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co
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[
1
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2
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atellite
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[
3
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.
C
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I
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I
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N:
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Gen
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tem
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s
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(
M.
M.
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lr
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b
y
)
2825
m
ed
iu
m
s
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[
4
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T
h
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d
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to
p
lace
th
e
P
MU
s
s
o
th
at
at
ea
ch
s
tag
e
t
h
e
s
elec
tio
n
s
at
is
f
ies
s
o
m
e
d
esig
n
cr
iter
ia
[
9
]
.
I
n
o
r
d
e
r
to
o
b
tain
a
s
u
f
f
icien
t
a
m
o
u
n
t
o
f
o
b
s
er
v
ab
ilit
y
o
f
a
p
o
w
er
s
y
s
te
m
P
MU
s
,
i
n
s
tal
l
atio
n
s
ite
s
ar
e
d
is
p
er
s
ed
o
v
er
a
w
id
e
ar
ea
.
I
n
r
ec
en
t
y
ea
r
s
,
m
an
y
i
n
v
e
s
ti
g
ato
r
s
p
r
esen
ted
d
if
f
er
en
t
m
et
h
o
d
s
f
o
r
f
in
d
in
g
t
h
e
m
in
i
m
u
m
n
u
m
b
er
an
d
o
p
tim
al
p
lace
m
e
n
t
o
f
P
MU
s
w
it
h
d
if
f
er
en
t
d
eg
r
ee
o
f
o
b
s
er
v
ab
ilit
y
[
1
0
]
.
T
h
e
ac
tu
al
s
u
b
p
r
o
b
le
m
is
th
e
is
s
u
e
o
f
s
eq
u
en
t
iall
y
ad
d
in
g
P
MU
s
to
a
s
y
s
te
m
s
tar
tin
g
w
it
h
a
lo
w
d
eg
r
ee
o
f
o
b
s
er
v
ab
ilit
y
a
n
d
en
d
in
g
w
it
h
co
m
p
lete
o
b
s
er
v
ab
ilit
y
w
it
h
r
ed
u
n
d
a
n
c
y
.
Gen
er
all
y
,
o
b
s
er
v
ab
il
it
y
a
n
a
l
y
s
i
s
ca
n
b
e
d
o
n
e
u
s
in
g
e
ith
er
a
n
u
m
e
r
ica
l
ap
p
r
o
ac
h
o
r
a
to
p
o
lo
g
ical
ap
p
r
o
ac
h
[
1
1
]
.
I
n
n
u
m
er
ical
o
b
s
er
v
ab
ilit
y
a
n
al
y
s
is
,
f
o
r
s
p
ec
if
ic
ap
p
licatio
n
,
a
n
et
w
o
r
k
i
s
o
b
s
er
v
ab
le
if
-
a
n
d
o
n
l
y
if
-
it
s
m
ea
s
u
r
e
m
e
n
t
g
ai
n
m
atr
i
x
i
s
o
f
f
u
l
l
co
lu
m
n
r
a
n
k
[
1
2
]
.
I
n
th
is
ap
p
r
o
ac
h
t
h
e
o
b
s
e
r
v
ab
ilit
y
u
s
u
a
ll
y
is
d
er
iv
ed
f
r
o
m
E
n
er
g
y
Ma
n
ag
e
m
en
t
S
y
s
te
m
(
E
MS)
ap
p
licatio
n
s
[
1
3
,
1
4
]
.
Ho
w
e
v
er
,
f
o
r
a
lar
g
e
-
s
ca
le
s
y
s
te
m
,
th
e
co
m
p
u
tatio
n
al
b
u
r
d
e
n
o
f
t
h
is
ap
p
r
o
ac
h
is
h
ea
v
y
,
a
n
d
it
s
u
ck
s
in
t
h
e
id
en
t
if
ica
tio
n
o
f
t
h
e
r
ea
l
ze
r
o
d
iag
o
n
al
ele
m
e
n
ts
o
f
t
h
e
m
atr
i
x
d
u
e
to
th
e
p
o
s
s
ib
le
er
r
o
r
s
in
r
o
u
n
d
i
n
g
n
u
m
b
er
s
.
Mo
s
t
p
ap
er
s
,
as
a
r
esu
lt,
h
a
v
e
g
o
n
e
th
r
o
u
g
h
u
s
i
n
g
th
e
to
p
o
lo
g
ical
ap
p
r
o
ac
h
es
to
v
er
if
y
t
h
e
s
y
s
te
m
f
u
ll
o
b
s
er
v
a
b
ili
t
y
[
1
5
]
.
On
th
e
o
t
h
er
h
an
d
,
th
e
to
p
o
lo
g
ical
o
b
s
er
v
ab
ilit
y
ap
p
r
o
ac
h
d
eter
m
i
n
es
n
et
w
o
r
k
o
b
s
er
v
ab
ilit
y
s
tr
ictl
y
b
ase
d
o
n
th
e
t
y
p
e
an
d
lo
ca
tio
n
o
f
m
ea
s
u
r
e
m
en
t
s
in
t
h
e
en
tire
s
y
s
te
m
.
T
h
e
to
p
o
lo
g
ical
o
b
s
er
v
ab
ilit
y
an
al
y
s
is
u
s
es
g
r
ap
h
co
n
ce
p
ts
.
T
h
e
n
et
w
o
r
k
is
o
b
s
er
v
ab
le
to
p
o
lo
g
icall
y
i
f
-
a
n
d
o
n
l
y
if
-
a
s
p
an
n
i
n
g
tr
ee
ca
n
b
e
f
o
u
n
d
i
n
t
h
e
g
r
ap
h
.
R
e
ad
er
s
m
a
y
r
e
f
er
to
[
1
0
,
1
6
,
1
7
]
f
o
r
m
o
r
e
d
etails
ab
o
u
t
to
p
o
lo
g
ical
o
b
s
er
v
ab
ilit
y
an
a
l
y
s
is
.
S
in
ce
in
t
h
e
p
o
w
er
s
y
s
te
m
s
,
m
ea
s
u
r
in
g
a
n
d
its
ap
p
licatio
n
lie
w
i
th
i
n
t
h
e
p
o
w
er
s
y
s
te
m
s
t
u
d
ies,
p
o
w
er
s
y
s
te
m
e
n
g
i
n
ee
r
s
m
ai
n
l
y
f
o
cu
s
o
n
t
h
ese
o
b
s
er
v
ab
ilit
y
p
r
o
b
le
m
s
i
n
t
h
eir
r
esear
c
h
es.
