Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
23
,
No.
1
,
Ju
ly
2021
, p
p.
575
~
582
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v
23
.i
1
.
pp
575
-
582
575
Journ
al h
om
e
page
:
http:
//
ij
eecs.i
aesc
or
e.c
om
Optimi
zed r
outi
ng alg
or
i
thm fo
r maximi
zin
g t
rans
mission
rate
in D2D n
etwork
Ma
rw
a
K
. F
ar
ha
n
1
,
Mua
yad S
.
C
r
oock
2
1
Coll
ege of
Infor
m
at
ion
Eng
ine
e
r
ing,
Al
-
Nah
rai
n
Univer
sit
y
,
Bag
hdad,
I
raq
2
Control
and
S
y
s
te
m
s E
ngineeri
n
g
Depa
rtment
,
Univer
sit
y
of Technolog
y
-
Ir
aq, B
aghda
d,
Ira
q
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Ja
n
8
, 2021
Re
vised Ju
n
1
1
, 2021
Accepte
d
J
un
21
, 202
1
W
ire
le
ss
devi
c
e
s
have
bee
n
eq
uipi
ng
extensive
servic
es
over
rec
en
t
y
ea
rs.
Since
m
ost of
th
ese
device
s
are
r
andoml
y
d
istri
bu
te
d,
a
fund
ament
al
tr
ade
-
of
f
to
be
addr
essed
i
s the
tra
nsm
ission ra
te,
l
at
en
c
y
,
a
nd
pac
ke
t
loss of
the
ad
ho
c
route
sel
ection
i
n
devi
c
e
to
d
ev
ic
e
(D2D
)
ne
tworks
.
The
r
efo
re
,
thi
s
paper
int
roduc
es
a
notion
of
weight
ed
t
ran
sm
ission
rat
e
and
tot
a
l
dela
y
,
as
well
as
the
proba
bi
li
t
y
o
f
pac
ket
loss.
B
y
designi
ng
opti
m
al
tra
nsm
ission
al
gorit
hm
s,
thi
s
proposed
al
gorit
hm
ai
m
s
to
sele
ct
the
best
pat
h
for
devi
c
e
-
to
-
dev
ice
co
m
m
unic
at
ion
tha
t
m
axi
m
iz
e
s
the
tra
nsm
iss
ion
rat
e
whil
e
m
ai
nta
ini
ng
m
ini
m
um
del
a
y
and
pac
k
et
loss.
Us
ing
the
La
g
ran
ge
opti
m
i
za
t
i
on
m
et
hod,
the
la
gr
angi
an
o
pti
m
iz
ation
of
ra
te
,
de
lay
,
and
th
e
proba
bilit
y
of
pac
ke
t
loss
al
gorit
hm
(LOR
DP
)
is
m
odel
ed.
For
pra
ct
ical
d
esigna
ti
on
,
we
c
onsider
the
fad
ing
eff
ect
o
f
the
wir
el
ess
cha
nne
ls
sce
nar
io.
Th
e
propos
ed
opti
m
al
al
gorit
hm
is
m
odel
ed
to
compute
the
op
ti
m
al
c
ost
obje
ctive
fu
nct
ion
an
d
rep
rese
nts
the
b
e
st
poss
ibl
e
soluti
on
for
the
cor
res
ponding
pat
h
.
M
ore
over
,
a
si
m
ula
ti
on
for
t
he
opti
m
iz
ed
algorithm
is
pre
sente
d
base
d
on
opti
m
al
cost
obje
c
ti
ve
fun
ct
io
n.
Sim
ula
ti
on
r
e
sults
esta
bli
sh
th
e
eff
i
ci
en
c
y
of
t
he
proposed
LORDP
al
gorit
h
m
.
