
satisfactio
n
of tran
sit
users,
wh
ich
will u
ltimately resu
lt in
a d
e
crease in con
g
e
stio
n.
I
n
t
h
e
p
r
ev
ious wo
rk
, th
e Ta
ipei Bus C
o
mpany R
o
ute Pl
anne
r
A
pplication has a
feat
ure of
t
h
e bus
arriv
a
l
pred
ictio
n ti
m
e
. Th
is
ap
p
lication
featu
r
e
u
s
ed
a
p
r
ed
ictio
n
tim
e d
a
ta fro
m
Taip
ei Bu
s Co
m
p
any API
(Application Programm
ing Interface).
Goog
le application a
l
so has a
predi
c
ti
on feature, using data
that
they
are provide
d
. There
are
s
o
me
co
nd
itio
n
s
wh
en
th
e pred
icted
resu
lt is
to
o fast th
an
actu
a
l b
u
s
arri
v
a
l ti
m
e
, in
th
is case u
s
ers sh
ou
ld
wait a few min
u
t
es b
e
fo
re th
e
b
u
s
arriv
e
d
.
It also
h
a
s th
e conditio
n
wh
en
pred
iction
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Bus
Arrival P
r
ediction
– t
o
E
n
sure
Users
not to Miss t
h
e B
u
s
(Lu
tfi Fa
nani
)
33
4
resu
lt is t
o
o
slow th
an
act
u
a
l bu
s arri
v
a
l ti
m
e
, wh
ich
m
a
k
e
s
u
s
ers m
i
ssed
th
e
b
u
s
and
t
h
ey sh
ou
ld wait
fo
r t
h
e
n
e
x
t
bu
s t
h
at
sto
p
s
abou
t
15
–
20
m
i
n
u
t
es in
p
e
ak
ho
ur
an
d 30 – 40 m
i
n
u
t
es in
no
r
m
al h
o
u
r
[6]. Th
is
co
nd
itio
n can
mak
e
u
s
ers lo
ss o
f
a l
o
t of their p
r
eciou
s
time an
d
ex
p
e
nse. Th
e propo
sed
system
ai
min
g
t
o
p
r
ed
ict th
e bu
s arriv
a
l tim
e to
en
su
re
u
s
ers no
t to
m
i
ss th
e b
u
s
. Th
is system p
r
opo
sed
t
h
e Norm
al Distrib
u
tion
m
e
t
hod
usi
n
g
r
a
nd
om
t
r
avel
t
i
m
e vari
abl
e
,
t
o
m
a
ke t
h
e ar
ri
v
a
l
t
i
m
e
predi
c
t
i
o
n
.
A variety of the prediction model to predict the bus
arrival tim
e
has been
studie
d
by
m
a
ny in recent
y
ears. The t
r
e
e
m
o
st
wi
del
y
used m
odel
s
i
n
cl
u
d
e hi
st
o
r
i
c
al
dat
a
based
m
odel
,
regress
i
on m
odel
,
an
d t
i
m
e
seri
es m
odel
.
Hi
st
ori
cal
dat
a
base
d m
odel
s
pre
d
i
c
t
t
r
avel
t
i
m
e
for a
gi
v
e
n
t
i
m
e
peri
od
usi
ng t
h
e a
v
era
g
e
t
r
avel
t
i
m
e
fo
r the sam
e
tim
e
perio
d
o
b
t
a
ined
fr
om
a hi
st
ori
cal
dat
a
b
a
se. The
s
e m
ode
ls assu
m
e
th
at traffic p
a
ttern
s are
cyclical and the ratio of the historical
travel tim
e
on a speci
fic link to the
current tra
v
el tim
e
reported i
n
real-
ti
m
e
will re
m
a
in
con
s
tan
t
[1
]. Th
e pro
cedu
r
e requ
ires an
ex
ten
s
i
v
e set
o
f
h
i
storical d
a
ta and
it is d
i
fficu
lt to
install the syste
m
in a new se
tting [1]. Real-tim
e
m
odels
assum
e
that the m
o
st recen
tly
obs
erved t
r
ansit travel
ti
m
e
s will stay
co
nsisten
t
in
t
h
e fu
tu
re.
Th
e reg
r
ession
m
o
d
e
l is co
nv
en
tion
a
l app
r
o
ach
es for pred
ictin
g
th
e arriv
a
l ti
m
e
. Th
ese
m
o
d
e
ls
pre
d
i
c
t
an
d e
x
pl
ai
n a
de
pen
d
e
nt
va
ri
abl
e
wi
t
h
a m
a
t
h
em
atical
fu
nct
i
o
n f
o
rm
ed by
a set
i
nde
pe
nde
nt
va
ri
abl
e
s
[2]
.