O
n
t
h
e
o
th
er
h
a
n
d
,
in
s
o
m
e
r
esear
c
h
es,
telec
o
m
m
u
n
icatio
n
en
g
i
n
ee
r
s
h
a
v
e
p
aid
m
o
r
e
atten
t
io
n
to
co
m
m
u
n
icat
io
n
s
y
s
te
m
s
.
As
a
r
esu
lt,
f
e
w
r
esear
ch
e
s
h
a
v
e
co
n
s
id
e
r
ed
th
e
w
h
o
le
d
o
m
ai
n
s
o
f
t
h
e
o
b
s
er
v
ab
ili
t
y
an
d
C
I
co
m
p
r
e
h
e
n
s
i
v
el
y
[
1
8
]
.
A
n
u
m
b
er
o
f
li
m
itatio
n
s
w
h
il
e
d
esig
n
i
n
g
a
co
m
m
u
n
icat
io
n
s
y
s
te
m
g
iv
e
s
r
i
s
e
t
o
n
ee
d
f
o
r
an
o
p
ti
m
al
s
o
lu
tio
n
th
at
ta
k
es
i
n
to
ac
co
u
n
t
t
h
e
Qo
S
r
eq
u
ir
e
m
e
n
ts
s
u
c
h
as
r
eliab
ilit
y
,
d
ata
lo
ad
s
,
laten
c
y
ti
m
e,
an
d
co
n
g
es
tio
n
o
f
th
e
co
m
m
u
n
icatio
n
n
et
w
o
r
k
[
1
9
]
.
Ma
n
y
r
esear
ch
er
s
c
o
n
s
id
er
ed
t
h
e
P
MU
s
o
p
ti
m
i
za
tio
n
p
r
o
b
lem
as
a
m
i
n
i
m
izatio
n
o
f
th
e
P
MU
s
n
u
m
b
er
.
T
h
e
m
ain
l
y
u
s
ed
o
p
ti
m
izatio
n
tech
n
iq
u
e
s
ar
e
co
n
v
e
n
tio
n
al
s
u
ch
a
s
lin
ea
r
i
n
te
g
er
p
r
o
g
r
a
m
i
n
g
[
1
5
,
2
0
–
2
3
]
o
r
m
e
ta
-
h
e
u
r
is
tic
s
u
c
h
as
Ge
n
etic
Alg
o
r
it
h
m
s
(
G
A
)
[
2
4
,
2
5
]
,
s
im
u
lated
an
n
ea
l
in
g
[
4
,
1
1
,
2
6
]
,
tab
u
s
ea
r
ch
[
2
7
]
,
an
d
b
in
ar
y
p
ar
ticle
s
w
ar
m
o
p
t
i
m
izatio
n
[
2
8
]
.
I
n
[
1
4
]
,
th
e
a
u
th
o
r
ass
u
m
ed
a
p
r
e
-
k
n
o
w
n
in
s
talle
d
co
m
m
u
n
icatio
n
in
f
r
astr
u
ctu
r
e
f
o
r
th
e
s
y
s
te
m
an
d
ass
ig
n
ed
a
p
en
alt
y
f
ac
to
r
f
o
r
th
e
ca
s
e
w
h
en
a
P
MU
is
p
l
ac
ed
at
a
b
u
s
lack
i
n
g
C
I
.
I
n
o
th
er
w
o
r
d
s
,
in
th
i
s
ap
p
r
o
ac
h
,
co
m
m
u
n
icatio
n
in
f
r
astru
ct
u
r
e
is
al
s
o
co
n
s
id
er
ed
as
a
co
n
s
tr
ain
t.
I
n
[
1
8
]
,
th
e
m
ea
s
u
r
e
m
e
n
t
a
n
d
co
m
m
u
n
ic
atio
n
in
f
r
astr
u
ct
u
r
es
w
er
e
o
p
ti
m
al
l
y
d
esi
g
n
ed
u
s
i
n
g
th
e
G
A
.
T
h
e
y
f
o
r
m
u
lated
a
n
d
o
p
ti
m
ized
th
i
s
p
r
o
b
lem
w
i
th
a
G
A
m
o
d
el
i
n
b
o
th
s
i
m
u
lta
n
eo
u
s
a
n
d
in
d
e
p
en
d
en
t
ap
p
r
o
ac
h
es.
T
h
e
r
e
s
u
lt
s
i
n
d
icate
th
at
w
h
ile
th
e
to
tal
n
u
m
b
er
o
f
m
ea
s
u
r
e
m
e
n
t
d
ev
ices
f
o
r
s
y
s
t
e
m
o
b
s
er
v
ab
ilit
y
m
a
y
i
n
cr
ea
s
e
(
an
d
th
er
ef
o
r
e,
th
e
o
b
s
er
v
a
b
ilit
y
is
i
m
p
r
o
v
ed
)
,
th
e
to
tal
co
s
t
is
r
ed
u
ce
d
.
Ho
w
e
v
er
,
th
e
y
d
id
n
o
t
i
n
tr
o
d
u
ce
an
y
s
p
ec
i
f
ic
m
et
h
o
d
to
ev
a
l
u
ate
t
h
e
lo
ca
tio
n
o
f
th
e
C
C
B
S.
I
n
ad
d
itio
n
,
t
h
e
m
eter
p
lace
m
e
n
t
h
as
b
ee
n
ca
r
r
ied
o
u
t
o
n
l
y
f
o
r
P
MU
s
as
m
e
asu
r
e
m
en
t
d
e
v
ices.
A
l
s
o
,
th
e
a
u
t
h
o
r
s
co
n
s
id
er
ed
t
h
at
t
h
e
co
s
t
o
f
th
e
n
et
w
o
r
k
d
e
p
en
d
s
o
n
t
h
e
ac
cu
m
u
lati
v
e
le
n
g
t
h
o
f
th
e
OP
GW
o
n
l
y
,
a
n
d
d
id
n
o
t
co
n
s
id
er
t
h
e
allo
ca
tio
n
o
f
th
e
lin
k
ca
p
ac
it
y
.
Mo
r
eo
v
er
,
th
e
a
u
t
h
o
r
s
d
id
n
o
t
ta
k
e
i
n
to
ac
co
u
n
t
t
h
e
q
u
alit
y
o
f
s
er
v
ice
s
u
c
h
as
late
n
c
y
ti
m
e
o
f
t
h
e
co
m
m
u
n
icatio
n
n
et
w
o
r
k
,
r
eliab
ilit
y
,
an
d
t
h
e
d
eg
r
ee
o
f
th
e
o
b
s
er
v
ab
ilit
y
.
