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e
x
te
n
d
ed
o
u
r
d
is
cu
s
s
io
n
f
o
cu
s
ed
o
n
t
h
e
cl
o
u
d
w
h
ic
h
i
n
cl
u
d
es
d
y
n
a
m
ic
r
eso
u
r
ce
p
r
o
v
is
io
n
i
n
g
an
d
s
ch
ed
u
lin
g
d
ec
is
io
n
s
,
Qu
alit
y
o
f
Ser
v
ice
(
Qo
S),
Qu
alit
y
o
f
Data
(
Qo
D)
co
n
s
tr
ain
ts
,
s
c
h
ed
u
li
n
g
o
b
j
ec
ti
v
es a
n
d
Op
ti
m
izat
io
n
s
tr
ate
g
ie
s.
1
.
1
.
Clo
ud
Reso
urce
M
o
del
T
h
e
r
eso
u
r
ce
m
o
d
el
d
ef
i
n
es
th
e
co
m
p
o
n
en
t
s
o
f
p
r
o
ce
s
s
in
g
ele
m
en
t
s
a
n
d
co
n
n
ec
tio
n
s
a
m
o
n
g
p
r
o
ce
s
s
in
g
ele
m
e
n
ts
i
n
p
ar
all
el
co
m
p
u
ti
n
g
e
n
v
ir
o
n
m
en
t
[
1
]
.
I
n
I
aa
S,
clo
u
d
r
eso
u
r
ce
is
ca
lled
a
(
in
s
tan
tiated
as)
VM
.
A
VM
i
s
an
en
v
ir
o
n
m
en
t
t
h
at
i
s
i
n
s
ta
lled
o
n
s
o
f
t
war
e
th
at
b
e
h
av
e
s
as
i
f
it
is
a
s
e
p
ar
ate
OS.
Di
f
f
er
e
n
t
clo
u
d
p
r
o
v
id
er
s
p
r
o
v
id
e
d
if
f
e
r
en
t
VM
t
y
p
es
o
f
VT
=
{v
t1
,
v
t2
,
…….
,
v
t
|
VT
|
},
w
h
er
e
v
t
is
as
s
o
ciate
d
w
it
h
t
w
o
attr
ib
u
tes o
f
ca
p
ab
ilit
y
a
n
d
co
s
t.
1
.
2
.
Reso
urce
a
cc
ess
a
nd
pric
i
ng
m
o
de
ls
I
n
ter
f
ac
e
a
n
d
I
n
f
r
astr
u
ct
u
r
e
t
o
g
eth
er
f
o
r
m
s
a
clo
u
d
e
n
v
ir
o
n
m
e
n
t
[
2
]
.
Var
io
u
s
I
aa
S
p
r
o
v
id
er
s
o
f
f
er
d
iv
er
s
e
r
eso
u
r
ce
ac
ce
s
s
a
n
d
p
r
icin
g
o
p
tio
n
s
f
o
r
r
eser
v
ed
,
o
n
-
d
em
a
n
d
an
d
s
p
o
t in
s
ta
n
ce
s
.
a.
R
eser
v
ed
i
n
s
ta
n
ce
.
T
h
i
s
m
o
d
el
allo
w
s
th
e
u
s
er
s
to
r
eser
v
e
co
m
p
u
t
in
g
r
e
s
o
u
r
ce
s
f
o
r
a
lo
n
g
er
p
er
io
d
b
y
p
r
ep
a
y
in
g
t
h
e
r
eser
v
atio
n
f
ee
.
b.
On
-
d
e
m
a
n
d
in
s
ta
n
ce
.
T
h
is
m
o
d
el
allo
w
s
t
h
e
u
s
er
s
to
lease
t
h
e
r
eso
u
r
ce
in
a
f
in
e
-
g
r
ain
ed
m
an
n
er
b
ased
o
n
t
h
e
d
e
m
an
d
.
On
-
d
e
m
an
d
i
n
s
ta
n
ce
s
ar
e
u
s
u
all
y
c
h
ar
g
ed
m
o
r
e
th
a
n
th
e
r
eser
v
ed
in
s
ta
n
ce
s
f
o
r
th
e
s
a
m
e
VM
t
y
p
e.
O
n
-
d
e
m
an
d
o
p
tio
n
ad
o
p
ts
co
ar
s
e
-
g
r
ain
ed
b
ill
in
g
o
p
tio
n
,
f
o
r
e
x
a
m
p
le,
Am
az
o
n
E
C
2
c
h
ar
g
e
s
p
er
h
o
u
r
b
illi
n
g
c
y
cle,
w
h
er
ea
s
A
z
u
r
e
ch
ar
g
e
s
p
er
m
i
n
u
te
b
illi
n
g
c
y
cle.
P
ar
tial u
s
ag
e
o
f
i
n
s
tan
ce
s
is
r
o
u
n
d
ed
u
p
to
n
e
x
t b
illi
n
g
c
y
cle.
c.
Sp
o
t
i
n
s
ta
n
ce
.
So
m
e
o
f
th
e
I
aa
S
p
r
o
v
id
er
s
o
f
f
er
d
y
n
a
m
ic
p
r
icin
g
s
ch
e
m
e
f
o
r
th
eir
lar
g
e
q
u
an
titi
e
s
o
f
s
p
ar
e
ca
p
ac
it
y
u
n
s
o
ld
.
T
h
ese
d
y
n
a
m
icall
y
p
r
iced
VM
s
ar
e
ca
lled
as
s
p
o
t
in
s
tan
ce
s
,
w
h
o
s
e
p
r
ice
ch
an
g
e
s
b
ased
o
n
t
h
e
m
ar
k
et
s
u
p
p
l
y
an
d
d
e
m
a
n
d
p
att
er
n
s
.
T
h
is
m
o
d
el
allo
w
s
th
e
u
s
er
s
to
b
id
o
n
th
o
s
e
s
p
ar
e
ca
p
ac
ities
an
d
g
r
an
t
s
t
h
e
r
eso
u
r
ce
s
to
th
e
u
s
er
s
i
f
t
h
eir
b
id
p
r
ice
is
h
ig
h
er
th
an
th
e
s
p
o
t
i
n
s
tan
ce
p
r
ice.
Sp
o
t
in
s
ta
n
ce
p
r
ices
ar
e
u
s
u
all
y
m
u
ch
lo
w
er
t
h
an
th
e
o
n
-
d
e
m
a
n
d
i
n
s
ta
n
ce
p
r
ice.
Ho
w
ev
er
,
s
p
o
t
i
n
s
ta
n
ce
m
a
y
b
e
ter
m
i
n
ated
at
a
n
y
ti
m
e
w
h
en
th
e
b
id
d
in
g
p
r
ice
is
lo
w
er
th
an
t
h
e
s
p
o
t i
n
s
ta
n
ce
p
r
ice.
R
est
o
f
t
h
e
p
ap
er
is
as
f
o
llo
w
s
.
Sec
tio
n
2
in
tr
o
d
u
ce
s
th
e
o
v
er
v
ie
w
o
f
s
cie
n
ti
f
ic
w
o
r
k
f
lo
w
s
an
d
ap
p
licatio
n
m
o
d
el
ta
x
o
n
o
m
y
.
Sectio
n
3
d
is
c
u
s
s
es
w
o
r
k
f
lo
w
s
ch
ed
u
li
n
g
tech
n
iq
u
es
b
as
ed
o
n
th
e
liter
atu
r
e
s
u
r
v
e
y
f
o
r
b
o
th
r
eso
u
r
ce
an
d
w
o
r
k
f
lo
w
.
A
d
etailed
d
is
cu
s
s
i
o
n
o
f
o
u
ts
ta
n
d
i
n
g
a
l
g
o
r
ith
m
s
i
n
S
ec
tio
n
4
,
Fi
n
all
y
,
r
esear
ch
ch
alle
n
g
es i
n
S
ec
tio
n
5
a
n
d
co
n
clu
s
io
n
ar
e
d
escr
ib
ed
in
S
ec
tio
n
6
.
2.
O
VE
RVI
E
W
O
F
SC
I
E
N
T
I
F
I
C
WO
RK
F
L
O
W
S
W
o
r
k
f
lo
w
is
t
h
e
s
er
ie
s
o
f
o
r
ch
estra
ted
ac
tiv
it
ies
t
h
at
ar
e
n
ec
ess
ar
y
to
co
m
p
le
te
a
tas
k
.
I
t
h
as
its
r
o
o
t
s
in
co
m
m
er
cial
en
ter
p
r
is
e
s
o
f
o
f
f
ice
a
u
to
m
at
io
n
s
y
s
te
m
s
a
s
a
b
u
s
in
es
s
p
r
o
ce
s
s
in
g
to
o
l,
w
h
ic
h
is
a
m
at
u
r
ed
r
esear
ch
ar
ea
[
3
]
.
Scie
n
ti
fi
c
wo
r
k
fl
o
w
s
d
escr
ib
e
a
s
er
ies
o
f
co
m
p
u
tatio
n
s
th
at
e
n
ab
le
t
h
e
an
al
y
s
is
o
f
d
ata
i
n
a
s
tr
u
ct
u
r
ed
an
d
d
is
tr
ib
u
ted
m
an
n
er
an
d
allo
w
s
s
c
ien
t
is
t
s
to
m
o
d
el,
d
esig
n
,
ex
ec
u
te,
d
eb
u
g
,
r
e
-
co
n
f
i
g
u
r
e
an
d
r
e
-
r
u
n
a
n
al
y
s
is
a
n
d
v
i
s
u
al
izatio
n
p
r
o
ce
s
s
es
.
W
o
r
k
f
lo
w
s
ca
n
b
e
e
x
p
r
ess
ed
an
d
p
r
o
ce
s
s
ed
as
b
est
ef
f
o
r
t,
s
u
p
er
s
ca
lar
,
an
d
s
tr
ea
m
in
g
p
ip
elin
es.
W
e
f
o
cu
s
o
n
Dir
ec
ted
ac
y
clic
g
r
a
p
h
s
(
D
A
Gs)
as
th
e
y
ar
e
co
m
m
o
n
l
y
u
s
ed
b
y
s
cie
n
ti
f
ic
a
n
d
r
esear
ch
co
m
m
u
n
it
y
.
DAGs
b
y
d
ef
i
n
itio
n
d
o
n
o
t
h
av
e
c
y
cles
o
r
co
n
tr
o
l
d
ep
e
n
d
en
cie
s
.
Fo
r
ex
a
m
p
le,
w
o
r
k
f
lo
w
m
a
n
ag
e
m
e
n
t
s
y
s
te
m
s
s
u
ch
a
s
P
eg
asu
s
,
C
l
o
u
d
b
u
s
W
f
M
S
,
ASK
AL
ON
,
a
n
d
DAGM
an
s
u
p
p
o
r
t
th
e
w
o
r
k
f
lo
w
s
m
o
d
eled
as
DAGs.
Fo
r
m
all
y
,
a
D
AG
ca
n
b
e
r
ep
r
esen
ted
as W
=
G(
T
,
E
)
,
w
h
er
e
T
i
s
a
s
et
o
f
v
=
|
T
|
ta
s
k
s
{
t
1
,t
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,...,t
n
}
an
d
ea
ch
tas
k
is
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s
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o
f
i
n
s
tr
u
ctio
n
s
t
h
a
t
m
u
s
t
b
e
ex
ec
u
ted
,
An
d
E
is
a
s
et
o
f
e
=
|
E
|
d
ir
ec
ted
ed
g
es {
e
i
j
|
(
t
i
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)
∈
E
}
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lin
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Tech
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ith
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esen
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ter
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ta
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k
d
ata
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ep
en
d
en
cies,
i
n
w
h
ich
ti
i
s
s
ai
d
to
b
e
th
e
p
ar
en
t
task
o
f
tj
an
d
tj
is
s
aid
to
b
e
ch
ild
tas
k
o
f
ti.
E
ac
h
e
d
g
e
e
i
j
r
ep
r
esen
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a
p
r
ec
ed
en
c
e
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elatio
n
w
h
ich
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n
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icate
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th
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t
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t
j
s
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ld
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t
its
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ec
u
ti
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n
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t
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t
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ata
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le
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tas
k
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h
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h
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o
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o
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h
a
v
e
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ar
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t
ta
s
k
is
ca
lled
an
en
tr
y
ta
s
k
,
w
h
er
e
as
a
ta
s
k
w
h
ic
h
d
o
es
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o
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h
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lled
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e
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i
t
task
.
T
o
g
en
er
alize
th
e
D
A
G
s
tr
u
ctu
r
e
w
it
h
o
n
l
y
o
n
e
en
tr
y
t
ask
a
n
d
o
n
e
e
x
it
tas
k
,
t
w
o
d
u
m
m
y
tas
k
s
t
start
a
n
d
t
end
ar
e
u
s
u
all
y
ad
o
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ted
an
d
ad
d
ed
to
th
e
b
eg
in
an
d
en
d
o
f
th
e
w
o
r
k
fl
o
w
,
w
h
ic
h
h
a
v
e
ze
r
o
co
m
p
u
tatio
n
w
o
r
k
lo
ad
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d
ze
r
o
co
m
m
u
n
ic
atio
n
d
ata
to
ac
tu
al
s
tar
t
tas
k
s
an
d
en
d
tas
k
s
.