T
o
est
a
bl
i
s
h t
h
e re
gres
si
on m
odel
s
, t
h
e
depe
nde
nt
va
r
i
abl
e
s need t
o
be an i
n
dep
e
n
d
ent
.
M
i
shal
a
n
i
,
et
.al
.
[5
] p
r
op
osed
a
m
u
lti
lin
ear reg
r
essi
on
to
p
r
ed
ict th
e b
u
s
arriv
a
l ti
m
e
s u
s
i
n
g
th
e
d
a
ta co
llected
b
y
Au
tomatic
Passen
g
e
r
C
o
unt
e
r
(A
PC
).
They
use
d
di
s
t
ance, n
u
m
b
er of st
op
s, d
w
el
l
tim
es, boardi
ng an
d al
i
g
ht
i
ng
passe
nge
rs
an
d
weat
he
r
des
c
ri
pt
o
r
s a
s
i
n
d
e
pen
d
e
n
t
vari
a
b
l
e
s.
H
o
we
ve
r
,
t
h
i
s
ap
pr
oac
h
i
s
rel
i
a
bl
e
w
h
en t
h
e
d
e
p
e
nd
en
t
v
a
ri
ab
le h
a
s a correlatio
n
with
the in
d
e
p
e
nd
en
t v
a
riab
le. In
th
is case we h
a
v
e
tried
to
i
m
p
l
emen
t
t
h
i
s
m
e
t
hod i
n
ou
r e
x
peri
m
e
nt
, b
u
t
t
h
e
dat
a
t
h
at
we
have
ca
n’t
be
p
r
oces
se
d
usi
n
g t
h
i
s
m
e
t
h
o
d
beca
use
of
n
o
cor
r
el
at
i
on bet
w
een
t
h
e de
pe
nde
nt
vari
a
b
l
e
(t
im
e
t
r
avel
)
with
th
e ind
e
p
e
nd
en
t
v
a
riab
le (d
istan
ce). Th
e
farth
e
r
distance t
h
ere
should
ha
ve
been the
lon
g
er trav
el tim
e,
bu
t th
e ex
isti
n
g
d
a
ta are d
i
fferen
t
.
W
e
h
a
v
e
t
h
e
di
ffe
re
nt
di
st
an
ces wi
t
h
sam
e
t
r
avel
t
i
m
e
, for
exam
pl
e, i
n
5
00 a
n
d 1
5
00 m
e
t
e
rs i
t
has ar
o
u
n
d
50
seco
n
d
t
o
1
0
0
seco
nd o
f
t
r
av
el
t
i
m
e
. In t
h
i
s
expe
ri
m
e
nt
di
st
ance can’t
be
use
d
t
o
be an i
nde
pe
nde
nt
va
ri
abl
e
. Thi
s
i
s
caus
e
d
b
y
th
e t
r
affic co
nd
itio
n, sp
eed of
b
u
s
, an
d o
t
h
e
r p
a
ram
e
ters th
at in
cl
u
d
e
d
i
n
th
is lin
e.
Ti
m
e
series
mo
d
e
ls assu
m
e
t
h
at th
e h
i
sto
r
ical traffic p
a
ttern
s will re
m
a
in
th
e sa
m
e
in
th
e
fu
ture. The
accuracy
of time series m
odels is a functi
on of the
si
milarity between the real
-t
im
e and
historical
traffic
pat
t
e
rns
[2]
.
V
a
ri
at
i
on i
n
hi
st
ori
cal
dat
a
o
r
chan
ges i
n
t
h
e
rel
a
t
i
ons
hi
p
b
e
t
w
een
hi
st
ori
cal
dat
a
and
re
al
-t
im
e
data could
significantly caus
e
inaccur
acy in the
prediction res
u
lts [1].
Th
ey used a
non-linear tim
e
serie
s
m
o
d
e
l to
p
r
ed
ict a co
rrido
r
trav
el ti
m
e
o
n
a
h
i
gh
way
[1
].
He com
p
are
d
two ca
ses: the first
m
odel use
d
onl
y
spee
d dat
a
as
a vari
a
b
l
e
, w
h
i
l
e t
h
e seco
nd
m
odel
used s
p
eed,
occ
upa
nc
y
,
and
v
o
l
u
m
e
dat
a
t
o
pre
d
i
c
t
t
r
avel
ti
m
e
. It was fo
und
th
at th
e sin
g
l
e v
a
riab
le
m
o
d
e
l u
s
ing
sp
eed
was b
e
tt
er th
an
th
e m
u
ltiv
ariab
l
e p
r
ed
iction
m
odel. W
e
ha
ve the bus spee
d data from
Taipei Bus Com
p
any API, but we could not
use
this data because is
n
o
t
v
a
lid
, th
e
valu
e of
bu
s
d
a
ta sp
eed
alw
a
ys b
e
low
10
k
m
/
h
.
