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il
it
y
n
o
r
t
h
e
r
e
m
o
te
s
er
v
er
’
s
f
r
eq
u
en
c
y
.
B
esid
es,
t
h
e
y
co
n
s
id
er
task
s
w
it
h
t
h
e
s
a
m
e
d
ea
d
lin
e
T
d
.
I
n
th
is
w
o
r
k
,
w
e
s
t
u
d
y
th
e
g
e
n
er
al
m
u
lt
i
-
task
o
f
f
lo
ad
in
g
s
e
n
ar
io
w
h
er
e
w
e
in
tr
o
d
u
ce
th
e
co
n
tr
o
l
o
f
t
h
e
av
ailab
le
lo
ca
l
en
er
g
y
,
an
d
co
n
s
id
er
th
e
ed
g
e
s
er
v
er
’
s
f
r
eq
u
e
n
c
y
as
a
d
ec
i
s
io
n
p
ar
a
m
eter
in
o
u
r
o
p
ti
m
iz
atio
n
p
r
o
b
le
m
.
Mo
r
eo
v
er
,
w
e
co
n
s
id
er
a
g
e
n
er
al
s
etti
n
g
w
h
er
e
ea
c
h
o
f
f
lo
ad
ab
le
tas
k
h
a
s
to
b
e
e
x
ec
u
ted
w
it
h
in
it
s
s
p
ec
i
f
ic
d
ea
d
lin
e
t
i
m
ax
.
A
c
co
r
d
in
g
to
o
u
r
v
is
io
n
,
w
e
ca
n
p
r
o
lo
n
g
t
h
e
b
at
ter
y
li
f
e
o
f
th
e
m
o
b
ile
d
ev
ice
b
y
co
n
s
id
er
i
n
g
th
e
a
m
o
u
n
t
o
f
its
a
v
ailab
le
p
o
w
er
,
an
d
r
ed
u
ce
th
e
tas
k
s
’
p
r
o
ce
s
s
in
g
ti
m
e
b
y
ad
j
u
s
ti
n
g
t
h
e
e
d
g
e
s
er
v
er
’
s
f
r
eq
u
e
n
c
y
.
Su
b
s
eq
u
en
tl
y
,
w
e
h
a
v
e
f
o
r
m
u
lated
an
o
p
ti
m
izatio
n
p
r
o
b
lem
th
at
m
in
i
m
ize
s
t
h
e
e
n
e
r
g
y
co
n
s
u
m
ed
b
y
j
o
in
tl
y
d
ec
id
in
g
t
h
e
lo
ca
l
a
n
d
ed
g
e
co
m
p
u
ti
n
g
f
r
eq
u
en
cie
s
,
as
w
ell
as
t
h
e
o
f
f
lo
ad
i
n
g
d
ec
is
io
n
s
.
D
u
e
to
it
s
co
m
b
i
n
ato
r
ial
n
atu
r
e
an
d
a
f
ter
it
s
d
ec
o
m
p
o
s
itio
n
,
w
e
p
r
o
p
o
s
e
a
h
eu
r
i
s
tic
s
o
l
u
tio
n
b
ased
o
n
a
s
i
m
u
lated
an
n
ea
li
n
g
al
g
o
r
it
h
m
to
j
o
in
t
ly
d
ec
i
de
th
e
task
s
’
o
f
f
lo
a
d
i
n
g
an
d
t
h
e
allo
ca
tio
n
o
f
co
m
p
u
ti
n
g
r
eso
u
r
c
es
.
T
h
e
o
b
jectiv
e
is
to
m
in
i
m
ize
th
e
co
n
s
u
m
e
d
en
er
g
y
v
ia
t
h
e
o
f
f
lo
ad
in
g
b
y
c
o
n
s
id
er
in
g
th
e
ta
s
k
s’
late
n
c
y
c
o
n
s
tr
ain
ts
a
n
d
a
th
r
es
h
o
ld
o
f
av
ailab
le
en
er
g
y
.
T
h
e
r
em
ai
n
d
er
o
f
th
i
s
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
t
he
s
y
s
te
m
’
s
m
o
d
el
an
d
th
e
o
p
ti
m
izatio
n
p
r
o
b
lem
f
o
r
m
u
latio
n
ar
e
p
r
esen
ted
i
n
Sectio
n
2
.
I
n
Se
ctio
n
3
,
w
e
p
r
e
se
nt
o
u
r
m
e
th
o
d
to
so
lv
e
t
h
e
o
p
tim
izatio
n
p
r
o
b
lem
.
I
n
s
ec
ti
o
n
4
w
e
p
r
ese
n
t
th
e
s
i
m
u
latio
n
r
es
u
lt
s
a
n
d
t
h
eir
d
is
c
u
s
s
io
n
.
Fi
n
all
y
,
Sectio
n
5
co
n
clu
d
es t
h
e
p
ap
er
.
2.
SYST
E
M
M
O
DE
L
AND
P
R
O
B
L
E
M
F
O
R
M
UL
AT
I
O
N
2
.
1
.
Sy
s
t
e
m
m
o
del
Fig
u
r
e
2
.
Sh
o
w
s
a
s
i
n
g
le
s
m
ar
t
m
o
b
ile
d
ev
ice
(
SM
D)
co
n
tai
n
in
g
a
n
o
f
f
lo
ad
ab
le
m
u
lt
i
-
tas
k
li
s
t.
I
n
th
i
s
w
o
r
k
,
w
e
p
lan
to
s
t
u
d
y
t
h
e
b
eh
a
v
io
r
o
f
th
e
o
f
f
lo
ad
in
g
p
r
o
ce
s
s
f
o
r
a
m
u
lti
-
tas
k
SMD
i
n
an
ed
g
e
en
v
ir
o
n
m
e
n
t,
w
h
ile
w
e
o
p
ti
m
i
ze
co
m
p
u
tatio
n
r
eso
u
r
ce
s
a
v
ai
lab
le
at
th
e
ed
g
e
s
er
v
er
as
w
e
ll
as
at
t
h
e
m
o
b
ile
d
ev
ice.
P
ar
ticu
lar
l
y
,
th
e
a
v
aila
b
le
en
er
g
y
at
t
h
e
SM
D
f
o
r
tas
k
s
e
x
ec
u
tio
n
is
li
m
ited
.
B
esid
es,
in
t
h
e
co
n
te
x
t
o
f
o
f
f
lo
ad
in
g
,
s
o
m
e
p
iece
s
o
f
a
co
m
p
u
t
atio
n
al
l
y
i
n
ten
s
i
v
e
ap
p
licatio
n
ar
e
d
iv
id
ed
in
to
m
u
lt
ip
le
m
u
tu
al
l
y
in
d
ep
en
d
en
t
o
f
f
lo
ad
ab
le
tas
k
s
[
2
2
,
2
3
]
.
T
h
er
ef
o
r
e,
ac
co
r
d
in
g
to
th
e
av
ai
lab
le
co
m
p
u
tatio
n
al
a
n
d
r
ad
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r
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r
ce
s
,
s
o
m
e
tas
k
s
ar
e
p
i
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-
u
p
f
r
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m
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r
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u
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n
g
ta
s
k
s
l
is
t
to
b
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o
f
f
lo
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to
th
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g
e
s
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v
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s
f
o
r
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m
p
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ti
n
g
.
T
h
e
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th
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s
ar
e
p
er
f
o
r
m
ed
lo
ca
ll
y
o
n
th
e
SMD
it
s
elf
.
T
h
e
ex
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u
tio
n
o
f
t
h
e
w
h
o
le
lis
t
m
u
s
t
h
ap
p
e
n
w
it
h
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n
th
e
ti
m
e
li
m
it
o
f
t
h
e
ap
p
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.
A
d
d
itio
n
all
y
,
it
is
ass
u
m
ed
th
a
t
th
e
SMD
co
n
cu
r
r
en
tl
y
p
er
f
o
r
m
s
co
m
p
u
tatio
n
an
d
w
ir
eles
s
tr
an
s
m
i
s
s
io
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
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I
n
t J
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lec
&
C
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m
p
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g
,
Vo
l.
9
,
No
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6
,
Dec
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b
er
2
0
1
9
:
4
9
0
8
-
49
1
9
4910
Fig
u
r
e
2
.