Ke
yw
or
ds:
D2D
c
omm
un
ic
at
ion
Lagr
a
nge m
ultip
li
ers
MANET
Rou
ti
ng
optim
i
zat
ion
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Ma
rw
a
K. Fa
rhan
Dep
a
rtm
ent o
f Info
rm
at
ion
and C
omm
un
ic
ation
Al
Ja
dr
iy
ah
B
r
idg
e,
Bag
hdad
64074
Em
a
il
:
m
arw
a.
k.far
han@
gm
a
il
.co
m
1.
INTROD
U
CTION
M
A
N
E
T
s
t
a
n
ds
f
o
r
m
o
b
i
l
e
a
d
h
o
c
n
e
t
w
o
r
k
t
h
a
t
is
a
sel
f
-
c
onfi
gured
an
d
i
nfrastr
uctu
re
-
free
netw
or
k
base
d
on
ad
-
hoc
com
m
un
ic
at
ion
s,
routin
g
in
m
ob
il
e
adho
c
netw
orks
is
ver
y
chall
e
ng
i
ng
due
to
the
r
ecurren
t
upgrade
in
to
polo
gies,
an
d
ac
ti
ve
routes
m
a
y
be
disco
nn
ec
te
d
as
wireless
m
ob
il
e
dev
ic
e
s
transf
e
re
nce
from
on
e
place
to
ano
t
her
[
1]
-
[2]
.
The
route
sel
ect
ion
pr
ot
oco
l
m
us
t
be
com
petent
to
ada
pt
to
these
changes
by
con
ti
nual
ly
m
on
it
or
i
ng the lin
k qu
al
it
ie
s and
route the
d
at
a a
ccordin
gly
[
3]
.
The
c
on
ce
pt
of
D
2D
c
omm
u
nicat
ion
s
has
be
en
intr
od
uce
d
to
al
low
local
peer
-
to
-
pee
r
transm
issi
on
a
m
on
g
m
ob
il
e
dev
ic
es
[
4]
by
direct
c
omm
un
ic
at
ion
with
out
the
ne
ed
f
or
i
nfrastr
uctu
re
(
ac
cess
points
or
ba
se
sta
ti
on
s)
.
Mo
bi
le
us
ers
in
to
day'
s
cel
lular
netw
orks
us
e
high
data
rate
serv
ic
es
s
uc
h
as
vid
e
o
sh
a
ri
ng
a
nd
gam
ing
in
wh
i
ch
they
cou
l
d
po
te
ntial
ly
be
i
n
range
f
or
dir
ect
co
m
m
un
ic
at
ion
s
(i.e.
,
D2D)
.
T
he
ad
van
t
ag
es
of
D2D
c
omm
un
ic
at
ion
s t
o
inc
re
ase sp
ect
ral ef
f
ic
ie
ncy an
d
im
pro
ves
th
r
ough
pu
t,
en
e
r
gy ef
fici
ency, and
del
ay
.
P
r
i
o
r
e
f
f
o
r
t
s
i
n
t
h
e
r
e
s
e
a
r
c
h
f
i
e
l
d
w
e
r
e
i
n
v
e
s
t
i
g
a
t
e
d
t
o
a
d
d
r
e
s
s
t
h
e
i
s
s
u
e
o
f
t
h
e
o
p
t
i
m
a
l
r
o
u
t
e
p
o
l
i
c
i
e
s
a
n
d
m
e
t
h
o
d
s
u
s
i
n
g
d
i
v
e
r
s
e
o
b
j
e
c
t
i
v
e
s
t
h
a
t
m
i
ni
m
i
z
e
o
r
m
a
x
i
m
i
z
e
t
h
e
d
u
r
a
t
i
o
n
,
t
h
e
e
n
e
r
g
y
c
o
n
s
um
p
t
i
on
,
a
n
d
n
u
m
b
e
r
o
f
h
o
p
s
.