A
n
d
w
e
don’
t h
a
v
e
a vo
lume tr
af
f
i
c d
a
ta
o
n
t
h
e
ro
ad
t
o
b
e
a
v
a
riab
le in th
is ti
me series m
o
d
e
l.
2.
R
E
SEARC
H M
ETHOD
The e
x
peri
m
e
nt
i
s
di
vi
d
e
d
by
t
w
o t
i
m
e condi
t
i
on, i
n
peak
h
o
u
r
a
n
d
n
o
r
m
a
l h
o
u
r
.
We c
h
o
o
se
one
b
u
s
st
op i
n
o
n
e l
i
n
e t
o
m
a
ke an expe
ri
m
e
nt
and t
e
st
i
ng, base
d
on st
o
p
s t
h
at
h
a
ve t
h
e m
o
st
err
o
r p
r
e
d
i
c
t
i
on,
i
n
t
h
i
s
case is the longe
st waiting
tim
e
. Norm
al
distribution m
e
thod with ra
ndom
variable travel tim
e
has been
cho
s
en t
o
m
a
ke a bet
t
e
r pr
ed
i
c
t
i
on/
est
i
m
a
tion
of t
r
av
el time between ea
ch bus st
op, a
n
d com
p
are the
resul
t
with
th
e ex
isti
n
g
app
licatio
n.
2.
1. N
o
rm
al
D
i
stri
buti
o
n Me
tho
d
In
p
r
ob
ab
ility th
eory, th
e
n
o
rm
al (o
r Gau
ssi
an)
d
i
strib
u
tion
is a
very co
mm
o
n
l
y o
ccurring
co
n
tinuo
us prob
ab
ility d
i
stribu
tio
n
–
a fu
nctio
n
th
at te
lls t
h
e prob
ab
ility
th
at an
y real ob
serv
ation
will fall
betwee
n a
n
y two real lim
its or
real
num
bers, as t
h
e c
u
rve
approaches
zero
on either
si
d
e
[
8
]
.
I
n
t
h
e
c
a
s
e
o
f
a
si
ngl
e real
-
v
al
ued
va
ri
abl
e
x,
t
h
e Gau
ssi
an d
i
st
ri
but
i
o
n
i
s
d
e
fi
ne
d by
[
11]
:
;
,
1
2
/
ex
p
1
2
(1
)
Whi
c
h i
s
g
o
v
e
r
ne
d
by
t
w
o
p
a
ram
e
t
e
rs:
μ
,
ca
lle
d
th
e me
a
n
,
an
d
σ
2
, calle
d t
h
e
varia
n
ce. The
s
qua
re
ro
ot
o
f
t
h
e
va
ri
ance,
gi
ve
n
by
σ
, is called
th
e stan
d
a
rd
d
e
v
i
atio
n
an
d
t
h
e recip
r
o
cal
of
th
e v
a
rian
ce, written
as
β
=1/
σ
2
, i
s
cal
l
e
d t
h
e
p
r
eci
si
o
n
[1
1]
. Fi
gu
re
1
sho
w
s
a
pl
ot
of
n
o
rm
al
(Gau
ss
i
a
n)
di
st
ri
b
u
t
i
o
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
33
3 – 3
3
9
3
35
Th
e pro
b
a
b
ility o
f
th
e no
rm
al as g
i
v
e
n
ab
ove is d
i
fficu
lt to work
with
in
d
e
term
in
in
g
areas u
n
d
e
r th
e
cur
v
e, a
n
d eac
h set
o
f
X
val
u
es ge
ne
rat
e
s anot
her c
u
r
v
e
as long as the
means an
d st
anda
r
d
de
vi
at
i
o
ns ar
e
translated t
o
a
new axis
, a Z
-axis,
with t
h
e t
r
anslation
defi
ned as:
(2
)
The G
a
ussi
a
n
di
st
ri
b
u
t
i
on a
r
i
s
es i
n
m
a
ny
di
ffe
rent
c
ont
e
x
t
s
and ca
n
be
m
o
ti
vat
e
d fr
o
m
a vari
et
y
of
diffe
re
nt perspectives. For e
x
a
m
ple, we ha
ve already seen
th
at for a sing
l
e
real v
a
riab
le, th
e d
i
stribu
tion
th
at
max
i
m
i
zes th
e
en
trop
y is th
e Gau
s
sian
[11
]
. Th
is pro
p
e
rt
y ap
p
lies also
to
th
e m
u
ltiv
a
r
iate Gau
ssian
. Th
e
n
o
rm
al d
i
strib
u
tio
n h
a
s an
infin
ite supp
ort
fo
r m
a
n
y
ap
p
licatio
n
s
. In
reality, we can no
t
g
e
t really an infin
ite
su
ppo
r
t
. So
m
e
au
th
or
s used
an
d
im
p
l
e
m
ent a truncated
norm
al distributi
on to thei
r res
earch. [A. Kua
n
g-17]
d
e
v
e
l
o
p a b
i
-lev
el programmi
n
g
m
o
d
e
l b
a
sed
o
n
t
h
e
OD
pa
ir trav
el tim
e
reliab
ility to
stu
d
y
t
h
e ro
ad
network
cap
acity reliab
ilit
y with
th
e assu
m
p
tio
n
that th
e lin
k
capacity fo
llo
ws
a tru
n
cated
norm
a
l
d
i
strib
u
t
i
o
n. For
next
e
x
perim
e
nt, researc
h
ers can use
t
h
e
truncated norm
al
d
i
stribu
tio
n to
so
lv
e th
is trav
el ti
m
e
p
r
ob
lem
.