S
y
s
te
m
m
o
d
el
illu
s
tr
atio
n
Fo
r
all
th
ese
co
n
s
id
er
atio
n
s
,
w
e
d
er
iv
e
a
m
a
th
e
m
atica
l
e
n
er
g
y
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n
s
u
m
p
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o
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el
th
at
co
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s
id
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s
th
r
ee
m
a
in
d
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i
s
io
n
s
:
t
h
e
o
f
f
l
o
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in
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d
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is
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n
f
o
r
ea
ch
tas
k
,
th
e
lo
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l
e
x
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u
tio
n
f
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e
n
c
y
o
f
t
h
e
SMD,
a
n
d
th
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s
er
v
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e
x
ec
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tio
n
f
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eq
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en
c
y
at
th
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e.
T
h
en
,
w
e
f
o
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m
u
l
ate
an
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g
y
m
i
n
i
m
izatio
n
p
r
o
b
lem
.
P
r
ac
tically
,
t
h
e
SMD
i
s
co
n
n
ec
ted
to
an
E
d
g
e
No
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e
(
E
N)
,
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d
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te
n
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ed
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e
A
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t
(
E
A
P
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itio
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s
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n
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t
h
e
w
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t
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co
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s
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t
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w
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k
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r
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f
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o
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f
f
lo
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s
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e
u
p
li
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r
ate
r
is
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u
m
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m
o
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t
u
n
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.
As
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
,
th
e
co
n
s
id
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s
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ar
t
m
o
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tain
s
N
in
d
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d
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tas
k
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as
τ
≜
{
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2
,
…
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τ
N
}
.
I
n
ad
d
itio
n
,
t
h
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s
e
tas
k
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u
m
ed
to
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co
m
p
u
ta
tio
n
all
y
i
n
ten
s
i
v
e
a
n
d
d
ela
y
s
en
s
iti
v
e
a
n
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h
a
v
e
to
b
e
co
m
p
leted
.
E
ac
h
tas
k
τ
i
ca
n
b
e
p
r
o
ce
s
s
ed
eit
h
er
lo
ca
ll
y
o
r
at
t
h
e
e
d
g
e.
I
t
r
ep
r
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t
s
an
ato
m
ic
i
n
p
u
t
d
ata
tas
k
t
h
at
ca
n
n
o
t
b
e
d
iv
id
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in
to
s
u
b
-
ta
s
k
s
.
Mo
r
eo
v
er
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it
is
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ar
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ter
iz
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y
th
e
f
o
llo
w
i
n
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th
r
ee
p
ar
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m
eter
s
τ
i
≜
〈
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i
,
λ
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m
ax
〉
.
T
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e
f
ir
s
t
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e
d
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d
i
[
b
its
]
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en
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a
m
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n
p
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t
p
ar
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eter
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d
p
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r
a
m
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es
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tr
an
s
f
er
f
r
o
m
th
e
u
s
er
’
s
l
o
ca
l
d
ev
ice
to
th
e
ed
g
e
s
er
v
e
r
.
T
h
e
s
ec
o
n
d
o
n
e
d
en
o
ted
λ
i
[
cy
cle
s
]
s
p
ec
if
ie
s
t
h
e
w
o
r
k
lo
ad
r
ef
er
r
in
g
to
th
e
co
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p
u
tat
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n
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m
o
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n
t
n
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d
e
d
to
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co
m
p
lis
h
th
e
p
r
o
ce
s
s
in
g
o
f
t
h
i
s
tas
k
.
T
h
e
th
ir
d
p
ar
am
eter
t
i
m
ax
r
ef
er
s
to
th
e
r
eq
u
ir
ed
m
a
x
i
m
u
m
late
n
c
y
f
o
r
th
is
ta
s
k
.
T
h
e
ex
ec
u
tio
n
n
at
u
r
e
d
ec
is
io
n
f
o
r
a
tas
k
τ
i
eith
er
lo
ca
ll
y
o
r
b
y
o
f
f
lo
ad
in
g
to
th
e
ed
g
e
s
er
v
er
i
s
d
en
o
ted
x
i
w
h
er
e
x
i
∈
{
0
;
1
}
.
x
i
=
1
in
d
icate
s
t
h
at
th
e
SMD
h
as
to
o
f
f
lo
ad
τ
i
to
th
e
ed
g
e
s
er
v
er
,
an
d
x
i
=
0
in
d
icate
s
t
h
at
τ
i
is
lo
ca
ll
y
p
r
o
ce
s
s
ed
.
Fro
m
t
h
is
p
o
in
t,
a
ll
ti
m
e
ex
p
r
ess
io
n
s
ar
e
g
i
v
en
i
n
S
ec
o
n
d
s
,
an
d
e
n
er
g
y
co
n
s
u
m
p
t
io
n
s
ar
e
g
i
v
e
n
i
n
Jo
u
le
.
T
h
en
,
if
th
e
SMD
lo
ca
l
l
y
ex
ec
u
tes
ta
s
k
τ
i
,
th
e
co
m
p
leti
o
n
ti
m
e
o
f
its
lo
ca
l
ex
ec
u
tio
n
is
t
i
L
=
λ
i
f
L
.
So
,
f
o
r
all
task
s
,
w
e
h
a
v
e
:
t
L
=
∑
(
1
−
x
i
)
λ
i
f
L
N
i
=
1
(
1
)
A
d
d
itio
n
al
l
y
,
th
e
co
r
r
esp
o
n
d
in
g
en
er
g
y
co
n
s
u
m
p
tio
n
is
g
iv
e
n
b
y
:
e
i
L
=
k
L
.
f
L
2
.
λ
i
[
2
4
]
.
Hen
ce
,
th
e
to
tal
e
n
er
g
y
co
n
s
u
m
p
tio
n
w
h
ile
e
x
ec
u
ti
n
g
a
ll tas
k
s
th
a
t
w
er
e
d
ec
id
ed
to
b
e
lo
ca
ll
y
e
x
e
cu
ted
in
th
e
SMD
i
s
g
iv
e
n
b
y
=
∑
(
1
−
)
=
1
=
.
2
.
∑
(
1
−
)
=
1
(
2
)
I
f
tas
k
is
o
f
f
lo
ad
ed
to
th
e
e
d
g
e
n
o
d
e,
th
e
o
f
f
lo
ad
in
g
p
r
o
ce
s
s
co
m
p
let
io
n
ti
m
e
is
:
=
+
+
,
w
h
er
e
t
i
C
o
m
is
th
e
ti
m
e
to
tr
an
s
m
it
th
e
task
to
th
e
E
A
P
,
an
d
it
is
g
i
v
en
b
y
t
i
C
o
m
=
d
i
r
.
t
i
Exec
is
th
e
ti
m
e
to
ex
ec
u
te
t
h
e
ta
s
k
τ
i
at
th
e
E
N,
a
n
d
it
ca
n
b
e
f
o
r
m
u
lated
as
t
i
Exec
=
λ
i
f
S
.
t
i
Res
is
th
e
t
i
m
e
to
r
ec
eiv
e
th
e
r
es
u
lt
o
u
t
f
r
o
m
t
h
e
ed
g
e
n
o
d
e.
B
ec
au
s
e
th
e
d
ata
s
ize
o
f
t
h
e
r
es
u
lt
i
s
u
s
u
all
y
i
g
n
o
r
ed
co
m
p
ar
ed
to
t
h
e
i
n
p
u
t
d
ata
s
ize,
w
e
ig
n
o
r
e
th
is
r
ela
y
ti
m
e
a
n
d
its
en
er
g
y
co
n
s
u
m
p
tio
n
as
ad
o
p
ted
b
y
[
2
5
]
.
He
n
ce
,
f
o
r
th
e
task
=
(
+
)
,
an
d
f
o
r
all
task
s
,
w
e
h
a
v
e:
t
O
=
∑
x
i
(
d
i
r
+
λ
i
f
S
)
N
i
=
1
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
E
fficien
t m
u
lti
-
ta
s
k
o
fflo
a
d
in
g
w
it
h
en
erg
y
a
n
d
c
o
mp
u
ta
tio
n
a
l res
o
u
r
ce
s
...