T
h
e
p
r
o
ce
s
s
o
f
s
c
h
ed
u
li
n
g
a
w
o
r
k
f
lo
w
r
ep
r
esen
t
s
ass
i
g
n
i
n
g
t
ask
s
to
r
eso
u
r
ce
s
an
d
o
r
ch
e
s
tr
atin
g
th
ei
r
ex
ec
u
t
io
n
to
p
r
eser
v
e
t
h
e
d
ep
en
d
en
cies
a
m
o
n
g
t
h
e
tas
k
s
.
Fo
r
m
all
y
,
a
s
ch
ed
u
le
[
4
]
,
S
is
r
ep
r
esen
ted
as
a
3
-
tu
p
le,
S=
<R,
M,
m
a
k
esp
a
n
>,
W
h
er
e
R
is
th
e
s
et
o
f
r
eso
u
r
ce
s
{r
1
,
r
2
,
r
3
….
r
n
}
an
d
M
co
n
s
is
t
s
o
f
tas
k
r
eso
u
r
ce
m
ap
p
in
g
s
.
T
h
e
m
a
k
e
s
p
an
i
s
t
h
e
s
c
h
ed
u
le
le
n
g
th
o
f
S
.
A
ll
t
h
e
al
g
o
r
ith
m
s
i
n
t
h
is
s
u
r
v
e
y
d
if
f
er
i
n
th
eir
ab
ilit
y
to
s
ch
ed
u
le
i
n
t
h
e
w
o
r
k
f
lo
w
m
u
ltip
licit
y
.
Al
g
o
r
ith
s
ar
e
d
esi
g
n
ed
to
s
c
h
ed
u
le
d
i
f
f
er
en
t
t
y
p
es
o
f
w
o
r
k
f
lo
w
s
w
it
h
d
i
f
f
er
e
n
t
m
u
ltip
licit
y
lik
e
a
Si
n
g
le
n
s
ta
n
ce
o
f
w
o
r
k
f
lo
w
s
,
o
r
m
u
lt
ip
le
in
s
tan
ce
s
o
f
t
h
e
s
a
m
e
w
o
r
k
f
lo
w
s
,
m
u
l
tip
le
w
o
r
k
f
lo
w
s
.
R
o
d
r
ig
u
ez
a
n
d
R
aj
[
5
]
id
en
tif
ied
3
t
y
p
es o
f
s
c
h
ed
u
li
n
g
p
r
o
ce
s
s
e
s
f
r
o
m
t
h
e
w
o
r
k
f
lo
w
m
u
lt
ip
licit
y
p
er
s
p
ec
ti
v
e.
a.
Sin
g
le
W
o
r
k
f
lo
w
Sin
g
le
w
o
r
k
f
lo
w
s
ar
e
e
x
ec
u
te
d
s
eq
u
en
tiall
y
a
n
d
in
d
ep
en
d
e
n
tl
y
.
T
h
is
is
th
e
tr
ad
itio
n
al
m
o
d
el
u
s
ed
in
g
r
id
s
,
cl
u
s
ter
s
,
a
n
d
clo
u
d
s
.
A
l
g
o
r
ith
m
s
i
n
th
is
clas
s
ar
e
f
o
cu
s
ed
o
n
co
s
t
o
p
ti
m
iza
ti
o
n
an
d
m
ee
ti
n
g
t
h
e
Qo
S [
6
]
r
eq
u
ir
e
m
en
ts
f
o
r
a
s
in
g
le
u
s
er
an
d
a
s
i
n
g
le
D
A
G.
b.
W
o
r
k
f
lo
w
E
n
s
e
m
b
les
W
o
r
k
f
lo
w
en
s
e
m
b
les
ar
e
i
n
te
r
r
elate
d
w
o
r
k
f
lo
w
s
w
h
ich
ar
e
g
r
o
u
p
ed
to
g
et
h
er
.
T
h
ese
w
o
r
k
f
lo
w
s
w
il
l
h
a
v
e
th
e
s
i
m
ilar
s
tr
u
ctu
r
e
b
u
t
d
if
f
er
in
t
h
eir
s
ize
an
d
in
p
u
t
d
ata.
A
lg
o
r
it
h
m
s
in
t
h
is
cl
ass
ar
e
f
o
cu
s
ed
o
n
ex
ec
u
ti
n
g
all
th
e
i
n
s
ta
n
ce
s
o
f
t
h
e
w
o
r
k
f
lo
w
i
n
th
e
en
s
e
m
b
le
w
it
h
av
ailab
le
r
eso
u
r
ce
s
.
Qo
S
r
eq
u
ir
e
m
e
n
ts
ar
e
o
n
l
y
s
p
ec
if
ied
f
o
r
m
u
ltip
le
w
o
r
k
f
lo
ws
b
u
t
n
o
t
f
o
r
s
i
n
g
le
w
o
r
k
f
lo
w
.
I
n
t
h
is
m
o
d
el,
a
n
u
m
b
er
o
f
i
n
s
ta
n
ce
s
ar
e
k
n
o
w
n
i
n
ad
v
a
n
ce
an
d
s
ch
ed
u
ler
u
s
e
t
h
is
f
o
r
p
lan
n
i
n
g
a
n
d
ex
ec
u
t
io
n
o
f
ta
s
k
s
.
c.
Mu
ltip
le
W
o
r
k
f
lo
w
s
Mu
ltip
les
w
o
r
k
f
lo
w
s
ar
e
s
i
m
i
lar
to
en
s
e
m
b
le
s
e
x
ce
p
t
t
h
at,
t
h
e
w
o
r
k
f
lo
w
s
s
c
h
ed
u
led
m
a
y
n
o
t
b
e
r
elate
d
to
ea
ch
o
th
er
an
d
also
v
ar
y
i
n
s
ize,
s
tr
u
c
tu
r
e,
an
d
d
ata.
Sch
ed
u
li
n
g
i
s
v
ie
w
ed
as
d
y
n
a
m
ic
as
th
e
n
u
m
b
er
an
d
t
y
p
e
o
f
w
o
r
k
f
lo
w
s
ar
e
u
n
k
n
o
w
n
i
n
ad
v
a
n
ce
.
E
ac
h
i
n
d
ep
en
d
en
t
w
o
r
k
f
l
o
w
w
il
l
h
av
e
it
s
o
w
n
Qo
S r
eq
u
ir
e
m
e
n
t
.
3.
T
AXO
NO
M
Y
O
F
W
O
RK
flO
W
S
CH
E
DU
L
I
NG
W
o
r
k
fl
o
w
s
c
h
ed
u
li
n
g
p
r
o
b
lem
h
as
b
ee
n
s
t
u
d
ied
ex
ten
s
i
v
el
y
o
v
er
p
ast
y
ea
r
s
an
d
m
a
n
y
h
eu
r
i
s
tic
s
h
av
e
b
ee
n
d
ev
e
lo
p
ed
f
o
r
s
c
h
ed
u
li
n
g
t
h
e
tas
k
s
i
n
d
is
tr
ib
u
ted
en
v
ir
o
n
m
e
n
ts
.
T
h
e
i
n
p
u
t
to
th
e
w
o
r
k
f
lo
w
s
ch
ed
u
lin
g
a
lg
o
r
it
h
m
is
th
e
a
b
s
tr
a
ct
w
o
r
kflo
w
s
w
h
ic
h
d
ef
i
n
e
t
h
e
ta
s
k
s
w
i
th
o
u
t
s
p
ec
if
y
i
n
g
t
h
e
lo
ca
tio
n
o
f
th
e
r
eso
u
r
ce
s
i
n
w
h
ich
t
h
ese
tas
k
s
ar
e
ex
ec
u
ted
.
A
b
s
tr
ac
t
w
o
r
k
f
lo
w
s
ar
e
ca
teg
o
r
ized
as
d
et
ermin
is
tic
a
n
d
non
-
d
etermin
is
tic
.
I
n
th
e
d
eter
m
i
n
i
s
tic
m
o
d
el,
ta
s
k
d
ep
en
d
e
n
cies
an
d
in
p
u
t
d
ata
ar
e
k
n
o
w
n
in
a
d
v
an
ce
,
w
h
er
ea
s
i
n
n
o
n
-
d
eter
m
i
n
i
s
tic
m
o
d
el
t
h
e
y
ar
e
k
n
o
w
n
at
t
h
e
r
u
n
ti
m
e
o
n
l
y
.
W
o
r
k
f
lo
w
s
c
h
ed
u
li
n
g
ca
n
b
e
ca
teg
o
r
ized
as
b
est
-
e
ff
o
r
t
b
as
ed
an
d
Qo
S
co
n
s
tr
ain
t
-
b
ased
s
ch
ed
u
lin
g
[
7
]
as
s
h
o
w
n
i
n
F
ig
u
r
e
1
.
T
h
e
B
est
-
e
f
f
o
r
t
s
c
h
ed
u
li
n
g
f
o
cu
s
e
s
o
n
m
i
n
i
m
izi
n
g
t
h
e
m
a
k
esp
a
n
,
i
g
n
o
r
i
n
g
v
ar
io
u
s
u
s
er
‘
s
Qo
S
co
n
s
tr
ai
n
t
s
.
T
h
e
Qo
S
co
n
s
tr
ai
n
t
-
b
ased
s
c
h
ed
u
l
in
g
at
te
m
p
ts
to
m
i
n
i
m
ize
t
h
e
p
er
f
o
r
m
an
ce
u
n
d
er
m
o
s
t
i
m
p
o
r
tan
t
Qo
S
co
n
s
tr
ai
n
ts
,
f
o
r
ex
a
m
p
le,
m
in
i
m
ize
c
o
s
t
u
n
d
er
d
ea
d
lin
e
co
n
s
tr
ain
t
s
o
r
m
i
n
i
m
ize
ti
m
e
u
n
d
er
b
u
d
g
et
co
n
s
tr
ai
n
t.
3
.
1
B
est
-
E
f
f
o
rt
ba
s
ed
S
cheduli
n
g
T
h
e
b
est
-
ef
f
o
r
t
s
ch
ed
u
l
in
g
att
e
m
p
ts
to
o
p
ti
m
ize
o
n
e
o
b
j
ec
ti
v
e
w
h
ile
i
g
n
o
r
in
g
o
t
h
er
f
ac
to
r
s
s
u
c
h
as
m
o
n
etar
y
co
s
t
an
d
v
ar
io
u
s
Qo
S
r
eq
u
ir
e
m
en
t
s
.
T
h
e
o
b
j
e
ctiv
e
o
f
b
est
-
ef
f
o
r
t
s
ch
ed
u
li
n
g
al
g
o
r
ith
m
s
i
s
to
m
i
n
i
m
ize
th
e
m
ak
e
s
p
an
.
T
h
e
m
a
k
e
s
p
an
o
f
a
w
o
r
k
f
lo
w
ap
p
licatio
n
is
th
e
to
tal
ti
m
e
tak
en
to
co
m
p
lete
t
h
e
ex
ec
u
t
io
n
o
f
a
w
o
r
k
f
lo
w
.
B
est
-
E
f
f
o
r
t
s
c
h
ed
u
li
n
g
alg
o
r
it
h
m
s
ar
e
eith
er
h
eu
r
is
tics
b
ase
d
o
r
meta
-
h
eu
r
is
tics
b
ased
ap
p
r
o
ac
h
.
T
h
e
h
eu
r
i
s
tic
b
ased
alg
o
r
ith
m
s
f
it
o
n
l
y
to
th
e
p
ar
ticu
lar
t
y
p
e
o
f
p
r
o
b
lem
s
w
h
ile
m
eta
-
h
eu
r
i
s
tic
s
b
ased
alg
o
r
ith
m
s
ar
e
b
ased
o
n
a
m
e
ta
-
h
e
u
r
is
tic
m
et
h
o
d
w
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ic
h
p
r
o
v
id
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t
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ev
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r
i
s
tic
to
f
it in
to
a
s
p
ec
if
ic
p
r
o
b
le
m
.
3
.
1
.
1
.
H
euristics
T
h
er
e
ar
e
f
o
u
r
class
es
o
f
s
ch
ed
u
lin
g
h
e
u
r
is
tics
f
o
r
a
w
o
r
k
f
lo
w
ap
p
licatio
n
.
I
n
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al
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k
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lis
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s
ter
an
d
d
u
p
licat
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ased
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h
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li
n
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.
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r
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ith
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3
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1
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1
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L
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t
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ates
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o
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s
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ased
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itie
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Set
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i
th
a
r
an
k
v
a
l
u
e
f
r
o
m
t
h
e
s
c
h
ed
u
lin
g
li
s
t;
b.
R
eso
u
r
ce
Selectio
n
Selects
t
h
e
task
in
t
h
e
o
r
d
er
o
f
p
r
io
r
ity
an
d
allo
ca
tes
th
e
tas
k
to
th
e
o
p
ti
m
al
r
eso
u
r
ce
.
T
h
e
s
ch
ed
u
l
in
g
l
is
t
ca
n
b
e
co
n
s
tr
u
cted
eit
h
er
s
ta
ticall
y
o
r
d
y
n
a
m
ical
l
y
.
I
f
al
l
t
h
e
p
r
io
r
itie
s
o
f
tas
k
s
ar
e
co
n
s
tr
u
cted
b
ef
o
r
e
a
n
y
ta
s
k
allo
ca
tio
n
,
is
ca
l
led
as
s
ta
tic
lis
t
s
ch
ed
u
li
n
g
.
W
h
er
ea
s
i
f
t
h
e
p
r
io
r
ities
o
f
u
n
s
ch
ed
u
led
tas
k
s
ar
e
r
ec
o
m
p
u
ted
af
ter
ea
c
h
ta
s
k
s
c
h
ed
u
l
in
g
s
tep
,
it
is
ca
lled
as
d
y
n
a
m
ic
ta
s
k
s
c
h
ed
u
l
in
g
.