2.2. E
x
perime
nt
Design
Fi
gu
re
1
sh
o
w
s t
h
e e
x
peri
m
e
nt
d
e
si
g
n
i
n
t
h
i
s
resea
r
ch
.
W
e
co
nst
r
uct
t
h
e
m
odel
by
usi
n
g
dat
a
fr
om
Taip
ei Bu
s Com
p
an
y. Co
llect
in
g
trai
n
i
ng
d
a
ta n
eed
ed
fo
r t
h
is exp
e
rim
e
n
t
to
m
a
k
e
th
e d
a
taset th
at we u
s
e for
m
a
ke t
h
e
pre
d
i
c
t
i
on sy
st
em
.
Fi
gu
re
1.
Ex
pe
ri
m
e
nt
sy
st
em
desi
g
n
2.
3. D
a
t
a
Col
l
ecti
n
g
The dat
a
use
d
fo
r t
h
i
s
st
udy
were c
o
l
l
ect
ed from
bus r
out
e num
ber 2
43
i
n
Tai
p
ei
area.
The ro
ut
e
l
e
ngt
h i
s
ap
pr
oxi
m
a
t
e
l
y
14 km
and 53 m
i
nut
es o
f
t
r
av
el
t
i
m
e
bet
w
een t
h
e so
urce
and dest
i
n
at
i
o
n
,
an
d
spa
nni
ng
2
5
b
u
s
st
o
p
s i
n
eac
h
di
rect
i
o
n.
The
ro
ut
e st
art
s
at
Zh
on
g
h
e St
at
i
o
n
l
o
cat
ed
i
n
Ji
nhe
R
o
a
d
a
n
d
st
op
i
n
Zho
ngh
u
a
Ro
ad
n
ear Tai
p
ei Mu
seu
m
Xi
m
e
n
.
Th
e sch
e
d
u
l
e o
f
bu
s op
erat
io
n
start at 5
.
30
AM un
til 9
.
00
PM
o
n
th
e
week
d
a
y an
d start at 5.30
AM un
til 6.00
PM at
t
h
e
week
end
,
and
t
h
e tim
e in
terv
al b
e
tween
each bu
s
di
vi
de
d
by
t
w
o c
o
n
d
i
t
i
ons
, i
n
t
h
e
pea
k
ho
ur:
15
–
2
0
m
i
nut
e a
n
d i
n
t
h
e n
o
rm
al
hou
r:
30
–
4
0
m
i
nut
e [6]
.
Fi
gu
re
2 s
h
ows
t
h
e m
a
p o
f
bu
s r
out
e
n
u
m
b
er 2
4
3
i
n
Tai
p
ei
wi
t
h
t
h
e
bl
ue c
o
l
o
r i
n
al
l
b
u
s
st
ops
.
Data were co
llected
u
s
ing
Ad
am
’s Au
to
m
a
tic Data Co
lle
cto
r
(ADC
) Syste
m
[1
2
]
. Dat
a
co
llecting
pr
ocess s
h
o
w
e
d
i
n
Fi
g
u
re
3.
In t
h
e
system
we insert
data from
Taipei
Bus Com
p
any API to our system
.
The
Tai
p
ei
B
u
s C
o
m
p
any
pro
v
i
d
e
d
t
h
e B
u
s L
o
c
a
t
i
on dat
a
wi
t
h
a GPS t
ech
nol
ogy
f
o
r eac
h
b
u
s o
n
t
h
e r
o
ut
e
.
The
estim
a
tion time and eac
h time the bus
stoppe
d,
the bus location was reco
rde
d
using
the GPS
receiver a
nd
send
s th
e d
a
ta t
o
th
e d
a
tab
a
se
th
at w
e
co
llected
f
o
r
th
is study.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Bus
Arrival P
r
ediction
– t
o
E
n
sure
Users
not to Miss t
h
e B
u
s
(Lu
tfi Fa
nani
)
33
6
Fi
gu
re
2.