(
Mo
h
a
med
E
l G
h
ma
r
y)
4911
S
o
,
th
e
e
n
er
g
y
co
n
s
u
m
p
tio
n
o
f
t
h
e
co
m
m
u
n
icatio
n
p
r
o
ce
s
s
ca
n
b
e
o
b
tain
ed
b
y
m
u
ltip
l
y
i
n
g
t
h
e
r
esu
lti
n
g
tr
an
s
m
i
s
s
io
n
p
er
io
d
b
y
t
h
e
tr
an
s
m
i
s
s
io
n
u
n
d
er
tak
e
n
p
o
w
er
,
an
d
th
e
r
est
o
f
th
e
e
x
ec
u
t
io
n
p
er
io
d
b
y
t
h
e
id
le
m
o
d
e
p
o
w
er
.
T
h
u
s
,
th
is
e
n
er
g
y
is
:
e
C
=
p
T
∑
=
1
r
+
p
I
∑
=
1
f
S
(
4
)
Si
m
i
lar
l
y
,
en
er
g
y
co
n
s
u
m
p
tio
n
at
th
e
ed
g
e
s
er
v
er
w
h
ile
ex
ec
u
ti
n
g
is
g
iv
e
n
b
y
:
=
.
2
.
[
8
]
.
T
h
e
ex
ec
u
tio
n
e
n
er
g
y
f
o
r
all
th
e
o
f
f
lo
ad
ed
task
s
is
:
e
S
=
k
S
.
f
S
2
.
∑
λ
i
x
i
N
i
=
1
(
5
)
Fin
all
y
,
g
i
v
en
t
h
e
o
f
f
lo
ad
i
n
g
d
ec
is
io
n
v
ec
to
r
f
o
r
all
tas
k
s
,
t
h
e
lo
ca
l
ex
ec
u
tio
n
f
r
eq
u
en
c
y
o
f
th
e
SMD,
an
d
t
h
e
s
er
v
er
e
x
ec
u
ti
o
n
f
r
eq
u
e
n
c
y
at
th
e
e
d
g
e,
t
h
e
to
tal
en
er
g
y
co
n
s
u
m
p
tio
n
f
o
r
th
e
SM
D
is
co
m
p
o
s
ed
o
f
i
ts
lo
ca
l
e
n
er
g
y
co
n
s
u
m
p
tio
n
,
t
h
e
co
m
m
u
n
icat
io
n
e
n
er
g
y
a
s
w
el
l
a
s
t
h
e
e
x
ec
u
tio
n
en
er
g
y
at
t
h
e
E
N,
an
d
it
is
g
i
v
en
b
y
(
,
,
)
=
+
+
.
T
h
en
,
ac
co
r
d
in
g
to
E
q
u
atio
n
s
(
2
)
,
(
4
)
an
d
(
5
)
an
d
if
w
e
n
o
te
Λ
=
∑
=
1
,
th
e
to
tal
en
er
g
y
co
n
s
u
m
p
tio
n
ca
n
b
e
f
o
r
m
u
lated
as:
(
,
f
L
,
f
S
)
=
(
k
S
f
S
2
−
k
L
f
L
2
+
p
I
f
S
)
∑
λ
i
x
i
N
i
=
1
+
p
T
r
∑
d
i
x
i
N
i
=
1
+
k
L
f
L
2
Λ
(
6
)
2
.
2
.
P
ro
ble
m
f
o
r
m
u
la
t
io
n
In
th
i
s
s
ec
t
io
n
,
w
e
p
r
ese
n
t
o
u
r
o
p
tim
iza
tio
n
p
r
o
b
le
m
f
o
r
m
u
latio
n
t
h
at
ai
m
s
to
m
i
n
i
m
ize
t
h
e
o
v
er
all
en
er
g
y
co
n
s
u
m
p
t
io
n
in
t
h
e
lo
ca
l
ex
ec
u
tio
n
o
r
th
e
o
f
f
lo
ad
in
g
p
r
o
ce
s
s
.
I
n
itiall
y
,
to
p
r
ep
ar
e
th
e
p
r
o
b
lem
’
s
d
at
a
w
e
s
tar
t
w
it
h
an
in
itial
s
o
r
ti
n
g
o
f
th
e
task
s
lis
t
τ
≜
{
τ
1
,
τ
2
,
…
,
τ
N
}
ac
co
r
d
in
g
to
th
eir
d
ea
d
lin
es
t
i
m
ax
.
Hen
ce
,
th
e
tas
k
s
e
x
ec
u
tio
n
o
r
d
er
w
it
h
in
t
h
e
SMD
o
r
th
e
ed
g
e
s
er
v
er
in
th
e
f
i
n
al
s
o
l
u
tio
n
m
u
s
t
f
u
l
f
ill
th
e
i
n
itia
l
o
r
d
er
f
o
r
b
o
th
ca
s
es.
A
cc
o
r
d
in
g
l
y
,
t
h
e
o
b
tain
ed
p
r
o
b
lem
is
f
o
r
m
u
l
ated
as:
:
min
{
x
,
f
L
,
f
S
}
{
(
k
S
f
S
2
−
k
L
f
L
2
+
p
I
f
S
)
∑
λ
i
x
i
N
i
=
1
+
p
T
r
∑
d
i
x
i
N
i
=
1
+
k
L
f
L
2
Λ
}
s
.
t.
(
C
1
.
1
)
x
i
∈
{
0
;
1
}
;
i
∈
⟦
1
;
N
⟧
;
(
C
1
.
2
)
F
L
m
i
n
≤
f
L
≤
F
L
m
ax
;
(
C
1
.
3
)
0
<
f
S
≤
F
S
;
(
C
1
.
4
)
t
i
L
=
(
1
−
x
i
)
f
L
∑
λ
k
(
1
−
x
k
)
i
k
=
1
≤
t
i
m
ax
;
i
∈
⟦
1
;
N
⟧
;
(
C
1
.
5
)
t
i
O
=
x
i
∑
x
k
(
d
k
r
+
λ
k
f
S
)
i
k
=
1
≤
t
i
m
ax
;
i
∈
⟦
1
;
N
⟧
;
(
C
1
.
6
)
e
L
=
k
L
.
f
L
2
.
∑
λ
i
(
1
−
x
i
)
N
i
=
1
≤
E
m
ax
.
I
n
th
is
w
o
r
k
,
ea
c
h
o
n
e
o
f
th
e
av
ailab
le
ta
s
k
s
ca
n
b
e
eith
er
e
x
ec
u
ted
lo
ca
ll
y
o
r
o
f
f
lo
ad
ed
t
o
th
e
ed
g
e
n
o
d
e.
T
h
u
s
,
ev
er
y
f
ea
s
ib
le
o
f
f
l
o
ad
in
g
d
ec
is
io
n
s
o
l
u
tio
n
h
a
s
t
o
s
atis
f
y
t
h
e
ab
o
v
e
co
n
s
tr
ai
n
ts
:
T
h
e
co
n
s
tr
ain
t
(
C
1
.
1
)
r
ef
er
s
to
t
h
e
o
f
f
lo
ad
in
g
d
ec
i
s
io
n
v
ar
iab
le
x
i
f
o
r
tas
k
τ
i
w
h
ic
h
eq
u
al
s
0
o
r
1
.
T
h
e
s
ec
o
n
d
co
n
s
tr
ain
t
(
C
1
.
2
)
in
d
icat
es
th
at
t
h
e
allo
ca
ted
v
ar
iab
le
lo
ca
l
f
r
eq
u
en
c
y
f
L
b
elo
n
g
s
to
a
p
r
io
r
i
f
ix
in
ter
v
a
l
g
i
v
en
b
y
[
F
L
m
i
n
,
F
L
m
ax
]
.
Si
m
ilar
l
y
,
th
e
allo
ca
ted
v
ar
iab
le
r
em
o
te
ed
g
e
s
er
v
er
f
r
eq
u
e
n
c
y
f
S
b
elo
n
g
s
to
th
e
in
ter
v
al
]
0
,
F
S
m
ax
]
in
co
n
s
tr
ain
t
(
C
1
.
3
)
.
T
h
e
co
n
s
tr
ain
t
(
C
1
.
4
)
s
h
o
w
s
th
at
t
h
e
ex
ec
u
tio
n
ti
m
e
o
f
ea
ch
d
ec
id
ed
l
o
ca
l
task
m
u
s
t
s
ati
s
f
y
its
d
ea
d
lin
e
t
i
m
ax
.
Si
m
ilar
l
y
,
i
n
co
n
s
tr
ai
n
t
(
C
1
.