T
h
er
ef
o
r
e,
in
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
es,
th
e
p
o
w
er
s
y
s
te
m
o
b
s
er
v
ab
il
it
y
,
C
I
r
eq
u
ir
em
e
n
ts
,
s
y
s
te
m
r
eliab
ili
t
y
,
an
d
t
h
e
laten
c
y
ti
m
e
ar
e
co
n
s
id
er
ed
in
th
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
s
.
W
e
tak
e
in
to
ac
co
u
n
t
th
e
p
r
ed
esig
n
r
eq
u
ir
e
m
en
ts
s
u
ch
as
p
r
ed
ef
i
n
ed
lo
ca
tio
n
s
o
f
s
o
m
e
P
MU
s
a
n
d
an
y
ex
is
ti
n
g
C
Ds
i
n
s
o
m
e
b
u
s
es
an
d
C
C
B
S
lo
ca
tio
n
.
Fo
r
th
i
s
s
t
u
d
y
,
t
w
o
d
i
f
f
er
en
t
ap
p
r
o
ac
h
e
s
ar
e
u
s
ed
.
T
h
e
f
ir
s
t
ap
p
r
o
ac
h
u
s
e
s
B
P
SOGS
A
to
s
ea
r
ch
th
e
b
est
lo
ca
tio
n
o
f
th
e
P
MU
s
an
d
th
e
ch
an
n
el
ca
p
ac
it
y
o
f
t
h
e
C
o
m
m
u
n
icatio
n
L
i
n
k
s
(
C
L
s
)
w
h
ile
th
e
co
n
n
ec
tio
n
to
p
o
lo
g
y
is
d
o
n
e
u
s
in
g
M
ST
alg
o
r
ith
m
.
T
h
e
s
ec
o
n
d
ap
p
r
o
ac
h
u
s
e
s
BP
SOGS
A
to
s
ea
r
ch
th
e
b
est lo
ca
tio
n
o
f
t
h
e
P
MU
s
,
th
e
ch
a
n
n
e
l c
ap
ac
it
y
o
f
C
L
s
,
an
d
th
e
co
n
n
ec
tio
n
to
p
o
lo
g
y
.
T
h
e
r
est
o
f
th
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
Sect
io
n
2
d
escr
ib
es
th
e
o
b
s
er
v
ab
ilit
y
co
n
s
tr
ain
t.
Sectio
n
3
in
tr
o
d
u
ce
B
P
SOGS
A
.
Sectio
n
4
d
escr
ib
e
Mi
n
i
m
u
m
Sp
a
n
n
i
n
g
T
r
ee
.
Sectio
n
5
p
r
esen
ts
th
e
q
u
ali
t
y
o
f
s
er
v
ice.
Sectio
n
6
p
r
esen
ts
th
e
to
tal
co
s
t
ca
lc
u
latio
n
.
Sectio
n
7
p
r
esen
t
s
p
r
o
b
lem
f
o
r
m
u
latio
n
a
n
d
i
m
p
le
m
en
ta
tio
n
,
also
th
i
s
s
ec
t
io
n
d
is
cu
s
s
th
e
s
y
s
te
m
s
v
ar
ia
b
les
an
d
co
s
t
f
ac
to
r
s
.
Sectio
n
8
d
is
cu
s
s
th
e
t
w
o
ap
p
r
o
ac
h
es r
esu
lts
.
Fi
n
all
y
,
co
n
clu
s
io
n
s
ar
e
ex
tr
ac
ted
in
Sec
t
io
n
9
.
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.
10
,
No
.
3
,
J
u
n
e
2
0
2
0
:
2
8
2
4
-
2841
2826
2.
O
B
SE
RVAB
I
L
I
T
Y
CO
NS
T
RAIN
T
I
n
g
e
n
er
al,
g
i
v
en
a
P
MU
w
it
h
u
n
li
m
ited
n
u
m
b
er
o
f
ch
a
n
n
els
at
a
b
u
s
,
b
u
s
v
o
lta
g
e
p
h
a
s
o
r
an
d
all
cu
r
r
en
t
p
h
aso
r
s
alo
n
g
li
n
es
c
o
n
n
ec
ted
to
th
at
b
u
s
w
i
ll
b
e
a
v
ailab
le.
As
s
h
o
w
n
i
n
(
1
)
p
r
esen
t
s
o
b
s
er
v
ab
ilit
y
co
n
s
tr
ain
t
i
n
g
e
n
er
al
f
o
r
m
as
in
tr
o
d
u
ce
d
i
n
[
1
0
,
1
6
]
f
o
r
co
m
p
lete
o
b
s
er
v
ab
ilit
y
w
it
h
a
r
eq
u
ir
ed
d
eg
r
ee
o
f
r
ed
u
n
d
an
c
y
(
W
it
h
o
u
t
C
o
n
v
e
n
tio
n
al
Me
as
u
r
e
m
en
t
s
-
W
ith
C
o
n
v
en
tio
n
al
Me
as
u
r
e
m
e
n
ts
)
,
o
n
e
d
ep
t
h
o
f
u
n
o
b
s
er
v
ab
ilit
y
(
W
it
h
o
u
t
Z
er
o
I
n
j
ec
tio
n
Me
asu
r
e
m
e
n
t
-
W
it
h
Z
er
o
I
n
j
ec
tio
n
Me
asu
r
e
m
e
n
t
s
)
an
d
,
t
w
o
d
ep
t
h
o
f
u
n
o
b
s
er
v
ab
ilit
y
(
W
it
h
o
u
t
Z
er
o
I
n
j
ec
tio
n
Me
asu
r
e
m
en
t
-
W
it
h
Z
er
o
I
n
j
ec
tio
n
Me
as
u
r
e
m
e
n
t
)
.
Ob
s
e
r
va
b
il
ity
c
on
s
tr
a
in
t
:
TX
≥
B
(
1
)
T
an
d
B
ar
e
a
m
atr
ix
a
n
d
v
ec
to
r
d
ep
en
d
o
n
ea
ch
ca
s
e
[
1
0
,
1
6
]
.
X
is
th
e
P
MU
s
p
lace
m
e
n
t
v
ar
ia
b
les
X
=
[
x
1
x
2
…
x
n
]
,
x
i
=
{
1
if
PMU
at
b
us
i
,
0
if
No
PMU
at
b
us
i
,
T
h
e
m
i
n
i
m
u
m
n
u
m
b
er
o
f
P
MU
s
(
PM
U
S
m
i
n
)
ca
n
b
e
f
o
r
m
u
lated
as
a
p
r
o
b
lem
o
f
I
n
te
g
er
L
i
n
e
ar
P
r
o
g
r
am
m
i
n
g
[
2
9
]
as sh
o
w
n
i
n
th
e
f
o
llo
w
i
n
g
eq
u
a
tio
n
.