B
u
s
l
i
n
e n
u
m
b
er
24
3 i
n
Tai
p
ei
[
6
]
Arrival a
n
d
de
part
ure
tim
e
records
at each s
t
op ar
e
the m
o
st im
porta
nt ones for pre
d
icting t
h
e tra
v
e
l
ti
m
e
. Th
e d
a
ta w
e
r
e
co
llected
in
Jun
e
2
014 f
r
o
m
b
u
s
rou
t
e n
u
m
b
e
r
243
in
Taip
ei ar
ea. Th
e d
a
ta co
ll
ectio
n
schem
e
i
s
present
e
d i
n
Fi
g
u
r
e
3 bel
o
w
.
B
u
s
ro
ut
e n
u
m
b
er 24
3
has b
een c
hos
en
fo
r t
h
e c
a
se st
udy
beca
use i
t
has a longest tim
e
interval
between each
bus in Taipei
area (the tim
e
interval ha
s bee
n
explained
be
fore).
W
i
t
h
th
e long
est ti
m
e
in
terv
al, th
e
waiting
time at th
e stop
will b
e
long
er.
So
, our fo
cu
s i
s
to
im
p
r
ov
e t
h
e
p
r
ed
ictio
n ti
m
e
in
th
is line to
en
su
re u
s
ers th
at t
h
ey
will n
o
t
m
i
ss th
e
b
u
s,
because if they
m
i
ssed the bus, waiti
ng tim
e
for t
h
e next bus is very long,
about 20 –
40
m
i
nut
es in different
ti
m
e
co
n
d
ition
.
Fi
gu
re
3.
Dat
a
col
l
ect
i
ng sc
he
m
e
[1
2]
In t
h
i
s
dat
a
col
l
ect
i
on we
ha
v
e
sepa
rat
e
d
bas
e
d
on
t
i
m
e
con
d
i
t
i
on,
i
n
t
h
e
p
eak
ho
ur
an
d
n
o
rm
al
ho
ur.
Because the travel ti
m
e
on both conditions
is differe
nt. The data we
re collect
ed in June 2, 2014 to June
9,
2
014
in w
e
ekday.
2.
4. Prel
i
m
i
n
a
r
y An
al
ysi
s
Taip
ei Bu
s Com
p
an
y ap
p
licatio
n
is Taiwan p
u
b
lic tran
sit
syste
m
th
at h
a
s b
e
en
d
e
v
e
lop
e
d
t
o
h
e
l
p
users
fo
r che
c
k
i
ng
bus l
i
n
e
,
t
i
m
es, and r
o
ut
es. The
bus
sy
st
em
operat
e
d
u
nde
r co
o
p
erat
i
on
bet
w
ee
n 1
5
pri
v
at
e
ag
en
cies, so
tran
slatio
n
is no
t
always co
n
s
ist
e
n
t
. It is reco
m
m
en
d
e
d
t
o
always k
eep
a Ch
i
n
ese written
v
e
rsion
of
y
o
u
r destina
tion fo
r
c
o
m
p
ariso
n
[7]
.
In
th
is
p
a
p
e
r we u
s
ed
so
m
e
te
rm
s to
ex
p
l
ain
so
m
e
co
n
d
ition
in
pred
ictin
g a b
u
s
arriv
a
l time. First is
Travel tim
e, is defi
ned as
pure
running tim
e in sections
, doe
s
not contain
s
h
ort dela
ye
d time because
of
traffic
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
33
3 – 3
3
9
3
37
signal control, the tim
e
for passeng
ers
getting
on a
nd
off at each stop st
a
tion and the s
t
op tim
e
for vehicle
technical probl
e
m
s
[10].
The
travel
t
i
m
e
on
sect
i
ons
fr
om
the b
u
s
’
s c
u
r
r
en
t ru
nn
ing
lo
catio
n
of th
e
pred
ictio
n
sto
p
statio
n
is
calcu
lated
from
arriv
a
l ti
m
e
(
AT
)
d
a
ta in
st
o
p
S
i+1
m
i
nus s
t
op
S
i
.
1
(3
)
Wh
ere Ti
d
e
notes th
e trav
el time fro
m
Si to
sto
p
S;
AT
d
e
no
tes th
e arriv
a
l
ti
m
e
in
Stop
i.
Secon
d
is waitin
g
ti
m
e
o
ccu
rs wh
en
waiting
for a b
u
s
at a b
u
s
stop
, when
th
e du
ration
o
f
th
e wait
may exceed the ti
m
e
neede
d
t
o
a
rri
ve at a
de
stination
by
a
n
othe
r m
eans [5]. It
will be
worst if waiting ti
me in
bus
st
o
p
i
s
m
o
re t
h
a
n
1
5
m
i
nut
es.