A
s
e
r
i
e
s
o
f
n
e
w
t
e
c
h
n
o
l
o
g
i
e
s
a
n
d
t
e
c
h
n
i
q
u
e
s
h
a
v
e
b
e
e
n
e
x
p
l
o
i
t
e
d
i
n
p
r
i
o
r
w
o
r
k
[5]
.
T
h
e
a
u
t
h
o
r
s
of
[6]
a
d
d
r
e
s
s
e
d
d
i
r
e
c
t
e
n
d
d
e
v
i
c
e
s
c
om
m
u
n
i
c
a
t
i
o
n
i
n
r
e
s
t
r
i
c
t
e
d
c
e
l
l
ul
a
r
c
o
nn
e
c
t
i
v
i
t
y
d
u
e
t
o
e
m
e
r
g
e
n
c
i
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
23
, N
o.
1
,
Ju
ly
2021
:
5
7
5
-
582
576
In
[7]
,
i
n
t
r
o
d
u
c
e
d
a
n
o
v
e
l
Q
o
S
r
o
u
t
i
n
g
i
n
M
A
N
E
T
s
u
s
i
n
g
e
m
e
r
g
e
n
t
i
n
t
e
l
l
i
g
e
n
c
e
.
T
h
e
y
d
i
v
i
d
e
d
M
A
N
E
T
i
n
t
o
c
l
u
s
t
e
r
s
b
y
s
t
a
t
i
c
a
n
d
m
o
bi
l
e
a
g
e
n
t
s
.
M
o
r
e
ov
e
r
,
f
o
r
d
a
t
a
l
o
s
s
m
i
n
i
m
i
z
a
t
i
o
n
,
s
u
g
g
e
s
t
e
d
e
n
e
r
g
y
-
e
f
f
i
c
i
e
n
t
m
u
l
t
i
p
l
e
-
p
a
t
h
r
o
u
t
i
n
g
p
r
o
t
o
c
o
l
s
f
o
r
M
A
N
E
T
a
n
d
e
n
h
a
n
c
e
d
Q
o
S
a
n
d
Q
o
E
m
e
t
r
i
c
s
.
A
n
e
n
e
r
g
y
-
e
f
f
i
c
i
e
n
t
c
l
u
s
t
e
r
i
n
g
w
a
s
i
n
t
r
o
d
u
c
e
d
u
s
i
n
g
t
h
e
P
S
O
a
n
d
f
u
z
z
y
o
p
t
i
m
iz
a
t
i
o
n
a
p
p
r
o
a
c
h
t
h
a
t
p
e
r
f
o
r
m
e
d
b
e
t
t
e
r
i
n
t
e
r
m
s
o
f
n
o
d
e
s
’
r
e
d
u
c
e
d
e
n
e
r
g
y
c
o
n
s
u
m
p
t
i
o
n
.
I
n
t
e
r
m
s
o
f
d
i
s
a
s
t
e
r
r
e
s
p
o
n
s
e
,
t
h
e
a
u
t
h
o
r
s
o
f
[8]
f
o
c
u
s
e
d
o
n
d
i
r
e
c
t
d
e
v
i
c
e
c
om
m
u
n
i
c
a
t
i
o
n
s
t
o
e
x
t
e
n
d
t
h
e
c
o
v
e
r
a
g
e
.
T
h
e
y
u
s
e
d
c
o
n
t
r
o
l
l
e
d
a
s
s
i
s
t
e
d
r
o
u
t
i
n
g
t
o
i
n
c
r
e
a
s
e
t
h
e
t
o
t
a
l
e
n
d
-
to
-
e
n
d
t
h
r
o
u
g
h
p
u
t
t
o
m
a
xi
m
um
u
s
i
ng
a
n
t
c
ol
o
n
y
o
pt
i
m
i
z
a
t
i
o
n
t
h
a
t
o
u
t
p
e
r
f
o
r
m
e
d
s
h
o
r
t
e
s
t
-
p
a
t
h
b
a
s
e
d
r
o
u
t
i
n
g
i
n
t
e
r
m
s
o
f
t
h
r
o
u
g
h
p
u
t
a
n
d
r
a
t
e
s
a
l
l
o
c
a
t
i
on
.