PM
U
S
m
i
n
=
{
min
∑
x
k
N
k
=
1
Sub
je
c
t
to
:
Ob
s
e
r
va
b
il
ity
c
on
s
tr
a
in
t
(
2
)
w
h
er
e
N
is
th
e
n
u
m
b
er
o
f
b
u
s
es
3.
B
I
NARY
O
P
T
I
M
I
Z
A
T
I
O
N
USI
N
G
H
YB
RID P
SO
AN
D
G
SA
T
h
e
P
SOGSA
is
a
h
y
b
r
id
o
p
ti
m
izatio
n
alg
o
r
it
h
m
,
co
m
b
i
n
in
g
s
tr
en
g
t
h
s
o
f
b
o
th
P
SO
an
d
GS
A
.
T
h
is
alg
o
r
it
h
m
p
er
f
o
r
m
s
b
o
th
P
SO
a
n
d
GS
A
i
n
ter
m
s
o
f
i
m
p
r
o
v
ed
e
x
p
lo
r
atio
n
a
n
d
ex
p
lo
itatio
n
[
3
0
]
.
T
h
is
tech
n
iq
u
e
h
as
t
h
e
n
at
u
r
e
o
f
m
eta
-
h
e
u
r
is
tic
o
p
ti
m
iz
atio
n
tech
n
iq
u
es.
On
e
o
f
t
h
e
m
ai
n
ad
v
an
ta
g
e
o
f
th
e
s
e
tech
n
iq
u
es
is
t
h
at
t
h
e
y
d
o
n
o
t
n
ee
d
a
f
u
n
ctio
n
f
o
r
m
u
latio
n
,
b
u
t r
at
h
er
n
ee
d
a
f
it
n
ess
f
u
n
ctio
n
o
n
l
y
o
r
an
y
o
t
h
er
w
a
y
f
o
r
d
is
tin
g
u
is
h
i
n
g
th
e
r
es
u
lts
.
A
s
a
r
esu
lt,
th
e
b
lack
b
o
x
p
r
o
b
lem
ca
n
b
e
s
o
lv
ed
u
s
i
n
g
th
ese
tec
h
n
iq
u
es.
T
h
e
B
P
SOGSA
a
lg
o
r
it
h
m
is
a
b
in
ar
y
v
er
s
io
n
o
f
h
y
b
r
id
P
SOGS
A
.
R
ea
d
er
s
m
a
y
r
e
f
e
r
to
[
3
1
]
f
o
r
m
o
r
e
d
etailsab
o
u
t th
is
al
g
o
r
ith
m
.
Fo
r
th
e
ab
o
v
e
-
m
en
tio
n
ed
r
ea
s
o
n
s
,
th
is
v
er
s
io
n
w
i
ll b
e
u
s
ed
in
t
h
is
s
t
u
d
y
.
4.
M
I
NI
M
U
M
SPAN
NING
T
R
E
E
T
h
e
v
er
tices
(
n
o
d
es)
o
f
th
e
C
I
in
a
p
o
w
er
g
r
id
co
r
r
esp
o
n
d
to
P
MU
s
,
C
Ds,
an
d
C
C
B
S,
w
h
i
le
th
e
ed
g
es
co
r
r
esp
o
n
d
to
h
ig
h
-
v
o
lta
g
e
lin
e
s
[
3
2
]
o
r
a
n
e
w
d
ata
tr
an
s
m
i
s
s
io
n
p
ath
s
.
Dij
k
s
tr
a
'
s
alg
o
r
it
h
m
,
co
n
ce
iv
ed
b
y
Du
tc
h
co
m
p
u
ter
s
c
ien
ti
s
t
E
d
s
g
er
Dij
k
s
tr
a
i
n
1
9
5
9
[
3
3
]
is
a
g
r
ap
h
s
ea
r
ch
alg
o
r
ith
m
t
h
at
s
o
lv
e
s
th
e
s
h
o
r
test
p
ath
p
r
o
b
le
m
f
o
r
a
g
r
ap
h
w
it
h
n
o
n
n
eg
a
tiv
e
ed
g
e
[
3
4
]
.
T
h
e
Dij
k
s
tr
a
’
s
alg
o
r
it
h
m
i
s
u
s
ed
to
s
ea
r
ch
th
e
s
h
o
r
t
p
ath
i
n
t
h
e
MST
alg
o
r
ith
m
.
T
h
e
co
m
p
le
te
p
s
e
u
d
o
co
d
e
f
o
r
MST
alg
o
r
ith
m
i
s
s
h
o
w
n
i
n
Fig
u
r
e
1
Step
3
in
t
h
is
al
g
o
r
it
h
m
co
u
ld
b
e
m
o
d
i
f
ied
to
s
tar
t
w
it
h
a
h
i
g
h
e
s
t
s
h
o
r
t
p
ath
a
n
d
en
d
w
i
th
th
e
lo
w
e
s
t
s
h
o
r
t
p
ath
.
T
h
is
m
o
d
if
icatio
n
is
p
r
ef
er
ab
le
w
h
en
s
m
al
l
p
r
o
p
ag
atio
n
tim
e
d
ela
y
is
r
eq
u
ir
ed
,
w
h
er
e
th
is
m
o
d
i
f
icatio
n
s
h
r
i
n
k
s
t
h
e
n
et
w
o
r
k
a
n
d
r
ed
u
c
es
th
e
m
a
x
i
m
u
m
p
r
o
p
ag
atio
n
t
i
m
e
d
ela
y
o
f
th
e
f
ar
t
h
est
s
ite.
I
n
s
tep
4
,
t
h
e
n
o
d
e
is
co
n
n
ec
ted
w
i
th
tr
ee
t
h
r
o
u
g
h
s
w
itch
.
Fig
u
r
e
1
.
MST
P
s
eu
d
o
co
d
e
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
Gen
era
liz
ed
o
p
tima
l p
la
ce
men
t o
f P
MUs
co
n
s
id
e
r
in
g
p
o
w
er sys
tem
o
b
s
erva
b
ilit
y
…
(
M.
M.
H.
E
lr
o
b
y
)
2827
5.
Q
UA
L
I
T
Y
O
F
SE
RVIC
E
T
h
e
W
id
e
A
r
ea
Me
as
u
r
e
m
en
t
S
y
s
te
m
(
W
A
M
S)
is
a
d
is
tr
ib
u
t
ed
co
m
m
u
n
icatio
n
n
et
w
o
r
k
.