In
bus
ar
r
i
val
p
r
edi
c
t
i
o
n
sy
st
em
, i
f
p
r
ed
i
c
t
i
on s
h
o
w
e
d
t
h
e w
r
on
g
val
u
e, f
o
r
exam
pl
e pre
d
i
c
t
i
on i
s
t
o
o sl
owe
r
t
h
an
t
h
e
bus
act
ual
ar
ri
ved
1 m
i
nut
e
or
5
m
i
nut
es i
t
m
eans use
r
s
m
u
st
t
o
wai
t
f
o
r t
h
e
ne
xt
b
u
s
.
Th
e
n
e
x
t
is ru
sh
h
o
u
r
or
p
e
ak ho
ur
, it is a par
t
of
th
e d
a
y
d
u
r
i
ng
wh
ich
t
r
aff
i
c cong
estio
n on
r
o
ads
and c
r
o
w
di
n
g
on
p
ubl
i
c
t
r
an
s
p
o
r
t
i
s
at
i
t
s
highe
st
. N
o
rm
all
y
, th
is h
a
pp
ens twice
a day-once i
n
the morning
and
o
n
ce i
n
t
h
e eve
n
i
n
g, t
h
e
t
i
m
e
s duri
n
g
w
h
en
t
h
e m
o
st
p
e
opl
e c
o
m
m
ute. Th
e t
e
rm
i
s
very
br
oa
d
but
oft
e
n
refers to
sp
ecifically p
r
iv
ate au
to
m
o
b
ile transp
ortatio
n
traffic, even
whe
n
t
h
ere is a large vol
um
e of cars
on a
roa
d
,
but
not
a
l
a
rge n
u
m
b
er
of
peo
p
l
e
,
or i
f
t
h
e v
o
l
u
m
e
i
s
no
rm
al
but
t
h
ere i
s
som
e
di
srupt
i
o
n
of s
p
ee
d [
9
]
.
In this e
x
perim
e
nt we
decide
d into
pea
k
hour and
norm
al hour c
o
ndition.
In norm
al cond
ition the
probability
user m
i
ssed t
h
e bu
s i
s
g
r
eat
e
r
t
h
a
n
i
n
pea
k
ho
u
r
.
We can
det
e
rm
i
n
e t
h
e peak
h
o
u
r
a
n
d
no
rm
al
hou
r b
a
sed
on
d
a
ta th
at
we
h
a
v
e
co
llected
for th
is exp
e
rim
e
n
t
. Fro
m
th
e data th
e cond
itio
n in
p
e
ak
h
our is fro
m
7
.
0
0
AM –
10
.0
0
AM
an
d
fr
om
3.00 P
M
– 6.
0
0
PM
.
No
rm
al
hour
i
s
from
11.
0
0
AM
– 2
.
00 P
M
and f
r
o
m
7.00
PM
–
9.
00
PM
3.
R
E
SU
LTS AN
D ANA
LY
SIS
Thi
s
i
s
a prel
i
m
i
n
ary
st
udy
, and
bus l
i
n
e
2
43
has bee
n
c
hos
en t
o
be an
expe
ri
m
e
nt
t
e
st
i
ng beca
use
th
at h
a
s a lo
ngest waitin
g
time. In
th
is exp
e
rim
e
n
t
testin
g
bu
s stop
num
b
e
r 1
4
h
a
s a lo
ng
est waiting
ti
m
e
,
with
th
e av
erag
e waiting
time is 1
0
.
2
min
u
t
es.
We ma
k
e
a testin
g
an
d
co
m
p
arison
with
th
e existin
g
appl
i
cat
i
o
n fr
o
m
st
op 7 t
o
1
4
wi
t
h
7 b
u
s st
ops
(S
7
,S
14
), st
op
8 t
o
1
4
wi
t
h
6 b
u
s st
ops
(
S
8
,S
14
), st
op
9 t
o
14
w
ith
5
bu
s stops (
S
9
,S
14
)
,
stop
1
0
t
o
14
w
ith
4 b
u
s
stop
s (
S
10
,S
14
),
st
o
p
11
t
o
14 wi
t
h
3
b
u
s st
ops (S
11
,S
14
), stop
12 t
o
14
wi
t
h
2
bus st
o
p
s (
S
12
,S
14
) i
n
pea
k
h
o
u
r a
nd
no
rm
al
ho
u
r
. Test
i
n
g was co
n
duct
e
d
10 t
i
m
e
s i
n
di
ffere
nt
ti
m
e
condition at each stop to know
how
many proba
b
ilities that user
do
not m
i
ss
the bus, a
nd c
o
m
p
are the
resu
lt with
th
e
ex
istin
g
ap
p
licatio
n
.
Fi
g
u
re 4 sh
ows th
e av
erag
e
waitin
g
time in
all
b
u
s
sto
p
s
in
b
u
s lin
e 2
4
3
.