5
)
,
th
e
o
f
f
lo
ad
in
g
ti
m
e
o
f
ea
ch
d
ec
id
ed
o
f
f
lo
ad
ab
le
tas
k
m
u
s
t
s
ati
s
f
y
th
e
s
a
m
e
d
ea
d
lin
e
t
i
m
ax
.
T
h
e
f
in
al
co
n
s
tr
ain
t
(
C
1
.
6
)
i
m
p
o
s
e
s
th
at
t
h
e
t
o
tal
lo
ca
l
ex
ec
u
t
io
n
en
er
g
y
m
u
s
t
n
o
t
ex
ce
ed
th
e
to
ler
ated
g
iv
en
a
m
o
u
n
t
E
m
ax
.
T
h
is
co
n
s
tr
ain
t
is
i
m
p
o
r
tan
t
esp
ec
iall
y
f
o
r
SMDs
w
it
h
cr
itical
b
atter
y
.
3.
P
RO
B
L
E
M
RE
SO
L
UT
I
O
N
I
n
th
i
s
s
ec
tio
n
,
w
e
w
ill
i
n
tr
o
d
u
ce
h
o
w
w
e
d
er
iv
e
o
u
r
s
o
lu
tio
n
f
r
o
m
t
h
e
o
b
tain
ed
o
p
ti
m
izatio
n
p
r
o
b
lem
.
3
.
1
.
P
ro
ble
m
d
ec
o
m
po
s
it
io
n
I
n
o
u
r
p
r
o
p
o
s
ed
m
o
d
el,
th
e
o
f
f
lo
ad
in
g
d
ec
i
s
io
n
v
ec
to
r
f
o
r
all
th
e
tas
k
s
is
d
e
n
o
ted
.
L
e
t
d
ef
i
n
e
th
e
v
ec
to
r
t
h
at
co
n
tai
n
s
t
h
e
o
f
f
lo
ad
ab
le
task
s
’
id
en
ti
f
ier
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
9
0
8
-
49
1
9
4912
1
=
{
i
∈
/
x
i
=
1
}
(
7
)
0
=
{
i
∈
/
x
i
=
0
}
(
8
)
A
d
d
itio
n
al
l
y
,
w
e
d
ef
in
e:
Λ
i
=
∑
λ
i
i
k
=
1
,
Λ
i
1
=
∑
x
i
λ
i
i
k
=
1
,
D
i
=
∑
d
i
i
k
=
1
,
D
i
1
=
∑
x
i
d
i
i
k
=
1
.
A
l
s
o
,
g
iv
e
n
th
e
d
ec
is
io
n
v
e
cto
r
1
,
co
n
s
tr
ain
t
(
C
1
.
4
)
f
o
r
a
lo
ca
l
task
ca
n
b
e
r
ef
o
r
m
u
lated
as
Λ
i
−
Λ
i
1
t
i
m
ax
≤
f
L
;
∀
i
∈
⟦
1
;
N
⟧
.
Fin
all
y
,
it
i
s
eq
u
iv
ale
n
t
to
o
n
e
co
n
s
tr
ain
t:
ma
x
i
{
Λ
i
−
Λ
i
1
t
i
m
ax
}
≤
f
L
.
L
i
k
e
w
i
s
e,
co
n
s
tr
ai
n
t
(
C
1
.
5
)
f
o
r
an
o
f
f
lo
ad
ab
le
task
m
ea
n
s
D
i
1
r
+
Λ
i
1
f
S
≤
t
i
m
ax
(
∀
i
∈
⟦
1
;
N
⟧
)
.
So
D
i
1
r
an
d
Λ
i
1
f
S
m
u
s
t b
e
s
tr
ictl
y
less
t
h
a
n
t
i
m
ax
(
∀
i
∈
⟦
1
;
N
⟧
)
;
p
ar
ticu
lar
l
y
min
i
{
t
i
m
ax
−
D
i
1
r
}
>
0
.
I
n
t
h
is
ca
s
e
co
n
s
tr
ai
n
ts
(
C
1
.
5
)
ca
n
b
e
r
ef
o
r
m
u
la
ted
as
Λ
i
1
t
i
m
ax
−
D
i
1
r
≤
f
S
;
∀
i
∈
⟦
1
;
N
⟧
.
Fin
all
y
,
it
is
eq
u
i
v
alen
t
to
o
n
e
co
n
s
tr
ai
n
t
:
ma
x
i
{
Λ
i
1
t
i
m
ax
−
D
i
1
r
}
≤
f
S
.
Si
m
ila
r
l
y
,
co
n
s
tr
ain
t
(
C
1
.
6
)
ca
n
b
e
r
ef
o
r
m
u
l
ate
d
as
f
L
≤
√
E
m
ax
k
L
(
Λ
N
−
Λ
N
1
)
.
Fo
r
ea
s
e
o
f
u
s
e,
let
n
o
te:
f
L
−
=
ma
x
i
{
Λ
i
−
Λ
i
1
t
i
m
ax
}
(
9
)
f
L
+
=
√
E
m
ax
k
L
(
Λ
N
−
Λ
N
1
)
(
1
0
)
f
S
−
=
ma
x
i
{
Λ
i
1
t
i
m
ax
−
D
i
1
r
}
(
1
1
)
T
h
u
s
,
f
o
r
a
g
i
v
en
o
f
f
l
o
ad
in
g
d
ec
is
io
n
v
ec
to
r
,
w
e
g
et
t
h
e
f
o
ll
o
w
i
n
g
o
p
ti
m
izatio
n
s
u
b
-
p
r
o
b
le
m
:
(
)
:
min
{
f
L
,
f
S
}
{
(
Λ
N
−
Λ
N
1
)
k
L
f
L
2
+
Λ
N
k
S
f
S
2
+
Λ
N
p
I
f
S
+
D
N
1
p
T
r
}
s
.
t.
(
C
2
.
1
)
F
L
m
i
n
≤
f
L
≤
F
L
m
ax
;
(
C
2
.
2
)
f
L
−
≤
f
L
;
(
C
2
.
3
)
f
S
−
≤
f
S
≤
F
S
;
(
C
2
.
4
)
k
L
f
L
2
(
Λ
N
−
Λ
N
1
)
≤
E
m
ax
.
C
o
n
s
id
er
in
g
t
h
e
co
n
ti
n
u
o
u
s
v
ar
iab
les
f
L
an
d
f
S
,
p
r
o
b
l
e
m
P
2
is
a
co
n
tin
u
o
u
s
m
u
lti
-
v
ar
iab
le
o
p
tim
izatio
n
p
r
o
b
le
m
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
(
f
L
,
f
S
)
=
(
Λ
N
−
Λ
N
1
)
k
L
f
L
2
+
Λ
N
1
k
S
f
S
2
+
Λ
N
1
p
I
f
S
+
D
N
1
p
T
r
ca
n
b
e
d
ec
o
m
p
o
s
ed
i
n
to
th
e
f
o
llo
w
i
n
g
t
w
o
in
d
ep
en
d
e
n
t
f
u
n
c
tio
n
s
1
(
f
L
)
an
d
2
(
f
S
)
w
h
er
e
1
(
f
L
)
=
(
Λ
N
−
Λ
N
1
)
k
L
f
L
2
an
d
2
(
f
S
)
=
Λ
N
1
k
S
f
S
2
+
Λ
N
1
p
I
f
S
+
D
N
1
p
T
r
.
Mo
r
eo
v
er
,
g
iv
en
th
e
d
is
j
u
n
ctio
n
b
et
w
ee
n
co
n
s
tr
ain
ts
(
C
2
.
1
)
,
(
C
2
.
2
)
a
n
d
(
C
2
.
4
)
o
n
th
e
o
n
e
h
a
n
d
,
an
d
(
C
2
.
3
)
in
p
r
o
b
le
m
P
2
o
n
th
e
o
th
e
r
h
an
d
,
th
is
las
t
ca
n
b
e
eq
u
iv
alen
tl
y
d
ec
o
m
p
o
s
ed
i
n
to
th
e
f
o
llo
w
in
g
t
w
o
i
n
d
ep
en
d
en
t o
p
ti
m
izatio
n
s
u
b
-
p
r
o
b
lem
s
.
.
(
)
:
min
{
f
L
}
{
1
(
f
L
)
=
(
Λ
N
−
Λ
N
1
)
k
L
f
L
2
}
s
.
t.
(
C
3
.
1
.