M
o
r
e
o
v
e
r
,
f
o
r
w
r
i
t
e
r
s
t
o
e
n
h
a
n
c
e
t
h
e
c
a
pa
c
i
t
y
o
f
o
f
f
l
o
a
d
i
n
g
f
o
r
c
e
l
l
u
l
a
r
D
2
D
r
e
l
a
y
s
,
a
ut
h
o
r
s
o
f
[9]
i
n
t
r
o
d
u
c
e
d
a
u
n
i
f
i
e
d
m
o
d
e
l
t
o
s
u
p
p
o
r
t
e
d
t
h
r
e
e
D
2
D
c
om
m
u
ni
c
a
t
i
o
n
m
o
d
e
s
.
T
h
e
y
d
e
s
i
g
n
e
d
a
r
a
d
i
o
a
r
c
h
i
t
e
c
t
u
r
e
f
o
r
t
h
e
t
h
r
e
e
D
2
D
m
o
d
e
s
a
n
d
s
u
g
g
e
s
t
e
d
a
n
a
l
g
o
r
i
t
hm
f
o
r
s
c
h
e
d
u
l
i
n
g
.
On
t
he
ot
her
ha
nd,
in
[10]
in
tro
du
ce
d
a
r
el
ia
bili
ty
awar
e
AOD
V
by
a
w
ard
i
ng
routes
s
ta
bi
li
ty
.
The
sel
ect
ed
r
ou
te
s
are
rest
rict
ed
with
a
var
ia
bles
ba
ndwidt
h
and
en
d
-
to
-
e
nd
de
la
y
and
th
ey
al
so
en
ha
nc
ed
the
reli
abili
ty
sp
eed
of
interm
ediat
e
nodes.
Au
t
hors
of
[
11]
intr
oduce
d
a
hy
br
id
op
ti
m
iz
e
d
li
nk
-
sta
te
r
outi
ng
protoc
ol
v2
th
at
is
m
ult
ipath
ene
rg
y
a
nd
QoS
-
a
war
e
t
o
so
lve
the
li
m
it
at
ion
of
e
nergy
res
ources,
nodes
m
ob
il
i
ty
,
and
traf
fic
congesti
on
in
WSN
ba
sed
MA
NET
f
or
I
oT
netw
ork
s.
The
re
searc
he
r
in
[
12
]
pres
e
nted
a
MATLAB
-
bas
ed
ad
-
hoc
on
-
dem
and
distan
c
e
vector
sim
ulati
on
prese
nted
to
pro
vid
e
a
m
eaningfu
l
m
e
thod
of
dem
on
strat
in
g
basic
routin
g
co
ncep
ts
an
d
facil
it
at
ing
vi
su
al
le
ar
ning.
The
a
uthor
s
e
nh
a
nce
d
a
f
uz
zy
-
ant
colo
ny
op
ti
m
i
zat
ion
r
ou
ti
ng
al
go
rithm
and
us
e
d
a
distr
ibu
te
d
fu
zzy
log
ic
unit
to
identify
an
d
e
xclu
de
m
isbehav
e
d
no
des
f
ro
m
the
ro
utin
g
procedu
re
that
perf
or
m
ed
bette
r
in
th
e
rati
o
pac
ket
delivery
an
d
e
nd
-
to
-
end
delay
.
In
[
13
]
,
int
rod
uced
a
trust
-
ba
sed
a
nd
sec
ure
Q
oS
routing
m
et
hod
that
de
pende
d
on
reli
evi
ng
nodes
with
var
i
ou
s
pa
cket
f
orwa
rd
i
ng
m
isbehav
io
r
a
nd
pat
h
dis
cov
e
ry
to
gua
r
antee
reli
able
com
m
un
ic
at
ion
with
QoS
va
ria
bles.