In th
is
p
a
rt,
we wo
u
l
d
lik
e to
see th
e co
m
p
ariso
n
resu
lt
o
f
ex
istin
g app
licatio
n
and
o
u
r
pro
p
o
s
ed
m
e
th
o
d
fro
m
expe
rim
e
nt above
. T
h
e c
o
m
p
aris
on res
u
lt of
use
r
aver
a
g
e waiting tim
e are prese
n
ted in Figure 5.
And the
resu
lt
o
f
prob
ab
ility u
s
ers
no
t to
m
i
ss th
e bus du
ri
n
g
p
e
ak
ho
ur and
n
o
rm
al
ho
ur are
p
r
esen
ted
i
n
Fi
g
u
re
6
.
Fig
u
re
4
.
Av
erag
e
waitin
g
ti
me in
bu
s lin
e
2
43
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Bus
Arrival P
r
ediction
– t
o
E
n
sure
Users
not to Miss t
h
e B
u
s
(Lu
tfi Fa
nani
)
33
8
Fig
u
re 5
.
Av
erag
e u
s
ers waitin
g
ti
m
e
Fig
u
re
6
.
Co
mp
ariso
n
of
p
r
obab
ility u
s
ers
not to
m
i
ss th
e b
u
s
From
our e
x
perim
e
nt result, we
obse
r
ve t
h
at
our proposed m
e
thod is
better tha
n
t
h
e e
x
isting
appl
i
cat
i
o
n (
T
a
i
pei
B
u
s
C
o
m
p
any
)
i
n
pre
d
i
c
t
i
ng t
h
e a
rri
val
t
i
m
e
t
o
ens
u
re
users
not
t
o
m
i
ss t
h
e
b
u
s.
W
e
hav
e
som
e
di
ffere
nt
arri
val
pre
d
i
c
t
i
on t
i
m
e
i
n
peak h
o
u
r a
nd
n
o
rm
al
hou
r be
cause t
h
e
num
ber
of
passe
ng
er a
n
d
traffic
co
nd
ition
in
p
eak
ho
ur (a)
an
d
no
rm
al
h
o
u
r
(b
)
are d
i
fferen
t
. Th
ere
are two
cond
itio
n
s
on
av
erag
e u
s
ers
waiting tim
e and the
probabi
lity users
not to m
i
ss the bus, peak
hour
(a)
and
norm
al hour (b) condition. T
h
e
users waiting
tim
e
from
o
u
r propos
ed m
e
thod have
a less waiting tim
e
than
bus c
o
m
p
any (existi
ng
ap
p
lication
)
, an
d th
e
prob
ab
ility o
f
u
s
ers no
t
to
m
i
ss th
e bus is greater t
h
an
ex
istin
g app
l
icatio
n
.
3.1.
Disc
ussion
Our exp
e
rim
e
n
t
d
e
sign
is
d
i
v
i
d
e
d
b
y
tim
e
con
d
ition
,
p
e
ak
h
our an
d no
rm
al h
o
u
r
. Peak
h
our and
norm
al hour c
o
ndition
obtained
from
da
ta
that provi
ded
by Taipei Bus
AP
I. The aim
s
of
divide
d the tim
e
co
nd
itio
n to
m
a
k
e
a
p
r
ed
iction
m
o
d
e
l is to
g
e
t a m
o
re
accu
rate
p
r
ed
ictio
n resu
lt, b
e
cau
se th
e cond
itio
n of
r
o
ad
i
n
p
eak ho
ur
and
n
o
r
m
al
ho
ur
is
d
i
ff
er
en
t.
3.
1.
1. Weeken
d
C
o
n
d
i
t
i
o
n
To obtain m
o
re accurate results, we
can a
d
d to the conditions
of th
e ti
m
e
in weekday a
nd
wee
k
end.
Because the
condition in 7.00 –
8.00 PM at
the wee
k
day
is differe
n
t in weekend,
in wee
kday we
c
o
nsidere
d
th
at ti
m
e
is n
o
rm
al
ti
m
e
, b
u
t
at th
e week
en
d it can
b
e
a p
e
ak
tim
e si
t
u
atio
n. In
t
h
is exp
e
rim
e
n
t
we u
s
ed
weekd
a
y tim
e
co
nd
itio
n.
3.
1.
2. Dw
el
l
T
i
me
In
ord
e
r to pred
ict trav
el ti
me
, in an acc
urate a
n
d timely
m
a
nner,
the c
onsi
d
erati
o
n of tra
ffic
co
nd
itio
n, in
cl
u
d
i
n
g
t
r
affic co
ng
estion
,
dwell ti
me at sto
p
s
, etc. The bu
s
d
w
ell tim
e a
t
a b
u
s stop
is
d
e
fin
e
d
as
t
h
e t
i
m
e
spent
by
a b
u
s at
t
h
e
bu
s st
o
p
f
o
r p
a
ssen
g
er al
i
g
ht
i
ng a
n
d
b
o
ar
di
ng
, i
n
cl
udi
ng t
i
m
e
of o
p
eni
n
g an
d
cl
osi
n
g
bus
do
ors
[
1
3]
. T
h
e
bus
dwel
l
t
i
m
e i
s
o
f
great
i
m
po
rt
ance
t
o
e
s
t
i
m
a
t
e
t
h
e capa
c
i
t
y
of a
b
u
s s
t
at
i
on,
and it is also a
major com
p
onent of
bu
s travel ti
m
e
. An
Auto
m
a
tic Passeng
er
Data
n
e
ed
ed
to pred
ict the dwell
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
33
3 – 3
3
9
3
39
t
i
m
e
at
a bus st
op.