1
)
F
L
m
i
n
≤
f
L
≤
F
L
m
ax
;
(
C
3
.
1
.
2
)
f
L
−
≤
f
L
≤
f
L
+
.
.
(
)
:
min
{
f
S
}
{
2
(
f
S
)
=
Λ
1
k
S
f
S
2
+
Λ
N
1
p
I
f
S
+
D
N
1
p
T
r
}
s
.
t.
(
C
3
.
2
.
1
)
f
S
−
≤
f
S
≤
F
S
.
3
.
2
.
P
ro
ble
m
s
r
eso
lutio
n
Fo
r
th
e
3
.
1
p
r
o
b
lem
,
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
1
(
f
L
)
is
a
s
tr
ictly
in
cr
ea
s
in
g
co
n
ti
n
u
o
u
s
f
u
n
c
tio
n
ac
co
r
d
in
g
to
its
v
ar
iab
le
f
L
.
Hen
ce
,
b
y
tak
i
n
g
in
to
co
n
s
id
er
atio
n
th
e
o
b
tain
ed
co
n
s
tr
ai
n
ts
(
C
3
.
1
.
1
)
an
d
(
C
3
.
1
.
1
)
,
w
e
ca
n
d
er
iv
e
th
e
f
o
llo
w
i
n
g
f
u
n
ctio
n
’
s
o
p
ti
m
u
m
f
L
∗
g
iv
e
n
b
y
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
E
fficien
t m
u
lti
-
ta
s
k
o
fflo
a
d
in
g
w
it
h
en
erg
y
a
n
d
c
o
mp
u
ta
tio
n
a
l res
o
u
r
ce
s
...
(
Mo
h
a
med
E
l G
h
ma
r
y)
4913
f
L
∗
=
{
0
if
=
1
∅
if
f
L
−
>
F
L
m
ax
or
f
L
+
<
F
L
m
i
n
or
f
L
−
>
f
L
+
F
L
m
i
n
f
L
−
if
f
L
−
<
F
L
m
i
n
othe
r
w
ise
(
1
2
)
Fo
r
th
e
3
.
2
p
r
o
b
lem
,
th
e
o
b
j
ec
t
iv
e
f
u
n
ctio
n
2
(
f
S
)
is
a
co
n
ti
n
u
o
u
s
f
u
n
ctio
n
ac
co
r
d
in
g
to
it
s
v
ar
iab
le
f
S
w
it
h
a
f
ir
s
t
o
r
d
er
d
er
i
v
ate:
∂
2
(
f
S
)
∂
f
S
=
2
Λ
N
1
k
S
f
S
−
Λ
N
1
p
I
f
S
2
;
co
n
s
eq
u
e
n
tl
y
,
2
(
f
S
)
d
ec
r
ea
s
es
o
n
]
0
,
√
p
I
2
k
S
3
]
an
d
in
cr
ea
s
es
o
n
[
√
p
I
2
k
S
3
,
+
∞
[
.
T
h
en
,
2
(
f
S
)
h
as
an
o
p
ti
m
al
m
in
i
m
u
m
v
a
lu
e
at
th
e
p
o
in
t
√
p
I
2
k
S
3
w
it
h
o
u
t
co
n
s
id
er
in
g
co
n
s
tr
ain
t
(
C
3
.
2
.
1
)
.
T
h
er
e
f
o
r
e,
w
it
h
(
C
3
.
2
.
1
)
,
w
e
ca
n
d
er
iv
e
th
e
f
o
llo
w
in
g
f
u
n
ctio
n
’
s
o
p
ti
m
u
m
f
S
∗
g
iv
e
n
b
y
:
f
S
∗
=
{
∅
if
min
i
{
t
i
m
ax
−
D
i
1
r
}
≤
0
or
f
S
−
>
F
S
F
S
if
p
I
2
k
S
≥
F
S
3
f
S
−
√
p
I
2
k
S
3
if
p
I
2
k
S
≤
(
f
S
−
)
3
othe
r
w
ise
(
1
3
)
3
.
2
.
1
.
P
ro
ce
s
s
ing
f
re
qu
encie
s
det
er
m
i
na
t
io
n
Fro
m
th
e
ab
o
v
e
r
es
u
lt
s
,
w
it
h
a
g
iv
e
n
o
f
f
lo
ad
in
g
d
ec
is
io
n
v
ec
to
r
,
w
e
p
r
ese
n
t
t
h
e
n
e
x
t
A
l
g
o
r
ith
m
1
th
at
g
iv
e
s
th
e
o
p
ti
m
al
allo
ca
te
d
lo
ca
l f
r
eq
u
en
c
y
f
L
as
w
ell
as t
h
e
r
em
o
te
ed
g
e
s
er
v
er
’
s
p
r
o
ce
s
s
in
g
f
r
eq
u
e
n
c
y
f
S
.
3
.
2
.
2
.
T
he
ener
g
y
co
ns
u
m
p
t
io
n det
er
m
ina
t
io
n
Si
m
i
lar
l
y
,
g
i
v
en
an
o
f
f
lo
ad
in
g
d
ec
is
io
n
v
ec
to
r
th
e
n
e
x
t
a
lg
o
r
ith
m
2
u
s
e
s
t
h
e
f
ir
s
t
al
g
o
r
ith
m
to
d
eter
m
in
e
t
h
e
m
in
i
m
al
e
n
er
g
y
co
n
s
u
m
p
tio
n
:
Alg
o
r
ith
m
1
:
f
re
q
u
e
n
c
ies
o
p
ti
m
u
m
f
o
r
a
g
iv
e
n
Inp
u
t:
T
h
e
o
ff
lo
a
d
in
g
p
o
li
c
y
.
O
u
t
p
u
t
:
f
L
a
n
d
f
S
.
1:
De
ter
m
in
a
te
1
a
c
c
o
rd
in
g
to
(
7
);
2:
if
=
1
th
e
n
3:
f
L
=
0
;
4:
g
o
to
1
6
;
5:
e
n
d
if
6:
Ca
lcu
late
:
f
L
−
,
f
L
+
a
c
c
o
rd
in
g
t
o
(9
)
a
n
d
(
1
0
)
re
sp
e
c
ti
v
e
ly
;
7:
if
f
L
−
>
F
L
ma
x
o
r
f
L
+
<
F
L
mi
n
o
r
f
L
−
>
f
L
+
th
e
n
8:
r
e
tu
r
n
∅
;
9:
e
lse
10:
if
f
L
−
<
F
L
mi
n
th
e
n
11:
f
L
=
F
L
mi
n
;
12:
e
lse
13:
f
L
=
f
L
−
;
14:
e
n
d
if
15:
e
n
d
if
16:
if
m
in
{
−
1
}
≤
0
th
e
n
17:
r
e
tu
r
n
∅
;
18:
e
lse
19:
Ca
lcu
late
:
f
S
−
a
c
c
o
rd
in
g
to
(1
1
);
20:
if
f
S
−
>
F
S
th
e
n
21:
r
e
tu
r
n
∅
;
22:
e
lse
if
p
I
2
k
S
≥
F
S
3
t
h
e
n
23:
f
S
=
F
S
;
24:
e
lse
if
p
I
2
k
S
≤
(
f
S
−
)
3
th
e
n
25:
f
S
=
f
S
−
;
26:
e
lse
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
9
0
8
-
49
1
9
4914
27:
f
S
=
√
p
I
2
k
S
3
;
28:
e
n
d
if
29:
e
n
d
if
30:
e
n
d
if
31:
e
n
d
if
32:
r
e
tu
r
n
(
f
L
,
f
S
)
;
Alg
o
r
ith
m
2
:
En
e
rg
y
c
a
lcu
latio
n
Inp
u
t:
T
h
e
li
st
o
f
N su
b
-
tas
k
s,
o
f
f
lo
a
d
in
g
p
o
l
icy
.
O
u
t
p
u
t
:
(
,
,
)
.
1:
Ca
ll
Alg
o
r
ith
m
1
to
c
a
lcu
late
(
,
)
u
sin
g
;
2:
if
=
∅
o
r
=
∅
th
e
n
3:
r
e
tu
r
n
∞
;
4:
e
lse
5:
Ca
lcu
late
(
,
,
)
a
c
c
o
rd
in
g
to
(6
);
6:
r
e
tu
r
n
(
,
,
)
;
7:
e
n
d
if
3
.
3
.