Also
,
in
[
14]
intr
oduce
d
an
a
nt
colo
ny
op
ti
m
iz
at
ion
ro
uti
ng
m
et
ho
d
to
i
m
pr
ov
e
d
m
ob
il
it
y
and
energy.
T
he
m
et
ho
d
re
duce
d
the
r
ou
te
di
sco
ver
y
pac
ke
ts
and
spe
ede
d
up
the
inter
change
of
the
routin
g
al
gorithm
us
ing
an
offset
val
ue
of
the
tra
nsi
ti
on
pro
bab
il
it
y.
In
te
rm
s
of
op
ti
m
al
ro
utes,
the
auth
or
s
of
[15]
pro
po
se
d
a
ne
w
on
-
dem
and
routin
g
prot
oc
ol
cal
le
d
perf
orm
ance
ro
utin
g
.
T
he
r
ou
te
is
sel
ect
ed
by
PRP
as
it
sat
isfie
d
thr
ou
ghput
as
well
as
hop
nu
m
ber
.
The
th
rou
ghpu
t
conditi
on
m
e
ans
that
the
t
hroug
hput
of
eac
h
l
ink
m
us
t achie
ve
the m
ini
m
u
m
thr
esh
old wit
h t
he
h
ig
hest t
hroughp
ut for t
he
e
ntire ro
ute.
A
n
e
w
c
o
n
c
e
p
t
o
f
r
o
u
t
e
a
v
a
i
l
a
bi
l
i
t
y
w
a
s
p
r
e
s
e
nt
e
d
i
n
[16]
a
s
a
m
e
a
s
u
r
e
m
e
n
t
o
f
r
o
u
t
e
n
o
u
n
i
f
o
r
m
i
t
y
i
n
a
M
A
N
E
T
a
s
i
t
r
e
p
r
e
s
e
n
t
s
t
h
e
Q
o
S
o
r
Q
o
E
o
f
v
i
d
e
o
s
t
r
e
a
m
i
ng
.
T
h
e
y
c
o
n
f
i
r
m
e
d
t
h
a
t
R
A
h
a
d
a
l
i
n
e
a
r
c
o
r
r
e
l
a
t
i
o
n
w
i
t
h
t
h
e
t
w
o
Q
o
S
m
e
t
r
i
c
s
a
n
d
f
o
u
n
d
e
d
t
h
a
t
R
A
i
s
m
o
r
e
a
f
f
e
c
t
e
d
b
y
t
h
e
v
i
d
e
o
q
u
a
l
i
t
y
.
M
o
r
e
o
n
v
i
d
e
o
s
o
v
e
r
M
A
N
E
T
s
,
a
u
t
h
o
r
s
o
f
[
1
7
]
s
t
r
e
a
m
e
d
h
i
g
h
d
e
f
i
n
i
t
i
o
n
v
i
d
e
o
s
.
T
h
e
y
d
e
s
i
g
n
e
d
a
t
r
a
n
s
m
i
s
s
i
o
n
s
y
s
t
e
m
f
o
l
l
o
w
e
d
b
y
a
d
i
s
t
o
r
t
i
o
n
s
y
s
t
e
m
t
o
e
v
a
l
u
a
t
e
p
a
c
k
e
t
l
o
s
s
r
a
t
e
a
n
d
e
n
d
-
to
-
e
n
d
d
e
l
a
y
.
T
h
e
y
u
t
i
l
i
z
e
d
t
h
e
a
va
i
l
a
b
l
e
b
a
n
d
w
i
d
t
h
i
n
M
A
N
E
T
s
e
f
f
i
c
i
e
n
t
l
y
,
m
i
ni
m
i
z
e
d
d
i
s
t
o
r
t
i
o
n
s
,
a
n
d
i
m
p
r
o
v
e
d
q
u
a
l
i
t
y
o
f
s
e
r
v
i
c
e
Q
o
S
.