W
h
eth
er
s
tatic
o
r
d
y
n
a
m
ic
lis
t,
d
if
f
er
en
t
p
r
io
r
itizin
g
attr
ib
u
tes
a
n
d
r
eso
u
r
ce
s
ele
ctio
n
s
tr
a
teg
ies
ar
e
r
eq
u
ir
ed
to
d
ec
id
e
task
p
r
io
r
ities
an
d
o
p
ti
m
al
r
eso
u
r
ce
f
o
r
ea
ch
tas
k
.
W
o
r
k
f
lo
w
lis
t
s
ch
ed
u
li
n
g
al
g
o
r
ith
m
s
ar
e
eith
er
b
atch
,
d
ep
en
d
en
c
y
o
r
d
ep
en
d
en
c
y
-
b
atc
h
m
o
d
e.
3
.
1
.
1
.
2
.
1
.
B
a
t
ch
M
o
de
B
atch
m
o
d
e
s
c
h
ed
u
li
n
g
al
g
o
r
ith
m
s
g
r
o
u
p
th
e
tas
k
s
i
n
to
s
e
v
er
a
l
in
d
ep
en
d
e
n
t
ta
s
k
s
,
s
u
c
h
a
s
a
b
a
g
o
f
task
s
an
d
p
ar
a
m
eter
tas
k
s
.
I
t
c
o
n
s
id
er
s
th
e
c
u
r
r
en
t
g
r
o
u
p
tas
k
s
to
co
m
p
lete
t
h
e
ex
ec
u
tio
n
at
th
e
ea
r
lies
t
ti
m
e.
So
m
e
clas
s
ic
b
atch
m
o
d
e
h
eu
r
is
tics
ar
e
Mi
n
-
Min
,
Ma
x
-
Min
,
Su
ff
er
ag
e
p
r
o
p
o
s
ed
b
y
Ma
h
e
s
w
ar
a
n
etal
[
8
]
.
3
.
1
.
1
.
2
.
2
.
Depende
ncy
M
o
de
Dep
en
d
en
c
y
m
o
d
e
s
ch
ed
u
li
n
g
alg
o
r
ith
m
s
ar
e
b
ased
o
n
s
c
h
ed
u
lin
g
a
tas
k
w
it
h
i
n
ter
d
ep
en
d
en
t
ta
s
k
alg
o
r
ith
m
s
.
Dep
e
n
d
en
c
y
m
o
d
e
in
ten
d
s
to
p
r
o
v
id
e
a
s
tr
a
teg
y
to
m
ap
w
o
r
k
f
lo
w
tas
k
s
o
n
h
eter
o
g
e
n
eo
u
s
r
eso
u
r
ce
s
b
ased
o
n
an
al
y
zi
n
g
th
e
d
ep
en
d
en
cies
o
f
th
e
e
n
t
i
r
e
task
g
r
ap
h
.
U
n
li
k
e
b
atch
m
o
d
e
al
g
o
r
ith
m
s
,
i
t
r
an
k
s
all
p
r
io
r
ities
o
f
all
tas
k
s
b
ased
o
n
w
h
o
le
ap
p
licatio
n
co
n
tex
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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&
C
o
m
p
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n
g
I
SS
N:
2
0
8
8
-
8708
W
o
r
kflo
w
S
ch
ed
u
lin
g
Tech
n
iq
u
es a
n
d
A
lg
o
r
ith
ms in
I
a
a
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lo
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d
:
A
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r
ve
y
(
K
.
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a
lya
n
a
C
h
a
kra
va
r
th
i
)
857
T
o
p
cu
o
g
lu
et
al.
[
9
]
p
r
o
p
o
s
ed
th
e
Hete
r
o
g
en
eo
u
s
-
E
ar
lie
s
t
-
Fi
n
is
h
-
T
im
e
(
HE
FT
)
alg
o
r
ith
m
t
h
a
t
ca
lcu
late
s
t
h
e
av
er
a
g
e
e
x
ec
u
t
i
o
n
ti
m
e
f
o
r
ea
c
h
ta
s
k
an
d
a
v
er
ag
e
co
m
m
u
n
ica
tio
n
t
i
m
e
b
et
w
ee
n
r
eso
u
r
ce
s
o
f
t
w
o
s
u
cc
ess
iv
e
tas
k
s
.
T
h
e
n
f
o
r
ea
ch
ta
s
k
,
a
r
an
k
v
al
u
e
is
ca
lcu
lated
i
n
a
r
ec
u
r
s
iv
e
m
a
n
n
er
b
ased
o
n
t
h
e
r
a
n
k
v
alu
e
o
f
it
s
d
ep
en
d
en
t
ta
s
k
s
.
E
x
it
ta
s
k
w
i
ll
h
av
e
t
h
e
lo
w
e
s
t
r
an
k
v
al
u
e
as
b
ei
n
g
th
e
a
v
e
r
ag
e
ex
ec
u
tio
n
ti
m
e.
T
h
e
p
r
e
d
ec
ess
o
r
s
o
f
th
e
ex
it
t
ask
w
ill
h
av
e
t
h
eir
av
er
ag
e
e
x
ec
u
t
io
n
ti
m
e
+
th
e
m
a
x
i
m
u
m
(
[
co
m
m
u
n
icatio
n
ti
m
e
f
r
o
m
a
r
eso
u
r
ce
to
an
o
t
h
er
r
eso
u
r
ce
]
+
[
th
e
r
an
k
v
al
u
e
o
f
t
h
e
s
u
cc
es
s
o
r
]
)
.
T
h
en
t
ask
w
i
th
t
h
e
h
ig
h
e
s
t
p
r
io
r
ity
w
ill b
e
s
c
h
ed
u
le
d
f
ir
s
t
.
3
.
1
.
1
.
2
.
3
.
Depende
ncy
-
B
a
t
ch
M
o
de
Z
h
ao
an
d
Sa
k
ellar
io
u
[
1
0
]
p
r
o
p
o
s
ed
a
h
y
b
r
id
h
eu
r
i
s
t
ic
ap
p
r
o
ac
h
f
o
r
s
ch
ed
u
li
n
g
DAG
in
h
eter
o
g
e
n
eo
u
s
s
y
s
te
m
s
.
T
h
is
h
eu
r
is
tic
ap
p
r
o
ac
h
co
m
b
i
n
e
s
d
ep
en
d
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c
y
m
o
d
e
an
d
b
a
tch
m
o
d
e.
I
t
f
ir
s
t
co
m
p
u
tes
th
e
r
an
k
o
f
ea
ch
ta
s
k
a
n
d
cr
ea
tes
a
g
r
o
u
p
o
f
i
n
d
ep
en
d
en
t
ta
s
k
s
.
T
h
en
it
o
r
g
an
izes
tas
k
s
g
r
o
u
p
b
y
g
r
o
u
p
an
d
u
s
es a
b
atch
m
o
d
e
a
lg
o
r
ith
m
to
r
ep
r
io
r
itize
th
e
s
ch
ed
u
lin
g
o
f
ta
s
k
s
in
t
h
e
g
r
o
u
p
.
T
ab
le
1
s
u
m
m
ar
izes
th
e
t
y
p
ical
lis
t
s
c
h
ed
u
l
in
g
h
e
u
r
is
tic
s
f
o
r
h
eter
o
g
e
n
eo
u
s
ea
r
lies
t
-
fin
i
s
h
-
ti
m
e
(
HE
FT
)
,
c
r
itical
-
p
ath
-
on
-
a
-
p
r
o
ce
s
s
o
r
(
C
P
OP
)
,
d
y
n
a
m
ic
lev
e
l
s
ch
ed
u
l
in
g
(
D
L
S),
d
y
n
a
m
ic
c
r
itical
p
ath
(
DC
P
)
.
T
ab
le
1
.
T
y
p
ical
lis
t sc
h
ed
u
lin
g
alg
o
r
it
h
m
s
H
e
u
r
i
st
i
c
A
t
t
r
i
b
u
t
e
S
t
a
t
i
c
/
D
y
n
a
mi
c
C
o
mp
l
e
x
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t
y
H
EFT
r
a
n
k
u
(
t
i
)
S
t
a
t
i
c
O
(
e
X
|
R
|
)
C
P
O
P
r
a
n
k
(
t
i
)
=
r
a
n
k
u
(
t
i
)
+
r
a
n
k
d
(
t
i
)
S
t
a
t
i
c
O
(
e
X
|
R
|
)
D
L
S
D
L
(
t
i
, r
l
)
=
r
a
n
k
u
(
t
i
)
-
EST
ti
rl
D
y
n
a
mi
c
O(V
3
X
|
R
|
)
D
C
P
L
S
T
(
t
i
)
–
EST
(
t
i
)
D
y
n
a
mi
c
O(V
3
)
3
.
1
.
1
.
3
.
Clus
t
er
ing
H
euri
s
t
ic
B
o
th
clu
s
ter
in
g
b
ased
an
d
d
u
p
licatio
n
b
ased
s
c
h
ed
u
li
n
g
(
in
3
.
1
.
1
.
4
)
a
r
e
d
esig
n
ed
to
o
p
ti
m
ize
t
h
e
d
ata
tr
an
s
m
is
s
io
n
ti
m
e
b
et
wee
n
d
ep
en
d
en
t
ta
s
k
s
.
I
n
m
o
s
t
s
ch
ed
u
li
n
g
h
e
u
r
is
tic
s
,
ta
s
k
s
ar
e
s
ch
ed
u
led
s
ep
ar
atel
y
.
A
s
c
h
ed
u
le
t
h
at
d
o
es
n
o
t
co
n
s
id
er
th
e
co
m
m
u
n
icatio
n
d
ela
y
g
e
n
er
ates
th
e
id
le
f
r
ag
m
en
t
s
in
t
h
e
r
eso
u
r
ce
.
C
lu
s
ter
i
n
g
h
eu
r
i
s
tic
co
n
s
is
t
s
o
f
t
w
o
p
ar
ts
:
a.
C
lu
s
ter
i
n
g
Ma
p
p
in
g
tas
k
s
to
clu
s
ter
s
;
b.
Or
d
er
in
g
Or
d
er
in
g
tas
k
s
i
n
t
h
e
s
a
m
e
cl
u
s
ter
.
C
lu
s
ter
i
n
g
o
f
a
D
A
G
i
s
t
h
e
m
a
p
p
in
g
o
f
all
ta
s
k
s
o
n
to
cl
u
s
ter
s
,
w
h
er
e
ea
c
h
cl
u
s
ter
is
a
s
u
b
s
et
o
f
ta
s
k
s
an
d
ex
ec
u
te
s
o
n
a
s
ep
ar
ate
r
es
o
u
r
ce
,
w
h
ic
h
m
in
i
m
ize
s
th
e
d
ata
tr
an
s
m
is
s
io
n
ti
m
e
b
et
w
ee
n
task
s
.
Hen
ce
t
h
er
e
is
a
tr
ad
e
-
o
f
f
b
et
w
ee
n
m
a
x
i
m
i
zin
g
t
h
e
p
ar
allelis
m
an
d
m
in
i
m
izi
n
g
t
h
e
co
m
m
u
n
ica
tio
n
d
ela
y
.
I
f
th
er
e
ar
e
t
w
o
in
d
ep
en
d
en
t ta
s
k
s
i
n
th
e
s
a
m
e
clu
s
ter
,
it i
s
ca
lled
n
o
n
lin
ea
r
cl
u
s
ter
; o
t
h
er
w
is
e
ca
lled
li
n
ea
r
.
A
li
n
ea
r
clu
s
ter
i
n
g
p
r
eser
v
es
p
ar
allelis
m
,
h
e
n
ce
it
d
o
es
n
o
t
in
cr
ea
s
e
th
e
p
ar
allel
ex
ec
u
t
io
n
ti
m
e.
W
h
er
ea
s
in
n
o
n
li
n
ea
r
clu
s
ter
in
g
,
p
ar
allel
task
s
ar
e
s
eq
u
en
t
ialize
d
w
h
ich
r
ed
u
ce
s
th
e
p
ar
allelis
m
an
d
i
n
cr
ea
s
es t
h
e
p
ar
allel
ex
ec
u
t
io
n
ti
m
e.
T
ab
le
2
o
v
er
v
ie
w
o
f
cl
u
s
ter
in
g
h
eu
r
i
s
tics
.
T
ab
le
2
.
C
o
m
p
ar
es f
o
u
r
t
y
p
ica
l c
lu
s
ter
i
n
g
h
e
u
r
is
tic
s
H
e
u
r
i
st
i
c
C
l
u
st
e
r
i
n
g
o
r
d
e
r
i
n
g
L
i
n
e
a
r
C
o
mp
l
e
x
i
t
y
D
S
C
[
1
1
,
1
2
]
C
h
o
o
se
s t
h
e
f
r
e
e
t
a
sk
w
i
t
h
h
i
g
h
e
st
r
a
n
k
.