P
ro
po
s
ed
s
o
lutio
ns
Nex
t,
t
h
e
p
r
o
b
le
m
r
elies
o
n
d
eter
m
in
i
n
g
t
h
e
o
p
ti
m
al
o
f
f
lo
ad
in
g
d
ec
is
io
n
v
ec
to
r
th
at
g
i
v
es
th
e
o
p
ti
m
al
e
n
er
g
y
co
n
s
u
m
p
t
io
n
.
Ho
w
e
v
er
,
to
iter
ate
o
v
er
all
p
o
s
s
ib
le
co
m
b
i
n
atio
n
s
o
f
a
lis
t
o
f
N
b
in
ar
y
v
ar
iab
les,
th
e
ti
m
e
co
m
p
le
x
it
y
is
e
x
p
o
n
en
t
ial
(
th
e
e
x
h
a
u
s
t
i
v
e
s
ea
r
ch
o
v
er
all
p
o
s
s
ib
le
s
o
lu
tio
n
s
r
eq
u
ir
es
2
N
iter
atio
n
s
)
.
S
u
b
s
eq
u
e
n
tl
y
,
t
h
e
to
ta
l
ti
m
e
co
m
p
le
x
it
y
o
f
t
h
e
w
h
o
le
s
o
l
u
tio
n
(
in
c
lu
d
i
n
g
A
l
g
o
r
ith
m
1
)
i
s
O(
2
N
)
*
O(
1
)
=O
(
2
N
)
th
at
i
s
n
o
t
p
r
ac
tical
f
o
r
lar
g
e
v
al
u
es
o
f
N
.
I
n
th
e
f
o
llo
w
in
g
,
w
e
p
r
o
p
o
s
e
a
lo
w
co
m
p
le
x
it
y
ap
p
r
o
x
im
a
te
alg
o
r
it
h
m
to
s
o
l
v
e
th
is
q
u
e
s
tio
n
.
3
.
3
.
1
.
B
rut
e
f
o
rc
e
s
ea
rc
h so
lutio
n
Fo
r
co
m
p
ar
is
o
n
p
u
r
p
o
s
e,
w
e
i
n
tr
o
d
u
ce
th
e
B
r
u
te
Fo
r
ce
Sea
r
ch
m
et
h
o
d
f
o
r
f
ea
s
ib
le
s
m
all
v
alu
e
s
o
f
N.
T
h
is
m
et
h
o
d
ex
p
lo
r
es
all
ca
s
es
o
f
o
f
f
lo
ad
i
n
g
d
ec
is
io
n
s
an
d
s
a
v
es
t
h
e
o
n
e
w
i
th
t
h
e
m
i
n
i
m
u
m
e
n
er
g
y
co
n
s
u
m
p
tio
n
as
w
el
l
as
its
co
m
p
let
io
n
ti
m
e.
No
w
,
th
e
n
e
x
t
alg
o
r
it
h
m
s
u
m
m
ar
izes
th
e
B
r
u
te
Fo
r
ce
Sear
ch
So
lu
tio
n
.
Alg
o
r
ith
m
3
:
Bru
te F
o
rc
e
S
e
a
rc
h
Of
f
lo
a
d
in
g
Inp
u
t:
T
h
e
li
st
τ
o
f
N su
b
-
tas
k
s;
O
u
t
p
u
t:
th
e
o
ff
lo
a
d
in
g
p
o
l
icy
∗
.
In
iti
a
li
z
e
:
m
in
En
e
rg
y
=
∞
;
1:
fo
r
i=
1
to
−
do
2:
Us
e
th
e
N
b
it
s rep
re
se
n
tati
o
n
o
f
in
teg
e
r
i
to
b
u
i
ld
th
e
p
o
li
c
y
;
3:
Ca
ll
Al
g
o
r
ith
m
2
to
g
e
t
n
e
w
En
e
r
g
y
u
sin
g
τ
a
n
d
;
4:
if
<
th
e
n
5:
←
;
6:
∗
←
;
7:
e
n
d
if
8:
e
n
d
fo
r
9:
r
e
tu
r
n
∗
;
3
.
3
.
2
.
Si
m
ula
t
ed
a
nn
ea
li
ng
o
f
f
lo
a
di
ng
ba
s
ed
o
n w
o
rk
lo
a
d dens
it
y
t
h
re
s
ho
ld
Fo
r
th
e
s
ec
o
n
d
s
o
l
u
tio
n
,
w
e
p
r
o
p
o
s
e
th
e
u
s
e
o
f
a
Si
m
u
la
ted
An
n
ea
lin
g
(
S
A
)
b
ased
m
eth
o
d
.
T
h
e
S
A
tech
n
iq
u
e
w
a
s
ad
o
p
ted
as
a
h
e
u
r
is
tic
s
o
lu
t
io
n
i
n
t
h
e
o
p
ti
m
izatio
n
f
iel
d
esp
ec
iall
y
f
o
r
h
ar
d
p
r
o
b
lem
s
.
T
o
im
p
r
o
v
e
a
s
o
lu
t
io
n
,
it
e
m
p
lo
y
s
iter
ativ
e
r
an
d
o
m
s
o
lu
tio
n
v
ar
iatio
n
.
I
n
ter
ested
r
e
ad
er
s
ca
n
r
ef
er
to
th
e
f
o
llo
w
i
n
g
w
o
r
k
s
[
2
6
]
an
d
[
2
7
]
f
o
r
m
o
r
e
d
etails
ab
o
u
t
th
is
is
s
u
e.
So
m
e
r
ef
e
r
en
ce
s
d
ea
lin
g
w
it
h
th
e
o
f
f
l
o
ad
i
n
g
in
clo
u
d
e
n
v
ir
o
n
m
e
n
t
s
[
1
9
,
2
8
,
2
9
]
u
s
e
tas
k
s
’
w
o
r
k
lo
ad
d
en
s
it
y
d
e
f
i
n
ed
as
ω
i
=
λ
i
d
i
[
cy
c
le
/
b
it
]
as
a
p
r
io
r
ity
f
ac
to
r
to
d
ec
id
e
th
e
tas
k
s
’
o
f
f
lo
ad
in
g
.
A
d
d
it
io
n
all
y
,
t
h
e
g
en
er
ated
ta
s
k
s
ar
e
g
en
er
all
y
w
it
h
d
if
f
er
e
n
t
w
o
r
k
lo
ad
d
en
s
ities
.
Mo
r
eo
v
er
,
if
t
w
o
tas
k
s
ar
e
g
iv
en
w
it
h
a
s
l
ig
h
tl
y
d
if
f
er
e
n
t d
at
a
s
izes,
t
h
e
o
n
e
t
h
at
co
n
s
u
m
e
s
les
s
en
er
g
y
is
t
h
e
o
n
e
g
i
v
e
n
b
y
t
h
e
s
m
alle
s
t
c
y
cl
es’
co
u
n
t.
B
esid
es,
w
i
th
a
l
m
o
s
t
th
e
s
a
m
e
c
y
cle
s
’
co
u
n
t,
t
h
e
o
n
e
t
h
at
co
n
s
u
m
e
s
less
o
f
f
lo
ad
i
n
g
e
n
er
g
y
i
s
th
e
o
n
e
g
iv
e
n
b
y
t
h
e
s
m
a
lles
t
d
ata
s
ize.
I
n
b
o
th
ca
s
e
s
,
th
e
tas
k
w
it
h
t
h
e
h
i
g
h
est
w
o
r
k
lo
ad
d
en
s
it
y
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s
f
a
v
o
r
ab
le
f
o
r
o
f
f
lo
ad
in
g
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r
o
v
id
ed
to
h
av
e
a
n
o
f
f
lo
ad
in
g
e
n
er
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er
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o
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ab
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n
t
h
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o
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tex
t,
w
e
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tr
o
d
u
ce
a
w
o
r
k
lo
ad
d
en
s
it
y
t
h
r
esh
o
ld
ω
T
s
u
c
h
t
h
at
:
ta
s
k
s
w
it
h
ω
i
>
ω
T
ar
e
m
o
r
e
f
av
o
r
ab
le
to
b
e
o
f
f
lo
ad
ed
.
T
h
e
o
th
er
s
ar
e
ex
ec
u
ted
lo
c
all
y
o
r
o
f
f
lo
ad
ed
w
it
h
a
p
r
o
p
o
r
tio
n
al
p
r
o
b
ab
ilit
y
to
t
h
eir
co
m
p
u
ta
tio
n
al
d
e
n
s
itie
s
.