T
h
e
Qo
S
in
th
e
W
A
MS
d
ep
en
d
s
o
n
t
h
e
la
ten
c
y
t
i
m
e,
d
ata
lo
s
s
e
s
a
n
d
r
eliab
ilit
y
o
f
t
h
e
s
y
s
te
m
.
T
h
e
laten
c
y
ti
m
e
p
er
f
o
r
m
a
n
ce
is
v
er
y
i
m
p
o
r
tan
t
esp
ec
iall
y
in
p
r
o
tectio
n
a
n
d
d
y
n
a
m
ic
co
n
tr
o
l
ap
p
licati
o
n
s
[
3
5
]
.
T
h
e
tr
ee
n
et
w
o
r
k
is
a
co
m
m
o
n
m
e
th
o
d
o
lo
g
y
i
n
o
r
d
er
to
d
esig
n
t
h
e
n
et
w
o
r
k
s
[
3
6
,
3
7
]
.
T
h
e
n
et
w
o
r
k
ar
ch
itec
tu
r
e
co
n
s
is
ts
o
f
s
e
v
er
al
P
MU
s
,
C
Ds,
an
d
P
h
a
s
o
r
Data
C
o
n
ce
n
t
r
ato
r
s
(
P
DC
s
)
as
s
h
o
w
n
in
Fi
g
u
r
e
2
.
P
DC
co
llect
s
th
e
d
ata
g
en
er
ated
b
y
th
e
s
e
P
MU
s
o
v
er
a
s
h
ar
ed
co
m
m
u
n
i
ca
tio
n
n
e
t
w
o
r
k
.
A
d
d
itio
n
all
y
,
it
p
er
f
o
r
m
s
q
u
alit
y
ch
ec
k
s
o
n
p
h
aso
r
d
ata
an
d
i
n
ter
p
r
ets
an
d
i
n
s
er
t
s
t
h
e
m
is
s
in
g
d
ata
at
t
h
eir
ap
p
r
o
p
r
iate
p
o
s
itio
n
[
3
8
,
3
9
]
.
T
y
p
icall
y
,
m
a
n
y
P
MU
s
lo
ca
ted
at
v
ar
io
u
s
s
u
b
s
ta
tio
n
s
g
ath
er
d
ata
an
d
s
en
d
it
i
n
r
e
al
ti
m
e
to
a
P
DC
.
Ma
n
y
P
DC
s
ca
n
b
e
co
n
n
ec
t
ed
to
a
co
m
m
o
n
ce
n
tr
al
P
DC
,
in
o
r
d
er
to
p
r
o
v
id
e
an
in
ter
c
o
n
n
ec
tio
n
w
id
e
s
n
ap
s
h
o
t
o
f
th
e
p
o
w
er
g
r
id
m
ea
s
u
r
e
m
en
t
s
.
I
n
lar
g
e
s
y
s
te
m
s
,
th
e
y
m
a
y
co
n
tai
n
m
o
r
e
t
h
an
o
n
e
P
DC
,
w
h
er
e
ea
ch
P
DC
is
p
lace
d
i
n
a
s
u
b
ar
ea
.
Fo
r
s
i
m
p
licit
y
i
n
t
h
i
s
s
tu
d
y
,
t
h
e
p
o
w
er
s
y
s
te
m
is
ass
u
m
ed
as
o
n
e
ar
ea
,
an
d
o
n
l
y
o
n
e
P
DC
i
s
u
s
ed
in
th
e
co
n
t
r
o
l
ce
n
ter
.
T
h
e
m
ea
s
u
r
e
m
en
ts
ar
e
m
ad
e
at
s
p
ec
i
f
ic
t
i
m
e
i
n
s
tan
ce
s
an
d
p
h
y
s
ical
d
is
ta
n
t lo
ca
tio
n
s
.
T
h
ey
ar
e
th
e
n
tr
an
s
m
i
tted
to
a
co
m
m
o
n
lo
ca
tio
n
f
o
r
u
s
e
b
y
w
id
e
ar
ea
ap
p
licatio
n
s
.
T
h
e
laten
c
y
ti
m
e
e
x
p
er
ie
n
c
ed
b
y
d
ata
b
et
w
ee
n
P
MU
an
d
th
e
d
esti
n
atio
n
n
o
d
e
(
C
C
B
S)
is
a
co
m
b
in
atio
n
o
f
P
MU
r
ep
o
r
tin
g
d
ela
y
,
t
h
e
n
et
w
o
r
k
p
r
o
p
ag
atio
n
d
ela
y
s
,
q
u
e
u
i
n
g
,
r
o
u
t
in
g
d
ela
y
s
,
a
n
d
P
DC
s
d
elay
[
4
0
]
.
A
r
ep
r
esen
tati
v
e
laten
c
y
ti
m
e
o
f
t
h
e
d
ata
n
et
wo
r
k
is
s
h
o
w
n
i
n
Fi
g
u
r
e
3
.
PMU
r
ep
o
r
tin
g
d
ela
y
is
d
ef
i
n
ed
as
t
h
e
m
a
x
i
m
u
m
ti
m
e
i
n
ter
v
a
l
b
et
w
ee
n
th
e
d
ata
r
ep
o
r
t
tim
e
a
s
in
d
icat
ed
b
y
t
h
e
d
at
a
ti
m
e
s
ta
m
p
,
a
n
d
th
e
ti
m
e
w
h
e
n
th
e
d
ata
b
ec
o
m
e
s
av
ailab
le
at
th
e
P
MU
o
u
tp
u
t.
T
h
is
d
e
la
y
i
n
clu
d
es
m
a
n
y
f
ac
to
r
s
,
s
u
c
h
as
th
e
w
in
d
o
w
o
v
er
w
h
ich
d
ata
is
g
at
h
er
ed
to
m
ak
e
a
m
ea
s
u
r
e
m
e
n
t,
m
ea
s
u
r
e
m
en
t
f
ilter
i
n
g
,
a
n
d
th
e
P
MU
p
r
o
ce
s
s
in
g
ti
m
e.
P
DC
d
elay
is
d
ef
in
ed
as
th
e
m
ax
i
m
u
m
ti
m
e
in
ter
v
al
b
et
w
ee
n
th
e
d
ata
in
p
u
t
ti
m
e
as
i
n
d
icate
d
b
y
t
h
e
d
ata
ti
m
e
s
ta
m
p
,
a
n
d
th
e
ti
m
e
w
h
e
n
th
e
d
ata
b
ec
o
m
e
s
av
a
ilab
le
at
th
e
P
DC
o
u
tp
u
t.