Z
e
r
o
i
t
s
i
n
c
o
mi
n
g
e
d
g
e
s i
f
i
t
r
e
d
u
c
e
s ra
n
k
d
(
t
i
)
N
o
n
-
i
n
s
e
r
t
i
o
n
No
O
(
l
o
g
v
(
v
+
e
)
)
K
B
/
L
[
1
3
]
C
l
u
st
e
r
i
n
g
a
l
l
t
a
s
k
s o
n
t
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(
v
x
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v
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S
a
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k
a
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‘
s
[
1
4
]
Z
e
r
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t
h
e
h
i
g
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e
st
c
o
mm
u
n
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k
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r
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No
O
(
e
x
(
v
+
e
)
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C
A
S
S
–
I
I
[
1
5
]
C
h
o
o
se
s
t
h
e
c
u
r
r
e
n
t
t
a
sk
w
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r
t
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No
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e
+
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v
x
l
o
g
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)
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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2
0
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8
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r
il 2
0
1
8
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–
8
6
6
858
3
.
1
.
1
.
4
.
Dupl
ica
t
io
n H
euristic
T
h
e
d
u
p
licatio
n
b
ased
h
e
u
r
is
t
ic
is
to
d
u
p
licate
ta
s
k
o
n
t
h
e
s
a
m
e
r
eso
u
r
ce
w
it
h
tar
g
e
t
tas
k
s
o
t
h
at
tr
an
s
m
is
s
io
n
ti
m
e
b
et
w
ee
n
t
h
o
s
e
t
w
o
ta
s
k
s
a
v
o
id
ed
.
T
h
e
m
o
t
iv
atio
n
o
f
d
u
p
licatio
n
h
e
u
r
is
t
i
c
is
,
it
m
a
y
h
ap
p
en
th
at
s
o
m
e
r
eso
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r
ce
s
m
a
y
b
e
id
le
d
u
r
in
g
d
i
f
f
er
en
t
ti
m
e
p
er
io
d
s
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au
s
e
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k
s
as
s
i
g
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ed
to
th
e
m
m
a
y
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e
w
ai
tin
g
f
o
r
th
e
d
ata
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r
o
m
o
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r
eso
u
r
ce
s
.
T
h
ese
id
le
ti
m
e
s
lo
ts
ar
e
e
f
f
ec
tiv
e
l
y
u
til
ized
b
y
i
d
en
ti
f
y
i
n
g
t
h
e
cr
itical
tas
k
s
an
d
allo
ca
tin
g
t
h
e
m
i
n
th
e
s
e
s
lo
ts
,
f
u
r
t
h
er
r
ed
u
ci
n
g
t
h
e
e
x
ec
u
tio
n
ti
m
e.
B
ased
o
n
t
h
e
s
elec
tio
n
o
f
ta
s
k
s
to
b
e
d
u
p
licated
,
d
up
licatio
n
-
b
ased
alg
o
r
ith
m
s
ar
e
d
i
v
id
ed
in
to
t
wo
class
es
;
s
ch
ed
u
li
n
g
w
i
th
f
u
ll
d
u
p
licatio
n
(
SF
D)
an
d
s
ch
ed
u
li
n
g
w
i
th
p
ar
tial
d
u
p
licatio
n
(
SP
D)
.
T
h
e
SF
D
d
u
p
licated
all
tas
k
s
f
r
o
m
h
ig
h
er
lev
els
o
f
tar
g
et
task
s
,
w
h
er
ea
s
SP
D
i
m
p
o
s
e
s
r
estrictio
n
s
d
u
r
i
n
g
tas
k
s
ele
ctio
n
p
r
o
ce
s
s
f
o
r
d
u
p
licatio
n
.
Du
p
licatio
n
-
b
ased
s
ch
ed
u
lin
g
ac
h
iev
e
s
s
h
o
r
ter
m
ak
e
s
p
an
s
,
it
also
m
a
k
e
s
t
h
e
s
ch
ed
u
li
n
g
m
o
r
e
d
if
fi
c
u
lt.
T
a
b
le
3
g
iv
es
a
n
o
v
er
v
ie
w
o
f
d
u
p
licatio
n
h
eu
r
i
s
t
ics.
T
ab
le
3
.
Ov
er
v
ie
w
o
f
d
u
p
licat
io
n
h
e
u
r
is
tic
s
H
e
u
r
i
st
i
c
F
e
a
t
u
r
e
L
i
st
\
C
l
u
st
e
r
i
n
g
D
u
p
l
i
c
a
t
i
o
n
t
y
p
e
T
D
S
[
1
6
]
C
r
i
t
i
c
a
l
p
a
r
e
n
t
i
s
d
u
p
l
i
c
a
t
e
d
C
l
u
st
e
r
i
n
g
P
a
r
t
i
a
l
D
u
p
l
i
c
a
t
i
o
n
L
W
B
[
1
7
]
L
o
w
e
r
b
o
u
n
d
o
f
st
a
r
t
t
i
me
i
s a
p
p
r
o
x
i
mat
e
d
C
l
u
st
e
r
i
n
g
P
a
r
t
i
a
l
D
u
p
l
i
c
a
t
i
o
n
P
L
W
[
1
8
]
L
o
w
e
r
b
o
u
n
d
o
f
st
a
r
t
t
i
me
i
s a
p
p
r
o
x
i
mat
e
d
C
l
u
st
e
r
i
n
g
P
a
r
t
i
a
l
D
u
p
l
i
c
a
t
i
o
n
D
F
R
N
[
1
9
]
D
u
p
l
i
c
a
t
i
o
n
f
i
r
st
a
n
d
r
e
d
u
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o
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n
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x
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L
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P
a
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t
i
a
l
D
u
p
l
i
c
a
t
i
o
n
D
S
H
[
2
0
]
U
t
i
l
i
z
a
t
i
o
n
o
f
i
d
l
e
sl
o
t
i
s m
a
x
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m
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d
L
i
st
F
u
l
l
D
u
p
l
i
c
a
t
i
o
n
B
T
D
H
[
2
1
]
Ex
t
e
n
si
o
n
o
f
t
h
e
D
S
H
L
i
st
F
u
l
l
D
u
p
l
i
c
a
t
i
o
n
L
C
T
D
[
2
2
]
O
p
t
i
mi
z
a
t
i
o
n
o
f
l
i
n
e
a
r
c
l
u
s
t
e
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i
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C
l
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st
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n
g
F
u
l
l
D
u
p
l
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c
a
t
i
o
n
C
P
F
D
[
2
3
]
T
a
sk
o
n
c
r
i
t
i
c
a
l
p
a
t
h
i
s c
o
n
si
d
e
r
e
d
f
i
r
s
t
L
i
st
F
u
l
l
D
u
p
l
i
c
a
t
i
o
n
P
Y
[
2
4
]
L
o
w
e
r
b
o
u
n
d
o
f
st
a
r
t
t
i
me
i
s a
p
p
r
o
x
i
mat
e
d
C
l
u
st
e
r
i
n
g
F
u
l
l
D
u
p
l
i
c
a
t
i
o
n
T
C
S
D
[
2
5
]
L
o
w
e
r
b
o
u
n
d
o
f
st
a
r
t
t
i
me
i
s a
p
p
r
o
x
i
mat
e
d
C
l
u
st
e
r
i
n
g
F
u
l
l
D
u
p
l
i
c
a
t
i
o
n
3
.
1
.
2
.
M
e
t
a
-
heuris
t
ics
As
D
A
G
s
c
h
ed
u
l
in
g
i
s
a
n
N
P
-
co
m
p
letep
r
o
b
lem
,
a
n
o
p
ti
m
al
s
o
lu
tio
n
ca
n
‘
t
b
e
f
o
u
n
d
i
n
p
o
ly
n
o
m
ial
ti
m
e
u
n
le
s
s
NP
=
P
[
2
6
]
.
M
eta
-
h
eu
r
i
s
tics
u
s
u
all
y
p
r
o
v
id
e
th
e
g
en
er
al
s
tr
u
ct
u
r
e
an
d
s
tr
ateg
y
g
u
id
elin
e
s
f
o
r
d
ev
elo
p
in
g
h
e
u
r
is
tic.
I
n
l
iter
atu
r
e,
f
e
w
m
eta
-
h
eu
r
i
s
tics
ar
e
p
r
o
p
o
s
ed
,
w
h
ic
h
p
r
o
v
id
e
s
an
ef
ficien
t
w
a
y
o
f
m
o
v
i
n
g
q
u
ic
k
l
y
to
w
ar
d
a
v
er
y
g
o
o
d
s
o
lu
tio
n
.
Gen
etic
A
l
g
o
r
ith
m
s
(
G
As)
ar
e
m
o
s
t
w
id
el
y
s
t
u
d
ied
m
et
a
-
h
e
u
r
is
tic,
w
h
ic
h
p
r
o
v
id
es
th
e
o
p
ti
m
a
l
s
o
lu
tio
n
f
o
r
lar
g
e
s
ea
r
ch
s
p
ac
e
u
s
i
n
g
t
h
e
p
r
in
cip
le
o
f
ev
o
lu
t
io
n
.
T
h
ese
GA
s
d
i
f
f
er
in
t
h
e
r
ep
r
esen
t
atio
n
o
f
t
h
e
s
ch
ed
u
les
i
n
th
e
s
ea
r
ch
s
p
ac
e,
g
en
et
ic
o
p
er
ato
r
s
f
o
r
g
e
n
er
ati
n
g
n
e
w
s
c
h
ed
u
le
s
,
fi
t
n
es
s
f
u
n
c
tio
n
to
e
v
al
u
ate
t
h
e
s
ch
ed
u
les
a
n
d
s
to
ch
a
s
tic
a
s
s
i
g
n
m
e
n
t
to
co
n
tr
o
l
th
e
g
e
n
etic
o
p
er
ato
r
s
.
L
iter
atu
r
e
s
u
r
v
e
y
s
h
o
w
s
t
h
at
G
A
-
b
ased
ap
p
r
o
ac
h
r
eq
u
ir
es a
r
o
u
n
d
o
n
e
m
i
n
u
te
to
p
r
o
d
u
ce
a
s
o
lu
tio
n
,
w
h
ile
o
t
h
er
h
e
u
r
is
tic
s
r
eq
u
ir
e
an
ex
ec
u
tio
n
o
f
f
e
w
s
ec
o
n
d
s
.
Gr
ee
d
y
R
a
n
d
o
m
ized
A
d
ap
tiv
e
Sear
ch
P
r
o
ce
d
u
r
e
(
GR
A
SP
)
is
a
r
an
d
o
m
ized
iter
ati
v
e
s
ea
r
ch
tech
n
iq
u
e
.
B
ly
th
e
et
al
.
[
2
7
]
i
n
v
e
s
ti
g
ate
d
GR
A
SP
,
w
h
ic
h
g
ets
b
etter
p
er
f
o
r
m
a
n
ce
t
h
an
Mi
n
-
M
in
h
e
u
r
is
tic
o
n
b
o
t
h
co
m
p
u
tatio
n
al
-
an
d
d
ata
-
i
n
ten
s
iv
e
ap
p
licatio
n
s
.
Si
m
u
la
ted
An
n
ea
lin
g
(
S
A
)
[
2
8
]
is
m
o
ti
v
ated
b
y
th
e
Mo
n
te
C
ar
lo
m
et
h
o
d
f
o
r
s
tati
s
ticall
y
s
ea
r
ch
i
n
g
t
h
e
g
lo
b
al
o
p
ti
m
al
b
et
w
ee
n
d
i
f
f
er
e
n
t
lo
ca
l
o
p
ti
m
a.
Yo
u
n
g
e
t
al
.
[
2
9
]
h
av
e
i
n
v
esti
g
ated
p
er
f
o
r
m
a
n
ce
s
o
f
S
A
alg
o
r
it
h
m
s
f
o
r
s
ch
ed
u
lin
g
w
o
r
k
fl
o
w
ap
p
lic
atio
n
s
i
n
a
Gr
id
en
v
ir
o
n
m
e
n
t
.
3
.
1
.
3
.
Co
m
pa
riso
n o
f
B
est
-
E
ff
o
rt
Schedu
lin
g
Alg
o
rit
h
m
s
Me
ta
-
h
eu
r
i
s
tics
p
er
f
o
r
m
b
etter
th
an
lo
ca
l
s
ea
r
c
h
b
ased
h
eu
r
is
tics
a
s
th
e
y
s
ea
r
c
h
s
c
h
ed
u
le
s
in
lar
g
er
s
ea
r
ch
s
p
ac
e.
Ho
w
e
v
er
,
w
h
en
th
e
n
u
m
b
er
o
f
tas
k
s
i
n
th
e
w
o
r
k
f
lo
w
D
A
G
i
n
cr
ea
s
es,
s
c
h
ed
u
li
n
g
ti
m
e
o
f
m
eta
-
h
eu
r
i
s
tics
in
cr
ea
s
e
s
r
ap
id
l
y
.
L
is
t
s
c
h
ed
u
li
n
g
h
eu
r
i
s
tics
a
s
s
u
m
es
a
b
o
u
n
d
ed
n
u
m
b
er
o
f
r
eso
u
r
ce
s
w
h
er
ea
s
clu
s
ter
i
n
g
h
e
u
r
is
tic
s
as
s
u
m
es t
h
e
u
n
b
o
u
n
d
ed
n
u
m
b
er
o
f
r
eso
u
r
ce
s
.
3
.
1
.
4
.
Dy
na
m
ic
Wo
r
k
fl
o
w
S
cheduli
ng
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
r
e
s
o
u
r
ce
s
v
ar
ies
o
v
er
ti
m
e.
A
‗
b
est
‘
r
es
o
u
r
ce
m
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b
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w
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v
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So
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et
al
.