T
h
o
s
e
w
i
th
s
m
al
l
d
en
s
itie
s
ar
e
f
av
o
r
ab
le
f
o
r
lo
ca
l
ex
ec
u
tio
n
,
an
d
t
h
o
s
e
w
it
h
h
i
g
h
d
en
s
itie
s
ar
e
f
a
v
o
r
ab
le
to
b
e
o
f
f
lo
ad
ed
.
A
cc
o
r
d
in
g
l
y
,
i
f
w
e
n
o
te
ω
m
i
n
=
min
i
{
ω
i
}
,
ω
m
ax
=
ma
x
i
{
ω
i
}
an
d
th
e
m
id
d
le
o
f
th
e
in
ter
v
al
[
ω
m
ax
,
ω
m
i
n
]
as
ω
T
=
(
ω
m
ax
+
ω
m
i
n
)
/
2
th
en
ω
T
ca
n
b
e
ch
o
s
en
s
u
c
h
t
h
at
ω
T
≤
ω
T
<
ω
m
ax
.
I
n
o
u
r
p
r
o
p
o
s
ed
s
ec
o
n
d
s
o
l
u
t
io
n
,
w
h
ich
w
e
d
e
n
o
te
W
o
r
k
l
o
ad
Den
s
it
y
b
ased
Si
m
u
lated
A
n
n
ea
li
n
g
Of
f
lo
ad
in
g
(
W
DS
A
O)
,
w
e
ad
o
p
ted
th
e
f
o
llo
w
i
n
g
g
e
n
er
al
th
r
esh
o
ld
p
r
o
b
ab
ilit
y
:
p
=
e
−
∆
E
i
/
T
0
(1
4
)
w
h
er
e
T
0
is
th
e
in
i
tial
te
m
p
er
at
u
r
e
co
n
s
tan
t.
∆
E
i
is
th
e
s
o
lu
tio
n
s
’
en
er
g
y
v
ar
iatio
n
w
h
ile
c
h
an
g
i
n
g
t
h
e
tas
k
i
s
tate.
T
h
en
,
in
ea
ch
s
ta
g
e
o
f
o
u
r
s
o
lu
tio
n
a
n
d
w
it
h
t
h
e
in
te
n
tio
n
to
av
o
id
lo
ca
l
o
p
tim
u
m
s
,
r
an
d
o
m
s
o
lu
tio
n
s
w
it
h
p
o
o
r
en
er
g
y
p
er
f
o
r
m
a
n
ce
ar
e
ac
ce
p
ted
in
lin
e
w
it
h
a
ce
r
tain
p
r
o
b
ab
il
it
y
t
h
r
es
h
o
ld
.
A
cc
o
r
d
in
g
l
y
,
A
l
g
o
r
ith
m
s
u
m
m
ar
izes o
u
r
h
e
u
r
is
tic
s
o
lu
tio
n
.
A
l
g
o
r
ith
m
4
ta
k
es
as
i
n
p
u
t
:
th
e
su
b
-
tas
k
s
’
li
st
,
th
e
in
i
ti
a
l
tem
p
e
ra
tu
re
T
0
,
th
e
c
o
o
li
n
g
f
a
c
to
r
CF
,
th
e
tem
p
e
ra
tu
re
tres
h
o
ld
,
a
n
d
th
e
w
o
r
k
lo
ad
d
en
s
it
y
t
h
r
es
h
o
ld
.
r
a
nd
o
m
(
0
,
1
)
is
a
f
u
n
c
tio
n
’
s
ca
ll th
at
g
en
er
ate
s
a
r
an
d
o
m
n
u
m
b
er
i
n
[
0
,
1
]
.
3
.
3
.
3
.
O
rig
ina
l si
m
ula
t
ed
a
nn
ea
li
n
g
o
f
f
lo
a
din
g
Fo
r
th
e
t
h
ir
d
s
o
l
u
tio
n
an
d
f
o
r
co
m
p
ar
is
o
n
p
u
r
p
o
s
e,
w
e
ta
k
e
t
h
e
v
er
s
io
n
o
f
t
h
e
s
o
lu
t
io
n
p
r
o
p
o
s
ed
b
y
[
5
]
an
d
d
en
o
te
it
Or
ig
in
al
Si
m
u
lated
An
n
ea
li
n
g
O
f
f
lo
ad
i
n
g
(
OS
A
O)
.
I
n
t
h
is
s
o
lu
tio
n
,
t
h
e
lo
ca
l
e
x
ec
u
tio
n
p
r
o
b
a
b
ilit
y
in
cr
ea
s
e
s
w
it
h
th
e
in
cr
ea
s
e
o
f
t
h
e
co
m
p
u
ti
n
g
d
en
s
it
y
.
T
h
is
f
ac
t
lead
s
to
o
f
f
lo
ad
task
s
w
it
h
b
ig
d
ata
s
ize
an
d
w
o
r
k
lo
ad
an
d
p
r
ev
en
t
task
s
w
it
h
lo
w
d
ata
s
ize
a
n
d
h
ig
h
w
o
r
k
lo
ad
to
tak
e
h
i
g
h
o
f
f
l
o
ad
p
r
i
o
r
ity
.
Alg
o
r
ith
m
4
:
w
o
rk
lo
a
d
d
e
n
sity
b
a
se
d
S
im
u
late
d
A
n
n
e
a
li
n
g
Off
lo
a
d
in
g
Inp
u
t:
T
h
e
li
st
o
f
N su
b
-
tas
k
s,T
0
,
CF
,
,
;
O
u
t
p
u
t
:
th
e
o
ff
lo
a
d
in
g
p
o
li
c
y
∗
.
In
iti
a
li
z
e
:
a
ra
n
d
o
m
p
o
li
c
y
;
1:
Ca
ll
Alg
o
r
ith
m
2
to
c
a
lcu
late
o
l
d
En
e
rg
y
u
sin
g
a
n
d
;
2:
m
in
En
e
rg
y
=
∞;
3:
w
h
il
e
T
0
>
do
4:
fo
r
e
a
c
h
i
in
do
5:
if
>
th
e
n
6:
if
tas
k
i
n
o
t
i
n
1
th
e
n
7:
a
d
d
i
to
1
;
8:
e
n
d
if
9:
e
lse
if
−
>
(
−
)
∗
ra
nd
om
(
0
,
1
)
t
h
e
n
10:
if
tas
k
i
in
1
th
e
n
11:
m
o
v
e
i
f
ro
m
1
to
0
;
12:
e
n
d
if
13:
e
lse
if
tas
k
i
in
0
th
e
n
14:
m
o
v
e
i
f
ro
m
0
t
o
1
;
15:
e
n
d
if
16:
e
n
d
if
17:
e
n
d
if
18:
Up
d
a
te
u
si
n
g
th
e
n
e
w
1
;
19:
Ca
ll
Alg
o
r
ith
m
2
to
g
e
t
n
e
w
En
e
rg
y
u
sin
g
a
n
d
;
20:
if
n
e
w
En
e
rg
y
≠
∞
th
e
n
21:
∆
=
ne
wEne
rgy
−
old
Ene
rgy
22:
if
∆
<
0
th
e
n
23:
o
ld
E
n
e
rg
y
=
n
e
w
En
e
r
g
y
;
24:
if
n
e
w
En
e
rg
y
<
m
in
En
e
rg
y
t
h
e
n
25:
m
in
En
e
rg
y
=
n
e
w
En
e
rg
y
;
26:
∗
=
;
27:
e
n
d
if
28:
e
lse
29:
Ca
lcu
late
p
a
c
c
o
rd
in
g
to
(1
3
);
30:
if
−
∆
/
0
>
ra
nd
om
(
0
,
1
)
th
e
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
9
0
8
-
49
1
9
4916
31:
o
ld
E
n
e
rg
y
=
n
e
w
En
e
rg
y
;
32:
e
lse
33:
P
u
t
b
a
c
k
i
to
it
s
o
rig
in
a
l
se
t;
34:
e
n
d
if
35:
e
n
d
if
36:
e
n
d
if
37:
e
n
d
fo
r
38:
T
0
=
T
0
*
CF
39:
e
n
d
w
il
e
40:
r
e
tu
r
n
∗
;
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
Si
m
ula
t
io
n set
u
p
T
h
e
p
r
esen
ted
r
esu
l
ts
i
n
t
h
i
s
w
o
r
k
ar
e
a
v
er
ag
ed
f
o
r
1
0
0
ti
m
e
e
x
ec
u
tio
n
s
.