T
h
is
d
ela
y
i
n
clu
d
e
s
m
a
n
y
f
ac
to
r
s
s
u
ch
a
s
p
r
o
ce
s
s
in
g
,
an
d
ali
g
n
m
e
n
t
r
ec
eiv
ed
d
ata
f
r
o
m
P
MU
s
/P
DC
s
.
T
h
e
P
DC
ali
g
n
s
r
ec
eiv
ed
d
ata
a
n
d
p
lace
s
th
at
d
ata
in
a
p
ac
k
et.
I
n
ad
d
iti
o
n
,
th
e
P
DC
d
ata
p
r
o
ce
s
s
in
g
m
a
y
i
n
clu
d
e
f
ilter
i
n
g
,
r
ep
o
r
tin
g
r
ate
co
n
v
er
s
io
n
,
in
ter
p
o
latio
n
,
ex
tr
ap
o
latio
n
,
p
h
ase
a
n
d
m
a
g
n
itu
d
e
ad
j
u
s
t
m
e
n
t,
etc.
Mo
s
t
o
f
th
e
ti
m
e
t
h
e
d
ata
f
r
a
m
e
is
tr
an
s
m
i
tted
co
n
t
i
n
u
o
u
s
l
y
f
r
o
m
t
h
e
P
MU
o
r
P
DC
at
th
e
d
esi
g
n
ated
r
ep
o
r
tin
g
r
ate.
Fig
u
r
e
2
.
C
Ds an
d
P
MU
s
n
et
w
o
r
k
Fig
u
r
e
3
.
L
aten
c
y
ti
m
e
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.
10
,
No
.
3
,
J
u
n
e
2
0
2
0
:
2
8
2
4
-
2841
2828
Qu
e
u
in
g
an
d
tr
an
s
it
io
n
s
d
elay
s
(
)
ar
e
ca
u
s
ed
b
y
th
e
a
m
o
u
n
t
o
f
d
ata
th
at
h
as
to
b
e
tr
an
s
p
o
r
ted
ac
r
o
s
s
th
e
m
ed
iu
m
an
d
th
e
d
ata
r
ate
o
f
th
e
m
ed
iu
m
.
C
o
n
s
id
er
in
g
an
M/M
/1
m
o
d
el,
can
b
e
ex
p
r
ess
ed
as
f
o
llo
w
s
[
4
1
]
:
T
qu
=
−
(
3
)
C
>
f
w
h
er
e
μ
is
t
h
e
a
v
er
ag
e
p
ac
k
e
t
len
g
t
h
in
b
its
,
an
d
,
r
esp
ec
tiv
el
y
,
r
ep
r
ese
n
t
t
h
e
ca
p
ac
it
y
a
n
d
th
e
f
lo
w
o
f
th
e
li
n
k
l i
n
b
p
s
.
T
h
e
p
r
o
p
ag
atio
n
d
ela
y
(
)
is
d
ep
en
d
en
t
o
n
t
h
e
m
ed
i
u
m
an
d
th
u
s
is
a
f
u
n
ctio
n
o
f
b
o
th
th
e
m
ed
iu
m
an
d
th
e
p
h
y
s
ical
d
is
ta
n
ce
s
ep
ar
atin
g
t
h
e
in
d
i
v
id
u
al
co
m
p
o
n
e
n
ts
o
f
W
A
MS.
I
n
th
e
f
ib
er
o
p
t
ic,
th
e
p
r
o
p
ag
atio
n
d
elay
ca
n
b
e
co
n
s
id
er
e
d
as in
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
[
4
2
]
.
t
p
=
NL
S
(
4
)
w
h
er
e
S is
th
e
s
p
ee
d
o
f
th
e
li
g
h
t in
a
v
ac
u
u
m
.
L
is
t
h
e
le
n
g
t
h
o
f
t
h
e
co
m
m
u
n
icatio
n
li
n
k
N
i
s
th
e
g
r
o
u
p
in
d
e
x
o
f
th
e
m
a
ter
ial≈
1
.
5
C
o
n
s
id
er
th
e
n
et
w
o
r
k
i
s
co
n
n
e
cted
u
s
i
n
g
b
ac
k
b
o
n
e
s
w
itc
h
es.
W
e
ca
n
co
n
cl
u
d
e
th
e
ab
o
v
e
-
m
en
tio
n
ed
f
ac
ts
a
n
d
s
u
m
m
ar
ize
t
h
e
to
tal
co
m
m
u
n
icatio
n
la
ten
c
y
ti
m
e
a
s
in
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
T
=
t
p
m
u
+
∑
t
p
i
n
i
=
1
+
∑
t
qu
i
S
W
n
i
=
1
+
t
p
d
c
p
d
c
(
5
)
w
h
er
e
T
is
th
e
to
tal
late
n
c
y
,
is
th
e
n
u
m
b
er
o
f
li
n
k
s
b
et
w
ee
n
P
MU
an
d
C
C
B
S
S
W
n
is
th
e
n
u
m
b
er
o
f
s
w
i
tch
e
s
b
etw
ee
n
P
MU
an
d
C
C
B
S
t
pdc
is
P
DC
d
ela
y
B
ased
o
n
t
h
e
t
y
p
ical
v
al
u
es
s
h
o
w
n
i
n
T
ab
le
C
.
2
i
n
[
4
3
]
,
an
d
w
it
h
ass
u
m
i
n
g
P
DC
u
s
e
s
d
ir
e
ct
f
o
r
w
ar
d
m
o
d
e
t
pdc
≈
2ms
,
an
d
t
p
m
u
≈
25ms
.
T
h
e
(
5
)
w
il
l b
e
as f
o
llo
w
s
:
T
≈
25
+
∑
t
p
i
n
i
=
1
+
∑
t
qu
S
W
n
i
=
1
+
2
(
6
)
Qu
e
u
in
g
p
ac
k
et
lo
s
s
e
s
m
o
s
tl
y
o
cc
u
r
b
ec
au
s
e
o
f
t
h
e
f
i
n
it
e
q
u
eu
e
ca
p
ac
it
y
o
f
p
ac
k
et
s
w
itc
h
in
g
n
et
w
o
r
k
s
.
T
o
co
m
p
u
te
t
h
e
av
e
r
ag
e
lo
s
s
r
ate
at
ea
c
h
s
w
itc
h
,
ea
ch
n
o
d
e
is
m
o
d
eled
w
ith
t
h
e
M/M
/1
/k
q
u
e
u
in
g
s
y
s
te
m
.