[
3
0
]
pr
o
p
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ed
a
tax
o
n
o
m
y
o
f
d
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ased
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s
s
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an
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k
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(
tas
k
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co
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Evaluation Warning : The document was created with Spire.PDF for Python.
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it
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m
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a
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t
d
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d
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h
ese
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ec
is
io
n
s
ar
e
b
ased
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cu
r
r
en
t state
o
f
t
h
e
r
eso
u
r
ce
an
d
task
i
n
f
o
r
m
atio
n
.
3
.
2
.
Q
o
S
-
Co
ns
t
ra
int
B
a
s
ed
Wo
r
k
fl
o
w
Schedu
lin
g
Mo
s
t
o
f
th
e
Qo
S
co
n
s
tr
ain
t
-
b
a
s
ed
w
o
r
k
f
lo
w
s
c
h
ed
u
li
n
g
h
e
u
r
is
tics
ar
e
b
ased
o
n
time
o
r
co
s
t
.
T
im
e
is
th
e
to
tal
ti
m
e
ta
k
en
to
ex
ec
u
te
all
task
s
o
f
t
h
e
w
o
r
k
f
lo
w
(
d
ea
d
lin
e)
.
C
o
s
t
is
th
e
to
tal
ex
p
e
n
s
e
f
o
r
ex
ec
u
ti
n
g
t
h
e
w
o
r
k
f
lo
w
(
b
u
d
g
et)
.
Sch
ed
u
li
n
g
al
g
o
r
ith
m
s
b
a
s
ed
o
n
ti
m
e
a
n
d
co
s
t
co
n
s
tr
ain
ts
,
ca
lled
De
ad
lin
e
co
n
s
tr
ain
ed
s
ch
ed
u
lin
g
a
n
d
b
u
d
g
et
co
n
s
tr
ain
ed
s
ch
ed
u
li
n
g
.
3
.
2
.
1
.
Dea
dli
ne
Co
ns
t
ra
ine
d Sched
uli
ng
Dea
d
lin
e
co
n
s
tr
ai
n
ed
s
ch
ed
u
lin
g
ai
m
s
to
m
i
n
i
m
ize
th
e
ex
ec
u
t
io
n
co
s
t
w
h
ile
m
ee
t
in
g
th
e
u
s
er
s
p
ec
if
ied
d
ea
d
lin
e
co
n
s
tr
ai
n
t.
I
n
liter
atu
r
e
s
u
r
v
e
y
,
t
w
o
h
e
u
r
is
tics
h
a
v
e
b
ee
n
d
e
v
elo
p
ed
to
m
i
n
i
m
ize
t
h
e
co
s
t
w
h
ile
m
ee
ti
n
g
t
h
e
ti
m
e
co
n
s
t
r
ain
t.
B
a
ck
-
tr
a
ck
in
g
p
r
o
p
o
s
ed
b
y
Me
n
asc
an
d
C
a
s
alicc
h
io
[
3
1
]
an
d
De
a
d
lin
e
Dis
tr
ib
u
tio
n
p
r
o
p
o
s
ed
b
y
Yu
et
al.
[
3
2
]
.
In
b
a
ck
tr
a
ck
in
g
h
eu
r
is
tic
,
av
a
i
lab
le
o
r
u
n
m
ap
p
ed
task
s
ar
e
ass
i
g
n
ed
to
th
e
lea
s
t
ex
p
en
s
i
v
e
r
eso
u
r
ce
.
I
n
ca
s
e
if
m
a
n
y
tas
k
s
ar
e
av
ai
lab
le,
it
ass
i
g
n
s
m
o
s
t
d
ata
in
t
en
s
i
v
e
tas
k
to
a
f
a
s
test
r
eso
u
r
ce
.
T
h
is
h
eu
r
is
tic
i
s
r
ep
ea
ted
u
n
til
a
ll
ta
s
k
s
ar
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as
s
ig
n
ed
to
a
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eso
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ce
.
Af
ter
e
ac
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iter
ati
v
e
s
tep
,
th
e
e
x
ec
u
ti
o
n
ti
m
e
o
f
c
u
r
r
en
t
ass
i
g
n
m
e
n
t
i
s
co
m
p
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ted
,
i
f
it
ex
ce
ed
s
t
h
e
t
i
m
e
co
n
s
tr
ain
t,
th
e
h
e
u
r
is
tic
b
ac
k
tr
ac
k
s
t
h
e
p
r
e
v
io
u
s
s
tep
,
r
e
m
o
v
e
s
th
e
least e
x
p
en
s
iv
e
r
eso
u
r
ce
f
r
o
m
i
ts
li
s
t a
n
d
r
ea
s
s
ig
n
s
t
h
e
ta
s
k
s
w
it
h
u
p
d
ated
r
eso
u
r
ce
lis
t.
I
n
d
ea
d
lin
e
d
is
tr
ib
u
tio
n
h
eu
r
i
s
tic
,
th
e
w
o
r
k
f
lo
w
is
p
ar
titi
o
n
e
d
an
d
d
is
tr
ib
u
tes
t
h
e
o
v
er
all
d
ea
d
lin
e
to
ea
ch
task
b
ased
o
n
th
eir
w
o
r
k
lo
ad
an
d
d
ep
en
d
en
cies.
W
o
r
k
f
lo
w
tas
k
s
ar
e
clu
s
ter
ed
in
to
p
ar
titi
o
n
s
an
d
d
ea
d
lin
e
is
d
is
tr
ib
u
te
d
o
v
er
ea
ch
p
ar
titi
o
n
,
th
e
n
ea
ch
p
ar
titi
o
n
i
s
as
s
i
g
n
ed
w
it
h
a
d
ea
d
li
n
e.
Fo
r
ea
ch
ta
s
k
i
n
t
h
e
p
ar
titi
o
n
,
a
s
u
b
-
d
ea
d
li
n
e
ca
n
a
ls
o
b
e
ass
ig
n
ed
.
3
.
2
.
2
.
B
ud
g
et
Co
ns
t
ra
ined Sched
ul
ing
B
u
d
g
et
co
n
s
tr
ain
ed
s
c
h
ed
u
li
n
g
ai
m
s
to
m
in
i
m
ize
w
o
r
k
flo
w
e
x
ec
u
tio
n
ti
m
e
w
h
ile
m
ee
t
in
g
u
s
er
s
‘
s
p
ec
i
fi
ed
b
u
d
g
ets.
T
s
iak
k
o
u
r
i
et
al
.
[
3
3
]
p
r
o
p
o
s
ed
b
u
d
g
et
co
n
s
tr
ain
ed
s
c
h
ed
u
lin
g
ca
lled
L
OS
S
an
d
G
A
I
N.
T
h
is
s
ch
ed
u
li
n
g
ad
j
u
s
ts
a
s
c
h
ed
u
le
g
e
n
er
ated
b
y
a
ti
m
e
o
p
ti
m
ized
h
eu
r
i
s
tic
a
n
d
a
co
s
t
o
p
ti
m
ized
h
eu
r
i
s
tic
to
m
ee
t
u
s
er
s
‘
b
u
d
g
e
t
co
n
s
tr
ai
n
t
s
.
A
t
i
m
e
o
p
ti
m
ized
h
e
u
r
is
tic
atte
m
p
ts
to
m
i
n
i
m
ize
ex
ec
u
tio
n
ti
m
e
w
h
ile
a
co
s
t
o
p
tim
izatio
n
atte
m
p
ts
to
m
i
n
i
m
ize
ex
ec
u
tio
n
co
s
t.
I
f
T
o
tal
ex
ec
u
tio
n
co
s
t
g
e
n
er
ated
b
y
ti
m
e
o
p
ti
m
ized
s
ch
ed
u
le
is
g
r
e
ater
t
h
an
th
e
b
u
d
g
e
t;
th
e
L
OS
S
ap
p
r
o
ac
h
is
ap
p
lied
.
I
f
th
e
T
o
ta
l
ex
ec
u
tio
n
co
s
t
g
en
er
ated
b
y
a
co
s
t
o
p
tim
ized
s
ch
ed
u
le
is
le
s
s
th
a
n
th
e
b
u
d
g
et,
th
e
G
A
I
N
ap
p
r
o
ac
h
is
ap
p
lied
in
o
r
d
er
to
u
s
e
th
e
s
u
r
p
lu
s
f
o
r
d
ec
r
ea
s
in
g
t
h
ee
x
ec
u
t
io
n
ti
m
e
.
4.
SURVE
Y
T
h
is
s
ec
tio
n
d
escr
ib
es a
s
et
o
f
e
x
is
t
in
g
al
g
o
r
ith
m
s
a
n
d
d
ep
icts
a
co
m
p
lete
class
if
ica
tio
n
w
it
h
a
f
o
cu
s
o
n
I
aa
S c
lo
u
d
s
.
R
es
u
lt
s
ar
e
s
u
m
m
ar
ized
in
T
ab
le
4
.
4
.
1
.
M
ultilev
el
Dea
dli
ne
-
co
ns
t
ra
i
ned Scient
if
ic
W
o
r
k
f
lo
w
s
Ma
la
w
s
k
i
et
al
.
[
3
4
]
p
r
o
p
o
s
ed
a
co
s
t
-
o
p
ti
m
izatio
n
m
o
d
el
f
o
r
s
ch
ed
u
lin
g
s
cie
n
t
if
ic
w
o
r
k
f
lo
w
s
in
I
aa
S
clo
u
d
s
,
u
s
i
n
g
m
ath
e
m
at
ical
p
r
o
g
r
a
m
m
in
g
lan
g
u
ag
e
s
(
A
MP
L
a
n
d
C
MP
L
)
w
h
ic
h
o
p
ti
m
iz
es
t
h
e
co
s
t
u
n
d
er
a
d
ea
d
lin
e
co
n
s
tr
ain
t
i
n
m
u
lt
i
-
clo
u
d
en
v
ir
o
n
m
e
n
t,
w
h
er
e
ea
ch
p
r
o
v
id
er
o
f
f
er
s
a
li
m
ited
n
u
m
b
er
o
f
h
eter
o
g
e
n
eo
u
s
VM
s
,
an
d
clo
u
d
o
b
j
ec
ts
to
r
esu
ch
as
Am
az
o
n
S
3
to
s
h
ar
e
in
ter
m
ed
iate
d
ata
f
iles
.
T
h
eir
m
e
th
o
d
p
r
o
p
o
s
es
d
if
f
er
e
n
t
m
o
d
els
s
u
ch
as
ap
p
licatio
n
m
o
d
el,
in
f
r
astru
ct
u
r
e
m
o
d
el,
an
d
th
e
s
c
h
ed
u
li
n
g
m
o
d
el
as
m
i
x
ed
in
te
g
er
p
r
o
g
r
a
m
m
i
n
g
(
MI
P
)
.
T
w
o
d
if
f
er
en
t
s
c
h
ed
u
li
n
g
m
o
d
els
ar
e
p
r
o
p
o
s
ed
,
o
n
e
f
o
r
C
o
a
r
s
e
-
g
r
ai
n
ed
task
s
in
w
h
ic
h
ta
s
k
s
h
a
v
e
a
v
er
ag
e
r
u
n
ti
m
e
in
t
h
e
o
r
d
er
o
f
o
n
e
h
o
u
r
,
an
d
o
th
er
f
in
e
-
g
r
ain
ed
tas
k
s
w
it
h
d
ea
d
lin
es
s
h
o
r
ter
th
an
o
n
e
h
o
u
r
.
T
h
is
m
o
d
el
tak
es
t
h
e
ad
v
a
n
tag
e
o
f
s
o
m
e
o
f
t
h
e
ch
ar
ac
te
r
is
tics
o
f
s
cie
n
ti
f
ic
w
o
r
k
f
lo
w
s
s
u
c
h
as
s
eq
u
e
n
tial
lev
els
o
f
i
n
d
ep
en
d
en
t
tas
k
s
.
I
n
ea
ch
le
v
el,
a
s
et
o
f
tas
k
s
a
r
e
p
ar
titi
o
n
ed
in
to
s
ev
er
al
g
r
o
u
p
s
b
ased
o
n
t
h
eir
co
m
p
u
tatio
n
al
co
s
t
a
n
d
in
p
u
t/
o
u
tp
u
t
d
ata
s
ize
w
it
h
a
co
n
s
tr
ain
t
o
f
in
s
ta
n
ce
s
t
h
at
ca
n
n
o
t
b
e
s
h
ar
ed
in
m
u
ltip
le
lev
els,
m
a
y
lead
to
lo
w
r
eso
u
r
ce
u
tili
za
tio
n
a
n
d
h
i
g
h
r
eso
u
r
ce
co
s
t.
Po
ten
tial
i
m
p
r
o
v
e
m
en
t c
o
u
ld
b
e
to
s
tu
d
y
th
e
p
o
s
s
ib
ilit
y
o
f
s
c
h
ed
u
li
n
g
f
o
r
ea
ch
lev
el
t
h
at
ca
n
b
e
co
m
p
u
ted
in
p
ar
allel.
4
.
2
.
Securit
y
-
Aw
a
re
a
nd
B
ud
g
et
-
Aw
a
re
(
SAB
A)
S
A
B
A
al
g
o
r
ith
m
[
3
5
]
f
o
cu
s
e
s
o
n
m
in
i
m
iz
in
g
t
h
e
m
a
k
esp
an
o
f
a
s
cie
n
ti
f
ic
w
o
r
k
f
lo
w
w
it
h
u
s
er
‘
s
s
ec
u
r
it
y
co
n
s
tr
ai
n
t
u
n
d
er
b
u
d
g
et
co
n
s
tr
ai
n
t
s
as
w
ell
as
s
ec
u
r
it
y
i
n
m
u
lt
i
-
clo
u
d
en
v
ir
o
n
m
en
t.