W
e
i
m
p
l
e
m
en
t
all
th
e
al
g
o
r
ith
m
s
o
n
th
e
C
++
la
n
g
u
a
g
e
.
A
d
d
itio
n
a
ll
y
,
th
e
y
ar
e
r
u
n
o
n
a
lap
to
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eq
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ip
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ed
w
i
th
a
2
.
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GHz
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n
te
l
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o
r
e
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r
o
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o
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d
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o
f
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A
M
.
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h
e
tr
an
s
m
is
s
io
n
b
a
n
d
w
id
t
h
b
et
w
ee
n
th
e
m
o
b
i
le
d
ev
ice
n
o
d
e
an
d
r
e
m
o
te
ed
g
e
s
er
v
er
i
s
s
et
to
r
=
1
0
0
Kb
/s
.
T
h
e
lo
ca
l
C
P
U
f
r
eq
u
en
c
y
f
L
o
f
th
e
m
o
b
ile
d
ev
ice
w
il
l
b
e
o
p
ti
m
ized
b
et
w
ee
n
F
L
m
i
n
=
1M
Hz
an
d
F
L
m
ax
=
60M
Hz
.
T
h
e
C
P
U
f
r
e
q
u
en
c
y
o
f
th
e
r
e
m
o
te
ed
g
e
s
er
v
er
n
o
d
e
w
ill
b
e
opt
im
ized
u
n
d
er
th
e
v
a
lu
e
F
S
=
6G
Hz
.
T
h
e
d
ea
d
lin
es
t
i
m
ax
ar
e
u
n
i
f
o
r
m
l
y
d
e
f
i
n
ed
f
r
o
m
0
.
5
s
to
2
s
.
T
h
e
th
r
esh
o
ld
en
er
g
y
E
m
ax
is
u
n
i
f
o
r
m
l
y
ch
o
s
e
n
in
[
0
.
6
,
0
.
8
]
∗
Λ
.
k
L
.
(
F
L
m
ax
)
2
.
A
d
d
itio
n
all
y
,
th
e
d
ata
s
ize
o
f
ea
ch
o
n
e
o
f
t
h
e
N
tas
k
s
is
ass
u
m
ed
to
b
e
in
[
3
0
,
3
0
0
]
Kb
.
Fo
r
th
e
c
y
c
le
a
m
o
u
n
t
o
f
ea
ch
t
ask
,
i
t
is
as
s
u
m
ed
to
b
elo
n
g
to
[
6
0
,
6
0
0
]
MCy
cle
s
.
T
h
e
id
le
p
o
w
er
an
d
tr
an
s
m
i
s
s
io
n
p
o
w
er
ar
e
s
et
to
b
e
p
I
=
0
.
01
W
att
an
d
p
T
=
0
.
1
W
att
r
esp
ec
tiv
el
y
.
Fo
r
t
h
e
en
er
g
y
e
f
f
icien
c
y
co
e
f
f
ic
ien
t
s
,
w
e
s
et
k
L
=
10
−
26
an
d
k
S
=
10
−
29
.
Fo
r
th
e
s
i
m
u
lated
an
n
ea
li
n
g
m
e
th
o
d
s
,
t
h
e
f
o
llo
w
i
n
g
p
ar
am
eter
v
a
l
u
es
ar
e
ad
o
p
ted
:
f
ac
to
r
=
0
.
5
,
ε
=
0
.
3
,
T
0
=
2
0
0
,
Δ
t =
0
.
0
2
(
in
OS
A
O)
,
an
d
C
F=0
.
8
5
.
4
.
2
.
P
er
f
o
r
m
a
nce
a
na
ly
s
is
W
e
p
r
esen
t
o
u
r
r
esu
lts
i
n
ter
m
s
o
f
av
er
ag
e
d
ec
is
io
n
ti
m
e
an
d
a
v
er
ag
e
en
er
g
y
co
n
s
u
m
p
tio
n
.
W
e
s
tar
t
b
y
s
t
u
d
y
in
g
th
e
av
er
a
g
e
en
er
g
y
’
s
co
n
s
u
m
p
t
io
n
th
r
o
u
g
h
p
u
t
f
o
r
ea
ch
m
et
h
o
d
.
T
h
u
s
,
w
e
ca
r
r
ied
an
ex
p
er
im
e
n
t
w
h
er
e
w
e
v
ar
y
th
e
n
u
m
b
er
o
f
t
ask
s
p
ar
a
m
eter
b
et
w
ee
n
2
an
d
5
0
task
s
.
4
.
2
.
1
.
T
he
p
a
ra
m
et
er
T
h
e
F
ig
u
r
e
3
s
h
o
w
s
a
r
ap
id
d
ec
r
ea
s
e
o
f
t
h
e
en
er
g
y
co
n
s
u
m
p
tio
n
u
s
in
g
t
h
e
W
DS
AO
m
et
h
o
d
f
o
r
ω
T
b
et
w
ee
n
0
.
3
an
d
0
.
4
5
f
o
r
N
in
{1
0
,
1
5
,
2
0
,
2
5
,
3
0
}
.
T
h
en
,
th
is
en
er
g
y
in
cr
ea
s
e
s
f
r
o
m
ω
T
=
0
.
5
to
ω
T
=
0
.
7
5
f
o
r
all
v
alu
e
s
o
f
N.
I
n
ad
d
itio
n
it
s
lig
h
tl
y
d
ec
r
ea
s
es
af
ter
ω
T
=
0
.
7
5
o
n
ly
f
o
r
N
=
1
0
an
d
N
=
3
0
.
A
s
a
r
esu
lt,
we
f
i
n
d
th
at
th
e
b
est
v
alu
e
o
f
ω
T
th
at
m
in
i
m
ize
s
th
e
e
n
er
g
y
c
o
n
s
u
m
p
tio
n
f
o
r
m
o
s
t
o
f
t
h
e
v
alu
e
s
o
f
N
i
s
ω
T
=
0
.
5
.
T
h
er
ea
f
ter
,
w
e
w
i
ll set
ω
T
to
th
e
v
al
u
e
0
.
5
.
Fig
u
r
e
3
.
Av
er
ag
e
E
n
er
g
y
co
n
s
u
m
p
tio
n
f
o
r
ω
T
b
et
w
ee
n
0
.
2
5
an
d
0
.
8
5
4
.
2
.
2
.
T
he
ener
g
y
co
ns
u
m
p
t
io
n
I
n
ter
m
s
o
f
en
er
g
y
co
n
s
u
m
p
ti
o
n
,
th
e
e
x
p
er
i
m
en
t
’
s
r
es
u
lts
a
r
e
d
ep
icted
in
th
e
f
o
llo
w
i
n
g
t
w
o
f
i
g
u
r
e
s
.
Fig
u
r
e
4
r
ep
r
esen
ts
th
e
o
b
tai
n
ed
r
esu
lts
f
o
r
t
h
e
t
h
r
ee
m
et
h
o
d
s
w
h
er
e
N
is
tak
e
n
b
et
w
ee
n
3
an
d
2
5
.
On
t
h
e
o
n
e
h
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d
,
it
s
h
o
w
s
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s
m
al
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et
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n
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lts
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th
e
o
p
tim
al
B
F
S
m
et
h
o
d
an
d
t
h
e
OS
A
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m
et
h
o
d
.
T
h
is
d
if
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er
e
n
ce
v
ar
ies
f
r
o
m
1
.
5
3
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t
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3
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On
th
e
o
t
h
er
h
an
d
,
th
e
W
D
S
AO
r
esu
lts
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e
al
m
o
s
t
t
h
e
s
a
m
e
a
s
th
e
o
p
ti
m
al
r
es
u
lt
s
.
T
h
e
d
if
f
er
en
ce
v
ar
ies
f
r
o
m
0
.
0
0
% to
2
.
8
8
%.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
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n
g
I
SS
N:
2
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(
Mo
h
a
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l G
h
ma
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4917
B
ey
o
n
d
th
e
v
al
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OS
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a
n
d
th
e
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Fig
u
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e
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lts
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ir
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t r
ep
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u
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n
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r
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et
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d
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