On
th
e
to
p
ic
o
f
[
4
4
]
,
th
e
to
tal
n
u
m
b
er
o
f
p
ac
k
et
lo
s
s
es
is
e
s
ti
m
ated
as
a
f
u
n
ctio
n
o
f
t
h
e
li
n
k
f
lo
w
an
d
th
e
ca
p
ac
it
y
o
f
b
u
f
f
er
s
a
n
d
lin
k
s
.
T
h
e
f
o
r
m
o
f
a
v
er
ag
e
p
ac
k
e
t lo
s
s
w
ill b
e:
A
ve
r
a
ge
pa
c
k
e
t
l
oss
=
1
∑
h
d
d
∑
1
−
ρ
e
1
−
ρ
e
be
+
1
e
ρ
e
be
(
7
)
w
h
er
e
ρ
e
=
f
e
y
e
h
d
=
Tr
a
ff
ic
vol
ume
for
all
PMU
s
a
n
d
C
Ds
b
e
=
B
uffe
r
c
a
pa
c
ity
of
l
in
k
e
,
y
e
=
C
a
pa
c
ity
of
l
in
k
e
,
f
e
=
Tr
a
ff
ic
fl
ow
of
l
in
k
e
.
Fo
r
a
s
y
s
te
m
,
w
h
ich
co
n
tai
n
s
5
0
0
P
MU
s
an
d
5
0
0
C
D
s
w
i
th
ea
ch
d
ata
f
lo
w
1
2
8
k
b
p
s
an
d
5
0
0
lin
k
s
w
it
h
f
lo
w
li
n
k
r
atio
eq
u
al
to
0
.
8
,
if
w
e
u
s
e
a
b
u
f
f
er
m
e
m
o
r
y
eq
u
al
to
o
n
e
m
e
g
a,
a
ve
r
a
ge
pa
c
k
e
t
l
oss
≈
0
.
T
h
er
ef
o
r
e,
th
e
b
u
f
f
er
m
e
m
o
r
y
ca
n
b
e
ass
u
m
ed
w
i
th
en
o
u
g
h
v
alu
e
an
d
th
e
co
s
t
o
f
th
is
m
e
m
o
r
y
r
elati
v
e
t
o
o
th
er
co
m
p
o
n
e
n
t
i
n
C
I
ca
n
b
e
n
eg
lecte
d
.
T
h
is
lead
s
to
r
ed
u
cin
g
v
ar
iab
les
in
t
h
e
o
p
ti
m
i
za
tio
n
p
r
o
b
lem
an
d
r
ed
u
cin
g
th
e
r
u
n
ti
m
e.
T
h
e
r
eliab
ilit
y
o
f
t
h
e
W
A
MS
d
ep
en
d
o
n
th
e
r
eliab
ilit
y
o
f
m
ed
ia
ch
an
n
el
an
d
n
o
d
es
ele
m
e
n
ts
.
B
ased
o
n
t
h
e
co
n
ce
p
t
i
n
[
4
5
]
we
ca
n
d
escr
ib
e
t
h
e
r
elatio
n
w
h
ich
ass
e
s
s
th
e
r
eliab
ilit
y
o
f
co
n
n
ec
tio
n
b
et
w
ee
n
a
n
y
R
eq
u
ir
ed
-
n
o
d
e
(
R
n
o
d
e)
an
d
C
C
B
S a
s
f
o
llo
w
s
:
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
Gen
era
liz
ed
o
p
tima
l p
la
ce
men
t o
f P
MUs
co
n
s
id
e
r
in
g
p
o
w
er sys
tem
o
b
s
erva
b
ilit
y
…
(
M.
M.
H.
E
lr
o
b
y
)
2829
RS
=
∏
R
i
s
(
8
)
Rp
=
1
–
∏
[
1
–
R
i
]
p
(
9
)
w
h
er
e
R
s
=ser
ies ele
m
en
t r
eliab
ili
t
y
,
R
p
=p
ar
allel
elem
e
n
t r
eliab
ilit
y
,
s
=
Nu
m
b
er
o
f
s
er
ies ele
m
en
ts
in
a
p
ath
p
=
Nu
m
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er
o
f
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m
e
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a
p
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s
.
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r
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r
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t
w
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s
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o
m
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o
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t
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n
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c
y
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n
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s
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s
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e
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o
n
l
y
o
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f
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h
e
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ca
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s
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cl)
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s
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o
w
n
i
n
Fig
u
r
e
4
(
a
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.
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f
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ted
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4
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ase2
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r
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6
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m
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lu
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T
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L
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.
Fig
u
r
e
4
.
C
o
m
p
lete
o
b
s
er
v
ab
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it
y
Fig
u
r
e
5
.
R
ed
u
n
d
a
n
c
y
w
i
th
P
MU
at
R
n
o
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e
an
d
N
n
o
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e
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.
10
,
No
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3
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J
u
n
e
2
0
2
0
:
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8
2
4
-
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2830
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u
r
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6
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y
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ch
s
w
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ass
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m
ed
as
0
.
9
9
an
d
th
e
r
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o
f
O
P
GW
an
d
tr
an
s
m
is
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io
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li
n
e
s
is
ca
lc
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d
as f
o
llo
w
s
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or
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.
L
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=
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lin
k
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R
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ase
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I
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h
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ase
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d
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ase
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g
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h
i
s
ass
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m
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m
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d
0
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9
9
r
esp
ec
tiv
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6.
CO
S
T
CA
L
CU
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AT
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N
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h
e
W
A
MS
co
s
t
d
ep
en
d
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o
n
C
I
co
s
t,
P
MU
s
co
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a
n
d
C
C
B
s
co
s
t.
T
h
e
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s
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o
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a
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I
is
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ai
n
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y
co
m
p
o
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ed
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f
t
w
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aj
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ts
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n
clu
d
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th
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t o
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as
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n
f
ib
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o
p
tic
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et
w
o
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k
s
,
th
e
p
r
ice
o
f
p
ass
i
v
e
co
m
p
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e
n
ts
m
ai
n
l
y
d
ep
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d
s
o
n
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len
g
t
h
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d
ca
p
ac
it
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t
h
e
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h
an
d
,
th
e
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s
t
o
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ac
ti
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e
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ic
es
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ai
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l
y
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ep
en
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t
h
e
n
u
m
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er
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f
s
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w
h
ic
h
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e
i
n
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tal
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ac
k
b
o
n
e
n
o
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es
[
4
6
]
.
A
s
a
r
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h
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co
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o
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I
co
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r
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m
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h
es,
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d
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ata
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an
s
m
is
s
io
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ed
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m
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i.e
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OP
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ice
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d
in
s
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n
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i
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cr
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ate
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ip
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o
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A
ct
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h
o
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e
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ld
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at
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ete
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n
ad
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itio
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t
o
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I
co
s
t,
t
h
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ar
e
th
e
co
s
t
o
f
P
MU
s
,
w
h
ic
h
eq
u
al
t
o
th
e
to
tal
p
r
ice
o
f
th
e
P
MU
s
an
d
its
i
n
s
tallatio
n
co
s
t.