T
h
e
y
p
r
o
p
o
s
ed
t
w
o
t
y
p
es
o
f
d
ata
s
ets,
i
m
m
o
v
ab
le
an
d
m
o
v
ab
le
d
atasets
.
Mo
v
ab
le
d
ata
s
ets
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o
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o
t
h
av
e
a
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y
s
ec
u
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it
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s
tr
ain
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h
e
n
ce
ca
n
b
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m
i
g
r
ated
o
r
r
ep
licated
f
r
o
m
o
n
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ata
ce
n
ter
to
an
o
t
h
er
d
ata
ce
n
ter
.
I
m
m
o
v
ab
le
Evaluation Warning : The document was created with Spire.PDF for Python.
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d
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d
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d
ca
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f
s
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a
n
d
co
s
t
co
n
s
tr
ai
n
t
s
.
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h
e
S
A
B
A
a
lg
o
r
it
h
m
co
n
s
is
t
s
o
f
3
p
h
ase
s
.
I
n
t
h
e
f
ir
s
t
p
h
ase,
clu
s
ter
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g
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d
p
r
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r
itizatio
n
p
h
ase
i
n
w
h
ic
h
d
ata
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d
task
s
ar
e
ass
i
g
n
ed
to
a
d
ata
c
en
ter
u
s
in
g
p
r
io
r
it
y
r
an
k
.
I
n
t
h
e
s
ec
o
n
d
p
h
a
s
e,
task
s
ar
e
ass
i
g
n
ed
to
VM
s
o
n
th
e
b
asis
o
f
p
er
f
o
r
m
an
ce
-
co
s
t
r
atio
.
I
n
t
h
e
f
i
n
a
l
p
h
ase,
in
ter
m
ed
iate
d
ata
ar
e
m
o
v
ed
d
y
n
a
m
ica
ll
y
at
r
u
n
ti
m
e
to
th
e
lo
ca
tio
n
o
f
th
e
task
s
th
at
ar
e
r
ea
d
y
f
o
r
ex
ec
u
t
io
n
.
T
o
esti
m
ate
r
u
n
t
i
m
es
in
s
tead
o
f
j
u
s
t
co
n
s
id
er
i
n
g
th
e
ca
p
ac
it
y
o
f
C
P
U,
SA
B
A
also
co
n
s
id
er
s
I
/O
,
n
et
w
o
r
k
b
an
d
w
id
th
,
m
e
m
o
r
y
,
an
d
s
to
r
ag
e.
I
t
also
co
n
s
id
er
s
t
h
e
d
ata
tr
an
s
f
er
co
s
t
f
r
o
m
o
n
e
d
atac
e
n
ter
to
an
o
th
er
as
w
ell
a
s
s
to
r
ag
e
u
s
e
d
f
o
r
in
p
u
t
an
d
o
u
tp
u
t.
S
A
B
A
d
id
n
o
t
co
n
s
id
er
t
h
e
b
illi
n
g
m
o
d
el
s
i
m
p
o
s
ed
b
y
d
if
f
er
e
n
t c
lo
u
d
p
r
o
v
id
er
s
w
h
ic
h
r
es
u
lt
i
n
h
i
g
h
er
VM
co
s
t t
h
a
n
e
x
p
ec
ted
.
A
u
th
o
r
s
u
s
ed
t
h
e
Op
ti
m
u
m
m
o
n
etar
y
C
o
s
t
(
OC
)
to
ex
a
m
i
n
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
d
if
f
er
en
t a
lg
o
r
i
th
m
s
u
n
d
er
v
ar
io
u
s
b
u
d
g
e
t c
o
n
s
tr
ai
n
ts
.
OC
is
g
i
v
en
b
y
∑
(
(
et
ti
is
th
e
e
x
ec
u
t
io
n
ti
m
e
o
f
a
ta
s
k
t
i,
co
un
t
(
t
i
)
is
th
e
n
u
m
b
er
o
f
r
eq
u
ir
ed
ty
p
e
o
f
p
h
y
s
ica
l h
o
s
t
h
f
o
r
tas
k
t
i
an
d
p
h
i
s
t
h
e
m
o
n
etar
y
co
s
t p
er
s
ec
o
n
d
o
f
h
o
s
t
h
4
.
3
.
P
a
rt
icle
Sw
a
rm
O
pti
m
i
za
t
io
n
–
b
a
s
ed
R
e
s
o
urce
P
ro
v
is
io
ni
ng
a
nd
Schedu
lin
g
A
lg
o
rit
h
m
R
o
d
r
ig
u
ez
a
n
d
B
u
y
y
a
[
3
6
]
p
r
o
p
o
s
ed
s
tatic
r
eso
u
r
ce
p
r
o
v
is
io
n
i
n
g
a
n
d
s
ch
ed
u
li
n
g
s
tr
ate
g
y
w
h
ic
h
m
i
n
i
m
izes
th
e
co
s
t
u
n
d
er
a
d
ea
d
lin
e
co
n
s
tr
ain
t
w
it
h
m
eta
-
h
eu
r
i
s
tic
a
s
an
o
p
ti
m
izat
io
n
s
tr
ate
g
y
.
T
h
is
alg
o
r
ith
m
also
co
n
s
id
er
s
th
e
b
asic
f
ea
tu
r
es
o
f
clo
u
d
co
m
p
u
ti
n
g
s
u
c
h
as
t
h
e
p
a
y
-
as
-
y
o
u
-
g
o
m
o
d
el,
e
last
ici
t
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,
d
y
n
a
m
icit
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a
n
d
h
eter
o
g
e
n
eit
y
o
f
th
e
u
n
li
m
ited
co
m
p
u
ti
n
g
r
eso
u
r
ce
s
,
as
w
ell
as
p
er
f
o
r
m
a
n
ce
v
ar
iat
io
n
s
a
n
d
th
e
b
o
o
t
ti
m
e
o
f
VM
s
.
B
o
th
r
e
s
o
u
r
ce
p
r
o
v
is
io
n
in
g
a
n
d
s
ch
ed
u
li
n
g
ar
e
m
er
g
ed
as
P
SO
p
r
o
b
le
m
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
h
as a
n
o
v
er
al
l c
o
m
p
lex
it
y
o
f
o
r
d
er
O
(
N
*
T
2
*
R
)
p
er
iter
atio
n
,
w
h
er
e
N
i
s
a
n
u
m
b
er
o
f
p
ar
ticles,
T
is
a
n
u
m
b
er
o
f
ta
s
k
s
an
d
R
i
s
a
n
u
m
b
er
o
f
r
eso
u
r
ce
s
b
ei
n
g
u
s
ed
.
B
o
th
r
eso
u
r
ce
p
r
o
v
is
io
n
in
g
a
n
d
s
c
h
ed
u
li
n
g
ar
e
co
m
b
in
ed
as
P
SOP
,
th
e
o
u
tp
u
t
is
a
n
ea
r
o
p
ti
m
al
s
c
h
e
d
u
le
w
h
ic
h
d
eter
m
i
n
es
th
e
n
u
m
b
er
an
d
t
y
p
es
o
f
VM
s
,
as
w
ell
as
t
h
eir
leasi
n
g
p
er
io
d
s
an
d
task
to
r
eso
u
r
ce
m
ap
p
in
g
.
T
h
e
ad
v
an
tag
e
o
f
th
e
al
g
o
r
ith
m
is
g
en
er
ati
n
g
th
e
h
ig
h
-
q
u
alit
y
s
ch
ed
u
le
s
w
it
h
g
lo
b
al
o
p
ti
m
izat
io
n
tech
n
iq
u
e.
T
h
e
y
also
in
tr
o
d
u
ce
d
a
p
er
f
o
r
m
a
n
ce
d
eg
r
ad
atio
n
p
er
c
en
tag
e
t
h
at
w
o
u
ld
b
e
ex
p
er
ien
ce
d
b
y
VM
s
w
h
e
n
ca
lcu
latin
g
th
e
r
u
n
ti
m
es.
4
.
4
.
M
ulti
-
o
bje
ct
iv
e
H
et
er
o
g
eneo
us
ea
rliest
F
ini
s
h T
i
m
e
Du
r
illo
an
d
P
r
o
d
an
d
ev
elo
p
ed
th
e
MO
HE
F
T
al
g
o
r
ith
m
[
3
7
]
as
an
ex
ten
s
io
n
o
f
t
h
e
clas
s
ical
D
A
G
s
ch
ed
u
lin
g
HE
FT
alg
o
r
ith
m
[
3
8
]
f
o
r
m
o
n
o
-
o
b
j
ec
tiv
e
s
c
h
e
d
u
lin
g
.
A
P
ar
eto
-
b
ased
li
s
t
s
ch
ed
u
li
n
g
h
e
u
r
is
tic
co
m
p
u
tes
a
s
et
o
f
tr
ad
eo
f
f
o
p
tim
a
l
s
o
l
u
tio
n
s
f
r
o
m
w
h
ic
h
t
h
e
u
s
er
ca
n
s
elec
t
t
h
e
o
n
e
w
h
ic
h
s
u
it
s
t
h
eir
r
eq
u
ir
e
m
en
ts
b
etter
.
MO
HE
F
T
b
u
ild
s
s
ev
er
al
in
ter
m
ed
iate
w
o
r
k
fl
o
w
s
o
lu
tio
n
s
i
n
p
ar
allel
in
ea
ch
s
tep
in
s
tead
o
f
a
s
i
n
g
le
o
n
e
as
d
o
n
e
b
y
HE
FT
.
MO
HE
FT
u
s
es
d
o
m
i
n
an
ce
r
elatio
n
s
h
ip
s
to
en
s
u
r
e
th
e
q
u
alit
y
o
f
th
e
tr
ad
eo
f
f
s
o
l
u
tio
n
s
an
d
a
m
e
tr
ic
ca
lled
cr
o
w
d
i
n
g
d
is
t
a
n
c
e
o
f
p
o
ly
n
o
m
ialco
m
p
le
x
it
y
to
g
u
ar
an
tee
th
eir
d
iv
er
s
it
y
.
T
h
e
alg
o
r
ith
m
is
g
en
er
ic
in
n
u
m
b
er
an
d
t
y
p
e
o
f
o
b
j
ec
tiv
es
f
o
r
o
p
ti
m
izi
n
g
t
h
e
m
ak
e
s
p
an
an
d
co
s
t
w
h
e
n
r
u
n
n
in
g
ap
p
licatio
n
s
in
an
Am
az
o
n
-
b
ased
co
m
m
er
ci
al
C
lo
u
d
.
A
P
ar
eto
f
r
o
n
t
i
s
a
n
e
f
f
icien
t
to
o
l
f
o
r
d
ec
is
io
n
s
u
p
p
o
r
t
w
h
ic
h
al
lo
w
s
t
h
e
u
s
er
to
s
elec
t
t
h
e
b
e
s
t
tr
ad
eo
f
f
s
o
lu
tio
n
s
o
n
th
eir
r
eq
u
ir
e
m
en
ts
.
T
h
eir
ex
p
er
i
m
e
n
ts
p
r
o
v
ed
th
at
p
r
ice
ca
n
b
e
r
ed
u
ce
d
b
y
h
a
lf
w
it
h
m
ar
g
i
n
al
5
%
in
cr
ea
s
e
o
f
m
ak
e
s
p
an
.
T
h
e
ap
p
r
o
x
im
a
te
ti
m
e
co
m
p
le
x
it
y
o
f
MO
HFET
is
O(
n
*
m
)
,
w
h
er
e
n
a
n
d
m
ar
e
t
h
e
n
u
m
b
er
o
f
t
ask
s
an
d
r
eso
u
r
ce
s
r
esp
ec
tiv
el
y
.
4
.
5
.
F
a
ult
-
t
o
lera
nt
S
cheduli
ng
us
ing
Sp
o
t
I
ns
t
a
nces
P
o
o
la
et
al
[
3
9
]
p
r
o
p
o
s
ed
an
alg
o
r
ith
m
w
i
th
an
o
b
j
ec
tiv
e
to
m
i
n
i
m
ize
th
e
ex
ec
u
tio
n
co
s
t
w
h
ile
m
ee
ti
n
g
d
ea
d
li
n
e
co
n
s
tr
ai
n
t
t
h
at
s
c
h
ed
u
le
s
tas
k
s
o
n
t
w
o
d
if
f
er
e
n
t
clo
u
d
p
r
icin
g
r
eso
u
r
ce
s
,
s
p
o
t
an
d
o
n
-
d
em
a
n
d
in
s
ta
n
ce
s
w
it
h
j
u
s
t
-
in
-
ti
m
e
an
d
ad
ap
tiv
e
s
c
h
ed
u
li
n
g
h
eu
r
i
s
tic.
Au
th
o
r
s
d
ef
in
e
th
e
n
e
w
ter
m
L
T
O
(
L
atest
T
i
m
e
to
O
n
-
De
m
an
d
)
w
h
ic
h
d
eter
m
i
n
es
wh
en
t
h
e
al
g
o
r
ith
m
s
h
o
u
ld
s
w
itch
to
o
n
-
d
em
a
n
d
i
n
s
ta
n
ce
s
to
s
atis
f
y
t
h
ed
ea
d
lin
ec
o
n
s
tr
ain
t.