Tai
p
ei
B
u
s AP
I di
d n
o
t
pr
o
v
i
d
e
us
an
APC data.
W
e
can use APC data at bus stops
t
o
p
r
ed
ict bu
s arri
v
a
l ti
m
e
with
dwell ti
m
e
to
mak
e
m
o
re accu
r
ate p
r
ed
ictio
n resu
lt.
4.
CO
NCL
USI
O
N
In th
is
p
a
p
e
r,
we
d
ealt with
th
e pro
b
l
em
o
f
bu
s arri
v
a
l time p
r
ed
ictio
n
in
th
e ex
isting app
licatio
n
s
.
So
m
e
ti
mes th
e pred
iction
o
f
b
u
s
arriv
a
l
ti
me in
t
h
e ex
is
ting
app
licatio
n
is too
late an
d someti
mes is to
o
early.
Th
is co
nd
itio
n can
cau
s
e
u
s
ers to m
i
ss th
e b
u
s
and
waiting
for a l
o
ng
ti
me fo
r th
e
n
e
xt b
u
s
.
We
p
r
opo
sed
a
no
rm
al
di
st
ri
but
i
o
n
m
e
t
hod t
o
pre
d
i
c
t
t
h
e
b
e
st
pr
edi
c
t
i
o
n
of
b
u
s
ar
ri
val
t
i
m
e
t
o
ens
u
re
users
not
t
o
m
i
ss t
h
e
bus
. T
h
i
s
p
r
o
p
o
se
d m
e
t
hod
i
s
base
d
o
n
ran
d
o
m
vari
abl
e
t
r
avel
t
i
m
e dat
a
bet
w
ee
n
b
u
s st
ops
i
n
a
pr
el
i
m
i
n
ary
stu
d
y
b
a
sed
on b
u
s
lin
e nu
m
b
er 24
3
in
Taipei. W
e
p
e
rformed
exp
e
rim
e
n
t
s o
n
two
typ
e
s o
f
tim
e
co
n
d
itio
n, i
n
peak
hours a
n
d norm
al hours. Because
the c
o
ndition in pea
k
hours a
n
d
norm
al hours a
r
e
differe
n
t, the t
r
ave
l
ti
m
e
s are d
i
fferen
t
too
.
In
th
i
s
ex
p
e
rim
e
n
t
,
we co
m
p
ared
t
h
e prob
ab
ility
u
s
er
n
o
t
to
m
i
ss th
e bu
s from o
u
r
pr
o
pose
d
m
e
tho
d
wi
t
h
t
h
e
exi
s
t
i
ng a
ppl
i
c
at
i
on. F
r
om
our ex
pe
ri
m
e
nt
, we concl
ude
d t
h
at
bot
h of
t
i
m
e
co
nd
itio
n showed
t
h
e
b
e
tter resu
lt th
an
t
h
e ex
istin
g app
l
icatio
n
to
g
i
v
e
a p
r
ob
ab
ility
to
en
sure u
s
ers no
t to
m
i
ss the bus.
W
i
t
h
the
probability aver
age
in pea
k
hour is 93% than
65%
, and in
norm
al hour is
85% tha
n
70
%
of a
n
e
x
i
s
t
i
ng a
ppl
i
cat
i
o
n.
ACKNOWLE
DGE
M
ENTS
The a
u
t
h
ors
wo
ul
d
l
i
k
e t
o
t
h
an
ks t
o
P
r
of
. De
r
on
Li
ang
an
d
Achm
ad B
a
s
uki
,
Ph
D.,
So
ft
wa
re
M
e
t
h
o
dol
ogy
Lab, Tai
p
ei
G
ove
r
n
m
e
nt
for
gi
ves t
h
e
bus
com
p
any
t
r
an
spo
r
t
a
t
i
on
dat
a
, Adam
Hen
d
r
a
B
r
at
a
for
p
r
ov
id
es auto
m
a
tic d
a
ta collecto
r
and
al
s
o
re
viewers for t
h
eir
valua
b
le c
o
mments.
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NC
ES
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Cheng, Shaowu. Liu, Bao
y
i.
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B
u
s
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e
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a
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[2]
Chien, S.I.J., Ding, Y.,
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