C
os
t
PMU
s
=
∑
p
m
u
i
=
1
pmu
c
i
(
1
2
)
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
Gen
era
liz
ed
o
p
tima
l p
la
ce
men
t o
f P
MUs
co
n
s
id
e
r
in
g
p
o
w
er sys
tem
o
b
s
erva
b
ilit
y
…
(
M.
M.
H.
E
lr
o
b
y
)
2831
w
h
er
e
p
m
u
=
n
u
m
b
er
o
f
t
h
e
P
MU
s
pmu
c
i
=
PMU
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ch
n
i
+
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n
i
PMU
p
ch
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i
=
P
MU
p
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ice
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ac
to
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ep
en
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th
e
n
u
m
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f
ch
a
n
n
al
o
f
t
h
e
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MU
)
PMU
i
n
i
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P
MU
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s
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co
s
t (
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ep
en
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tr
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ath
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k
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ted
as f
o
llo
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:
cd
i
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(
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a
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r
p
+
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in
i
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d
i
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tc
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L
av
i
d
i
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i
d
i
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d
vi
(
1
3
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d
vi
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d
i
(
L
av
i
+
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L
av
i
=
d
i
(
1
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i
L
av
i
)
=
d
i
(
1
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(
1
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w
h
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t f
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k
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a
v
cr
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n
e
w
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ath
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k
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t f
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f
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n
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i
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t d
is
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MU
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2
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n
ad
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t
h
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n
u
m
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Ds
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e
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n
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w
n
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p
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n
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is
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e
ap
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x
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m
ated
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llo
w
s
:
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av
≈
(
PM
U
S
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in
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PM
U
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at
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f
l
o
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s
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d
at
a
f
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1
5
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h
er
e
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at
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l
o
w
is
r
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f
th
e
p
m
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d
ata
f
lo
w
(
k
b
p
s
)
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d
at
af
l
o
w
is
r
ate
o
f
th
e
C
D
d
ata
f
lo
w
(
k
b
p
s
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r
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ch
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g
ec
o
n
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ic
s
tu
d
y
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et
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n
t
w
o
b
u
s
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ca
lc
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late
v
ir
t
u
al
d
is
tan
ce
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r
o
m
(
1
4
)
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o
r
al
l
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o
s
s
ib
le
n
e
w
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ata
tr
a
n
s
m
i
s
s
i
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n
p
ath
s
.
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ter
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g
v
ir
tu
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ce
t
h
er
e
ar
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t
w
o
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d
is
ta
n
ce
m
atr
ice
s
:
d
is
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m
atr
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co
r
r
esp
o
n
d
in
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to
tr
an
s
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li
n
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is
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m
a
tr
ix
(
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d
is
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atr
ix
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)
.
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g
e
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w
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m
atr
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e
s
in
o
n
e
m
atr
i
x
as f
o
llo
w
s
:
-
Fo
r
d
ir
ec
t c
o
n
n
ec
ted
b
u
s
es,
co
m
p
ar
e
t
h
e
li
n
k
d
is
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ce
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n
D
p
o
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h
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d
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is
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ce
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f
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le
s
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a
n
in
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p
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er
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t d
ir
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t c
o
n
n
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s
es
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tak
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th
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v
ir
tu
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n
g
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h
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d
is
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T
h
en
m
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if
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(
1
1
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as f
o
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s
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CI
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i
i
=
1
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i
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(
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+
1
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i
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i
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+
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Wc
i
S
W
n
i
=
1
(
1
6
)
w
h
er
e
f
r
o
m
1
to
lp
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th
e
lin
k
s
f
r
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m
p
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te
m
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w
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+1
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e
lin
k
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f
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m
n
e
w
ad
d
ed
p
ath
s
Fin
all
y
,
t
h
e
t
o
tal
co
s
t
w
ill b
e
as f
o
llo
w
i
n
g
To
ta
l
C
ost
=
C
os
t
CI
+
C
os
t
PMUs
+
C
os
t
CCBi
(
1
7
)
w
h
er
e
C
os
t
CCBi
is
th
e
co
s
t o
f
C
C
B
S (
I
n
c
lu
d
e
C
C
B
S s
ite
an
d
P
DC
co
s
t)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
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t J
E
lec
&
C
o
m
p
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n
g
,
Vo
l.
10
,
No
.
3
,
J
u
n
e
2
0
2
0
:
2
8
2
4
-
2841
2832
7.
P
RO
B
L
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M
F
O
R
M
UL
AT
I
O
N
AND
I
M
P
L
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M
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NT
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O
N
T
h
e
P
MU
s
o
p
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al
p
lace
m
e
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t
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lem
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n
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e
co
n
s
id
er
ed
a
s
n
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n
d
eter
m
i
n
i
s
tic
p
o
l
y
n
o
m
ial
co
m
p
lete
p
r
o
b
lem
[
4
7
]
.
Fo
r
a
s
y
s
te
m
with
N
b
u
s
e
s
,
t
h
e
s
ea
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is
2
w
it
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co
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I
to
p
o
lo
g
y
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n
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tio
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,
an
d
n
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m
b
er
o
f
P
MU
ch
an
n
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ls
.
T
h
er
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r
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th
e
P
MU
s
o
p
ti
m
al
p
r
o
b
l
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m
is
co
n
s
id
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a
co
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b
in
a
to
r
ial
o
p
ti
m
iza
tio
n
p
r
o
b
lem
[
4
8
]
.
Me
ta
h
e
u
r
is
ti
c
alg
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h
m
p
o
p
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latio
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ased
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et
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s
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s
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P
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A
,
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ca
n
d
id
ate
f
o
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o
lv
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p
r
o
b
lem
s
.
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n
th
e
f
o
llo
w
i
n
g
,
t
w
o
ap
p
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ac
h
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ar
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p
r
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i
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m
ize
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w
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n
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p
r
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b
lem
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ef
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as
f
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s
:
P
rob
.
∶
{
Min
:
(
T
ota
l
C
os
t
=
C
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+
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M
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+
+
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i
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the
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tio
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ased
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h
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n
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0
4
Sec.
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MU
an
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w
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.
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[
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w
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p
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s
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T
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2
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.
2
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
Gen
era
liz
ed
o
p
tima
l p
la
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men
t o
f P
MUs
co
n
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id
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M.
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2833
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