A
t
t
i
m
e
t,
L
T
O
is
th
e
d
i
f
f
er
e
n
ce
b
et
w
e
en
th
e
d
ea
d
li
n
e
an
d
cr
itical
p
ath
,
L
T
O
t
=
D
-
CP
t
.
As
t
h
e
r
u
n
t
i
m
e
an
d
cr
itical
p
ath
v
ar
y
d
ep
en
d
i
n
g
o
n
t
h
e
i
n
s
tan
ce
t
y
p
e,
au
t
h
o
r
s
p
r
o
p
o
s
ed
t
w
o
al
g
o
r
ith
m
s
n
a
m
el
y
C
o
n
s
er
v
ati
v
e
a
n
d
Ag
g
r
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i
v
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C
o
n
s
er
v
ati
v
e
al
g
o
r
ith
m
e
s
ti
m
ates
C
P
a
n
d
L
T
O
o
n
t
h
e
lo
w
e
s
t
co
s
t
o
f
t
h
e
in
s
tan
ce
w
h
er
e
as
Ag
g
r
ess
iv
e
alg
o
r
it
h
m
esti
m
ate
s
h
i
g
h
e
s
t
c
o
s
t
o
f
t
h
e
in
s
ta
n
ce
.
An
i
n
tel
lig
e
n
t
b
id
d
in
g
s
tr
ate
g
y
f
o
r
s
p
o
t
VM
s
i
s
p
r
o
p
o
s
ed
.
T
h
e
b
id
s
tar
ts
w
i
th
t
h
e
i
n
itial
s
p
o
t
p
r
ice
a
n
d
in
cr
ea
s
es
g
r
ad
u
all
y
w
it
h
th
e
p
r
o
g
r
ess
o
f
w
o
r
k
f
lo
w
e
x
ec
u
tio
n
an
d
e
n
d
s
clo
s
er
to
o
n
-
d
e
m
a
n
d
p
r
ice
as e
x
ec
u
tio
n
n
ea
r
s
th
e
L
T
O.
T
h
is
lo
w
er
s
t
h
e
r
is
k
o
f
o
u
t
-
of
-
b
id
ev
e
n
ts
a
s
th
e
ex
ec
u
tio
n
n
ea
r
s
th
e
L
T
O,
m
a
k
i
n
g
s
u
r
e
th
a
t
p
r
o
b
a
b
ilit
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o
f
m
ee
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n
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d
ea
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lin
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n
s
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ai
n
t.
T
h
is
a
lg
o
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it
h
m
ad
d
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ess
es
p
r
o
b
lem
o
f
m
ee
ti
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g
d
ea
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li
n
es
w
i
t
h
d
y
n
a
m
icall
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p
r
iced
u
n
r
eliab
le
VM
s
u
n
d
er
v
ar
iab
le
p
er
f
o
r
m
an
ce
.
Ho
w
ev
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,
t
h
e
d
r
a
w
b
ac
k
o
f
th
e
a
lg
o
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it
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m
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m
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co
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id
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ab
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i
n
cr
ea
s
e
th
e
in
f
r
a
s
tr
u
ct
u
r
e
co
s
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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kflo
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ch
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Tech
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iq
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es a
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A
lg
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ith
ms in
I
a
a
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C
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:
A
S
u
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ve
y
(
K
.
K
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a
kra
va
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)
861
4
.
6
.
I
a
a
S
Clo
ud
P
a
rt
ia
l C
rit
ica
l P
a
t
h
Saeid
et
al
[
4
0
]
p
r
o
p
o
s
ed
an
alg
o
r
ith
m
,
I
aa
S C
lo
u
d
P
ar
tial Critica
l P
ath
s
(
I
C
-
P
C
P
)
h
as a
n
o
b
j
ec
tiv
e
to
m
i
n
i
m
ize
t
h
e
ex
ec
u
tio
n
co
s
t
w
h
ile
s
atis
f
y
i
n
g
t
h
e
u
s
er
-
d
ef
i
n
ed
d
ea
d
lin
e
co
n
s
tr
ain
t.
T
h
e
alg
o
r
ith
m
f
ir
s
t
b
e
g
in
s
b
y
f
i
n
d
i
n
g
th
e
p
ar
tial
cr
it
ical
p
ath
(
P
C
P
)
ass
o
ciate
d
w
ith
ea
ch
ex
it
n
o
d
e
in
t
h
e
w
o
r
k
f
lo
w
.
T
h
e
task
s
o
n
ea
c
h
p
ath
ar
e
th
e
n
s
c
h
ed
u
led
o
n
t
h
e
ch
ea
p
es
t
s
er
v
ice
w
h
ich
ca
n
m
ee
t
th
e
latest
f
i
n
i
s
h
t
i
m
e
r
eq
u
ir
e
m
en
t
o
f
t
h
e
task
s
.
T
h
is
p
r
o
ce
d
u
r
e
co
n
tin
u
e
s
r
ec
u
r
s
i
v
el
y
u
n
til a
ll o
f
th
e
wo
r
k
f
lo
w
tas
k
s
ar
e
s
c
h
ed
u
led
.
A
lo
n
g
w
i
th
I
C
-
P
C
P
,
au
th
o
r
s
p
r
o
p
o
s
ed
th
e
I
C
-
P
C
P
D2
(
I
C
-
P
C
P
w
i
th
d
ea
d
lin
e
d
is
tr
ib
u
tio
n
)
.
T
h
e
d
if
f
er
e
n
ce
b
et
w
ee
n
t
h
e
t
w
o
alg
o
r
ith
m
s
is
I
C
-
P
C
P
s
c
h
ed
u
l
es
th
e
tas
k
s
o
f
th
e
p
ar
tial
cr
iti
ca
l
p
ath
o
n
t
h
e
s
a
m
e
VM
o
r
co
m
p
u
tatio
n
s
er
v
ice
(
ex
is
ti
n
g
o
r
a
n
e
w
)
w
h
ich
c
an
ex
ec
u
te
b
e
f
o
r
e
its
lates
t
f
i
n
is
h
ti
m
e.
W
h
er
ea
s
I
C
-
P
C
P
D2
s
ch
ed
u
le
ea
c
h
in
d
iv
id
u
al
tas
k
o
n
th
e
ch
ea
p
e
s
t
VM
th
at
ca
n
f
in
i
s
h
it
o
n
tim
e.
A
cc
o
r
d
in
g
to
ex
p
er
i
m
e
n
t
al
r
esu
lts
,
I
C
-
P
C
P
o
u
tp
er
f
o
r
m
s
I
C
-
P
C
P
D2
.
On
e
o
f
th
e
ad
v
an
ta
g
e
s
o
f
I
C
-
P
C
P
is
s
i
n
ce
all
t
h
e
ta
s
k
s
ar
e
s
c
h
e
d
u
led
o
n
th
e
s
a
m
e
in
s
ta
n
ce
d
ata
tr
a
n
s
f
er
ti
m
es
b
et
w
ee
n
t
h
e
ta
s
k
s
ar
e
ze
r
o
;
d
ata
tr
an
s
f
er
ti
m
es
w
ill
h
a
v
e
a
h
ig
h
i
m
p
ac
t
o
n
t
h
e
m
ak
e
s
p
an
a
n
d
ex
ec
u
tio
n
co
s
t
o
f
a
w
o
r
k
f
lo
w
.
A
d
is
ad
v
an
ta
g
e
o
f
th
is
al
g
o
r
ith
m
is
,
it
d
o
es
n
o
t
co
n
s
id
er
th
e
VM
s
tar
tu
p
ti
m
es a
n
d
r
eso
u
r
ce
p
er
f
o
r
m
a
n
ce
v
ar
iatio
n
.
4
.
7
.
E
nh
a
nce
d IC
-
P
CP
w
it
h R
eplica
t
io
n
C
alh
e
ir
o
s
an
d
B
u
y
y
a
[
4
1
]
p
r
o
p
o
s
e
th
e
E
I
P
R
alg
o
r
ith
m
w
h
i
ch
is
e
n
h
a
n
ce
d
I
C
-
P
C
P
w
it
h
r
ep
licatio
n
,
p
r
o
v
id
es
a
s
o
lu
tio
n
f
o
r
s
ch
ed
u
lin
g
an
d
p
r
o
v
is
io
n
i
n
g
u
s
i
n
g
id
le
ti
m
e
o
f
p
r
o
v
is
io
n
ed
VM
s
a
n
d
a
b
u
d
g
et
s
u
r
p
lu
s
to
r
ep
licate
th
e
tas
k
s
to
m
iti
g
ate
e
f
f
ec
ts
o
f
p
er
f
o
r
m
an
ce
v
ar
iatio
n
s
o
f
r
eso
u
r
ce
s
to
m
e
et
th
e
d
ea
d
lin
es
o
f
w
o
r
k
f
lo
w
ap
p
licatio
n
s
.
T
h
e
f
i
r
s
t
s
tep
o
f
E
I
P
R
al
g
o
r
ith
m
s
o
lv
es
t
w
o
s
u
b
-
p
r
o
b
lem
s
n
a
m
e
l
y
p
r
o
v
is
io
n
i
n
g
an
d
s
ch
ed
u
lin
g
.
T
h
e
p
r
o
v
is
io
n
i
n
g
p
r
o
b
lem
d
eter
m
in
e
s
n
u
m
b
er
a
n
d
t
y
p
e
o
f
VM
s
to
u
s
e
an
d
s
ch
ed
u
li
n
g
p
r
o
b
le
m
d
eter
m
in
e
s
t
h
e
o
r
d
er
an
d
p
l
ac
e
m
en
t
o
f
tas
k
s
o
n
th
e
s
el
ec
ted
r
eso
u
r
ce
s
d
eter
m
in
ed
d
u
r
in
g
p
r
o
v
is
io
n
i
n
g
p
r
o
b
lem
.
T
h
is
is
ac
h
ie
v
ed
u
s
i
n
g
t
h
e
h
eu
r
i
s
tic
o
f
I
C
-
P
C
P
,
th
at
is
id
en
ti
f
y
i
n
g
a
n
d
ass
i
g
n
i
n
g
o
f
all
th
e
ta
s
k
s
o
f
a
p
ar
tial
cr
itical
p
ath
(
P
C
P
)
o
f
th
e
w
o
r
k
f
lo
w
to
t
h
e
s
a
m
e
v
ir
tu
a
l
m
ac
h
in
e.
T
h
e
s
ec
o
n
d
s
tep
o
f
t
h
e
E
I
P
R
alg
o
r
ith
m
d
eter
m
in
e
s
th
e
s
tar
t
an
d
s
to
p
ti
m
e
s
o
f
VM
s
a
n
d
in
p
u
t
a
n
d
o
u
tp
u
t
d
ata
tr
a
n
s
f
er
t
i
m
es.
Fin
a
ll
y
,
ta
s
k
s
ar
e
r
ep
licated
in
id
le
tim
e
s
lo
t
s
o
f
p
r
o
v
is
io
n
ed
VM
s
o
r
o
n
n
ew
VM
s
if
t
h
e
r
ep
licatio
n
b
u
d
g
et
s
lo
w
s
f
o
r
it.
T
h
e
alg
o
r
ith
m
p
r
io
r
itizes
th
e
r
ep
licatio
n
o
f
tas
k
s
w
it
h
a
r
atio
b
etw
ee
n
e
x
ec
u
tio
n
to
av
ai
lab
le
ti
m
e,
t
h
en
tas
k
s
w
it
h
lo
n
g
e
x
ec
u
tio
n
ti
m
e
f
o
llo
w
ed
b
y
th
e
n
u
m
b
er
o
f
c
h
ild
r
en
.
E
I
P
R
m
iti
g
ate
s
t
h
e
e
f
f
ec
t
o
f
th
e
p
o
o
r
p
er
f
o
r
m
an
c
e
o
f
clo
u
d
r
eso
u
r
ce
s
b
y
e
x
p
lo
iti
n
g
t
h
e
elas
ticit
y
an
d
b
illi
n
g
s
c
h
e
m
e
o
f
clo
u
d
s
.
4
.
8
.
Wo
rk
f
lo
w
Schedu
l
ing
Co
ns
i
dering
2
SL
A
L
ev
el
s
Gen
ez
et
al
[
4
2
]
p
r
o
p
o
s
e
d
a
S
aa
S
p
r
o
v
id
er
o
f
f
er
in
g
a
w
o
r
k
f
l
o
w
ex
ec
u
tio
n
s
er
v
ice
to
its
cu
s
to
m
er
s
b
y
co
n
s
id
er
in
g
t
w
o
t
y
p
es
o
f
S
L
A
co
n
tr
ac
ts
t
h
at
ca
n
b
e
u
s
ed
to
lease
VM
s
f
r
o
m
I
aa
S
p
r
o
v
id
er
s
:
o
n
-
d
e
m
a
n
d
o
r
r
eser
v
ed
in
s
tan
ce
s
.
I
n
t
h
e
p
r
o
p
o
s
ed
m
o
d
el,
SaaS
h
as
a
p
o
o
l
o
f
r
eser
v
ed
in
s
ta
n
ce
s
u
s
ed
to
ex
ec
u
te
w
o
r
k
f
lo
w
s
s
u
b
m
itted
b
y
a
u
s
er
b
ef
o
r
e
u
s
er
d
ef
in
ed
d
ea
d
lin
e.
O
n
th
e
o
th
er
h
an
d
,
i
f
th
e
i
n
f
r
astr
u
ctu
r
e
is
n
o
t
en
o
u
g
h
to
s
atis
f
y
t
h
e
u
s
er
d
ea
d
li
n
e
t
h
en
o
n
-
d
e
m
a
n
d
r
eso
u
r
ce
s
ar
e
r
eq
u
ir
ed
to
m
ee
t
th
e
u
s
er
d
ef
in
ed
d
ea
d
lin
es.
T
h
e
y
p
r
o
p
o
s
ed
s
ch
e
d
u
li
n
g
p
r
o
b
le
m
as
t
h
e
i
n
teg
er
l
in
ea
r
p
r
o
g
r
a
m
m
i
n
g
(
I
L
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)
w
i
th
th
e
o
b
j
ec
tiv
e
o
f
m
in
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m
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g
t
h
e
m
o
n
etar
y
co
s
t
a
n
d
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v
io
latio
n
s
.
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o
d
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e
a
f
ea
s
ib
le
s
ch
ed
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le
f
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m
th
e
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L
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e
y
p
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p
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ed
t
w
o
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r
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tics
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m
e
l
y
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i
n
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m
i
n
i
m
u
m
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n
d
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m
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x
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m
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m
ti
m
e
s
(
B
ME
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)
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d
b
eg
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m
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m
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m
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T
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E
v
en
th
o
u
g
h
th
e
al
g
o
r
ith
m
is
d
ev
elo
p
ed
in
th
e
c
o
n
tex
t
o
f
Saa
S/P
aa
S
p
r
o
v
id
er
p
o
ten
tiall
y
s
er
v
in
g
m
u
ltip
le
cu
s
to
m
er
s
,
th
e
s
o
l
u
t
io
n
is
d
esi
g
n
ed
to
s
c
h
ed
u
le
a
s
in
g
le
w
o
r
k
f
lo
w
at
a
ti
m
e.
Si
m
u
latio
n
r
esu
l
ts
s
h
o
w
s
t
h
at
th
eir
alg
o
r
it
h
m
i
s
ca
p
ab
le
o
f
s
elec
tin
g
b
est
s
u
ited
I
aa
S
p
r
o
v
id
er
as
w
ell
as
VM
s
r
eq
u
ir
ed
to
g
u
ar
a
n
tee
t
h
e
Qo
S
p
ar
a
m
eter
s
.
On
e
o
f
th
e
co
n
ce
r
n
s
in
t
h
is
m
o
d
e
is
th
e
s
ca
lab
ilit
y
.
T
h
e
n
u
m
b
er
o
f
v
ar
iab
les
an
d
co
n
s
tr
ai
n
ts
i
n
cr
ea
s
es
r
ap
i
d
ly
w
h
e
n
th
e
n
u
m
b
er
o
f
p
r
o
v
id
er
s
an
d
n
u
m
b
er
an
d
t
y
p
e
o
f
VM
s
t
h
at
ca
n
b
e
leased
f
r
o
m
I
aa
S p
r
o
v
id
er
s
an
d
th
e
n
u
m
b
er
o
f
tas
k
s
in
t
h
e
s
u
b
m
itted
w
o
r
k
f
lo
w
.
4
.
9
.
P
a
rt
it
io
ned
B
a
la
nced
T
i
m
e
Schedu
lin
g
B
y
u
n
et
al
.
[
4
3
]
p
r
o
p
o
s
ed
an
al
g
o
r
ith
m
P
B
T
S
(
P
ar
titi
o
n
ed
B
alan
ce
d
T
i
m
e
Sc
h
ed
u
l
in
g
)
,
f
o
r
esti
m
ati
n
g
th
e
n
u
m
b
er
o
f
V
Ms
r
eq
u
ir
ed
to
ex
ec
u
te
th
e
w
o
r
k
f
lo
w
w
i
th
in
a
g
iv
e
n
d
e
ad
lin
e
i
n
a
s
et
o
f
h
o
m
o
g
en
eo
u
s
VM
s
b
y
p
ar
titi
o
n
in
g
t
h
e
ex
ec
u
tio
n
.
A
p
p
licat
io
n
r
u
n
n
i
n
g
ti
m
e
is
d
iv
id
ed
in
to
ti
m
e
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ar
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eq
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e
ch
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it
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aa
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r
eso
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r
ce
p
r
o
v
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y
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te
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Fo
r
ea
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p
ar
titi
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n
,
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B
T
S
f
ir
s
t
id
en
ti
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ie
s
th
e
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et
o
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tas
k
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to
r
u
n
t
h
en
it
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m
ates
t
h
e
to
tal
n
u
m
b
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o
f
V
Ms
r
eq
u
ir
ed
to
r
u
n
th
e
task
s
d
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r
in
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p
ar
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n
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s
i
n
g
b
alan
ce
d
ti
m
e
s
c
h
ed
u
li
n
g
alg
o
r
it
h
m
[
4
4
]
.
Fin
al
l
y
,
tas
k
s
ar
e
ex
ec
u
ted
o
n
t
h
e
allo
ca
ted
ac
t
u
al
VM
s
o
n
th
e
b
asis
o
f
s
c
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u
le
o
b
tai
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f
r
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m
r
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i
n
g
B
T
S.
T
h
e
d
is
ad
v
an
tag
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o
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is
al
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o
r
ith
m
is
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f
o
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f
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n
er
-
g
r
ain
ed
b
ill
in
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p
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io
d
s
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s
u
ch
as
1
m
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te,
m
a
y
n
o
t
b
e
s
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cc
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s
s
f
u
l
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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2
0
8
8
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8708
I
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&
C
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Vo
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8
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No
.
2
,
A
p
r
il 2
0
1
8
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8
5
3
–
8
6
6
862
4
.
1
0
.
Sta
t
ic
P
ro
v
is
io
nin
g
Sta
t
ic
Sc
hedu
li
ng
a
nd
Dy
na
m
ic
P
ro
v
is
io
nin
g
Dy
na
m
ic
Sc
hedu
l
ing
Ma
la
w
s
k
i
et
al
.
[
4
5
]
p
r
o
p
o
s
ed
DP
DS
an
d
W
A
-
DP
DS
d
y
n
a
m
ic
al
g
o
r
it
h
m
s
a
n
d
o
n
e
s
tatic
alg
o
r
it
h
m
,
SP
SS
to
s
ch
ed
u
le
w
o
r
k
f
lo
w
e
n
s
e
m
b
les
w
h
ic
h
m
a
x
i
m
ize
s
th
e
n
u
m
b
er
o
f
ex
ec
u
ted
w
o
r
k
f
lo
w
s
f
r
o
m
e
n
s
e
m
b
le
s
w
h
ile
m
ee
tin
g
b
o
th
b
u
d
g
et
a
n
d
d
ea
d
lin
e
co
n
s
tr
ain
t
s
.
D
y
n
a
m
ic
P
r
o
v
is
io
n
i
n
g
D
y
n
a
m
ic
Sch
ed
u
l
in
g
(
DP
DS)
alg
o
r
ith
m
co
n
s
i
s
ts
o
f
t
w
o
p
h
ases
,
p
r
o
v
is
io
n
i
n
g
an
d
s
c
h
ed
u
li
n
g
.
P
r
o
v
is
io
n
i
n
g
p
h
a
s
e
ca
l
cu
lates
t
h
e
i
n
itia
l
n
u
m
b
er
o
f
VM
s
to
u
s
e
o
n
t
h
e
b
asis
o
f
a
v
ailab
le
b
u
d
g
et
a
n
d
t
i
m
e.
O
n
t
h
e
b
asi
s
o
f
VM
u
tili
za
tio
n
,
VM
p
o
o
l
is
u
p
d
ated
p
er
io
d
icall
y
.
I
f
th
e
u
t
ilizatio
n
f
alls
b
elo
w
th
e
p
r
ed
ef
i
n
ed
th
r
es
h
o
ld
s
,
th
e
n
VM
s
ar
e
s
h
u
td
o
w
n
.
A
n
d
i
f
u
tili
za
t
io
n
is
ab
o
v
e
th
e
t
h
r
es
h
o
ld
an
d
b
u
d
g
et
allo
w
s
f
o
r
it
th
en
n
e
w
VM
s
ar
e
leased
.
I
n
th
e
s
ch
ed
u
li
n
g
p
h
ase,
r
ea
d
y
tas
k
s
f
r
o
m
w
o
r
k
f
lo
w
e
n
s
e
m
b
le
ar
e
ass
i
g
n
ed
to
th
e
p
r
io
r
ity
q
u
e
u
e.
I
f
th
e
p
r
io
r
it
y
q
u
eu
e
is
n
o
t
e
m
p
t
y
a
n
d
id
le
VM
s
ar
e
a
v
ailab
le,
th
e
n
t
h
e
ta
s
k
f
r
o
m
t
h
e
p
r
io
r
it
y
q
u
eu
e
is
s
u
b
m
itted
to
ar
b
itra
r
y
id
l
e
VM
.
T
h
is
s
tep
i
s
r
ep
ea
ted
u
n
til
th
e
p
r
io
r
it
y
q
u
eu
e
is
e
m
p
t
y
o
r
n
o
id
le
VM
s
av
ailab
le.
T
h
e
W
o
r
k
fl
o
w
-
A
w
ar
e
DP
DS
(
W
A
-
DP
DS)
alg
o
r
ith
m
is
v
ar
ia
n
t
o
f
a
DP
DS
w
h
ic
h
i
n
co
r
p
o
r
ates
an
ad
m
i
s
s
io
n
co
n
tr
o
l
p
r
o
ce
d
u
r
e
w
h
ic
h
ac
ce
p
t
s
n
e
w
w
o
r
k
f
lo
w
f
o
r
ex
ec
u
tio
n
o
n
l
y
w
h
en
t
h
er
e
is
en
o
u
g
h
b
u
d
g
et
is
av
ai
lab
le.
Oth
er
w
is
e,
w
o
r
k
f
lo
w
is
r
ej
ec
ted
an
d
tas
k
s
ar
e
r
e
m
o
v
ed
f
r
o
m
t
h
e
q
u
eu
e.
Static
P
r
o
v
is
io
n
i
n
g
S
tatic
Sc
h
ed
u
li
n
g
(
SP
SS
)
a
s
s
i
g
n
s
s
u
b
-
d
ea
d
lin
e
s
to
ea
ch
tas
k
b
ased
o
n
t
h
e
s
lac
k
ti
m
e
o
f
t
h
e
w
o
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k
f
lo
w
(
a
m
o
u
n
t
o
f
e
x
tr
a
ti
m
e
th
a
t
a
w
o
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k
fl
o
w
ca
n
ex
ten
d
it
s
cr
itical
p
ath
an
d
s
till
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e
co
m
p
leted
b
y
th
e
e
n
s
e
m
b
le
d
ea
d
lin
e)
.
I
f
th
er
e
ar
e
n
o
tim
e
s
lo
ts
,
th
en
n
e
w
VM
s
ar
e
leased
to
s
ch
ed
u
le
t
h
e
tas
k
s
.
S
i
m
u
latio
n
r
es
u
lt
s
s
h
o
w
th
at
s
ta
tic
alg
o
r
ith
m
o
u
tp
er
f
o
r
m
s
d
y
n
a
m
ic
al
g
o
r
ith
m
s
.
4
.
1
1
.
SPSS
-
E
D
a
n
d SPSS
-
EB
P
ietr
i
et
al
.
[
4
6
]
p
r
o
p
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s
ed
tw
o
e
n
er
g
y
-
a
w
ar
e
alg
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h
m
s
SP
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SP
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ce
p
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c
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le
w
o
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f
lo
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e
n
s
e
m
b
les
o
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b
asi
s
o
f
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f
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t
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m
ca
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ti
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en
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n
d
d
ea
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co
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s
tr
ai
n
t
s
w
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le
an
o
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s
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SP
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is
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ize
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m
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ted
w
o
r
k
f
lo
w
m
in
i
m
iz
in
g
en
er
g
y
co
n
s
u
m
p
t
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n
.
Fo
r
ea
ch
w
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k
f
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w
in
t
h
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en
s
e
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b
le
,
S
P
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B
p
lan
s
th
e
ex
ec
u
t
io
n
o
f
w
o
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k
f
lo
w
b
y
s
c
h
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u
li
n
g
ea
ch
tas
k
.
I
t
ac
ce
p
ts
th
e
p
la
n
o
n
l
y
o
n
m
ee
tin
g
en
er
g
y
an
d
b
u
d
g
e
t
co
n
s
tr
ain
ts
.
T
h
e
Sa
m
e
p
r
o
ce
s
s
is
u
s
ed
in
SP
SS
-
E
D,
in
s
tead
o
f
b
u
d
g
et,
d
ea
d
lin
e
co
n
s
tr
ai
n
t
is
u
s
ed
.
T
h
is
w
o
r
k
d
o
es
n
o
t
co
n
s
id
er
th
e
d
if
f
e
r
en
t
w
o
r
k
f
lo
w
s
tr
u
ct
u
r
es,
d
ata
tr
an
s
f
er
co
s
ts
,
p
r
o
v
is
io
n
i
n
g
an
d
d
ep
r
o
v
is
io
n
in
g
d
elay
s
.
4
.
1
2
.
Dy
na
Z
h
o
u
et
al
.
[
4
7
]
p
r
o
p
o
s
ed
a
f
r
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[
3
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S
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4
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S
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4
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S
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No
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G
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4
2
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S
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4
3
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S
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No
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Mu
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[
4
5
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En
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mb
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No
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S
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[
4
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En
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No
No
S
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Evaluation Warning : The document was created with Spire.PDF for Python.