T
h
e
a
u
t
h
o
r
s
a
l
s
o
u
s
e
d
a
n
e
r
r
o
r
c
o
n
c
e
a
l
m
e
n
t
t
o
r
e
c
o
v
e
r
t
h
e
l
o
s
t
/
d
r
o
p
p
e
d
v
i
d
e
o
f
r
a
m
e
s
t
o
i
m
p
r
o
v
e
Q
o
E
.
A
n
o
p
t
i
m
i
z
e
d
r
o
u
t
i
n
g
m
e
t
h
o
d
w
a
s
p
r
o
p
o
s
e
d
i
n
[18]
t
o
e
n
h
a
n
c
e
t
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
t
h
e
n
e
t
w
o
r
k
a
n
d
o
v
e
r
c
o
m
e
p
a
t
h
d
e
s
t
r
uc
t
i
o
n
w
i
t
hi
n
a
s
p
e
c
i
f
i
c
t
i
m
e
.
A
l
l
p
o
s
s
i
b
l
e
p
a
t
h
s
a
r
e
d
i
s
c
o
v
e
r
e
d
a
n
d
s
u
b
j
e
c
t
e
d
t
o
a
t
h
r
e
e
m
e
t
r
i
c
Q
o
S
t
h
a
t
i
s
:
a
m
a
x
i
m
um
bi
t
r
a
t
e
,
m
i
ni
m
um
p
a
c
k
e
t
l
o
s
s
r
a
t
e
,
a
n
d
m
i
n
i
m
um
d
e
l
a
y
.
T
h
e
de
c
i
s
i
o
n
o
f
p
a
t
h
s
e
l
e
c
t
i
o
n
r
e
l
i
e
s
o
n
w
e
i
g
h
t
e
d
s
um
o
p
t
i
m
i
z
a
t
i
o
n
,
w
e
i
g
h
t
e
d
s
um
-
g
e
n
e
t
i
c
o
p
t
i
m
i
z
a
t
i
o
n
a
n
d
g
e
n
e
t
i
c
a
l
g
o
r
i
t
hm
-
I
I
w
i
t
h
t
w
o
c
r
o
s
s
o
v
e
r
t
y
p
e
s
.
A
D
2
D
c
om
m
u
n
i
c
a
t
i
o
n
n
e
t
w
o
r
k
a
s
s
i
s
t
e
d
r
o
u
t
i
n
g
f
o
r
i
n
5
G
w
a
s
i
n
t
r
o
d
u
c
e
d
i
n
[
1
9
]
t
o
e
x
t
e
n
d
t
h
e
c
o
v
e
r
a
g
e
o
f
b
a
s
e
s
t
a
t
i
o
n
s
.
N
A
R
t
o
o
k
i
n
t
o
a
c
c
o
u
n
t
t
h
a
t
b
a
s
e
s
t
a
t
i
o
n
s
m
a
n
a
g
e
D
2
D
c
o
m
m
u
n
i
c
a
t
i
o
n
s
.
N
A
R
r
e
s
u
l
t
s
w
e
r
e
c
om
p
a
r
e
d
wi
t
h
t
h
e
l
o
a
d
b
a
l
a
n
c
i
n
g
b
a
s
e
d
s
e
l
e
c
t
i
v
e
m
ul
t
i
p
a
t
h
A
O
D
V
a
l
g
o
r
i
t
hm
.
E
v
e
n
t
u
a
l
l
y
,
a
ut
h
o
r
s
o
f
[20]
m
o
d
e
l
e
d
a
D2D
-
Q
o
S
r
o
u
t
i
n
g
a
n
d
p
r
o
p
o
s
e
d
a
d
i
s
t
r
i
b
u
t
e
d
m
u
l
t
i
-
a
g
e
n
t
r
o
u
t
i
n
g
a
l
g
o
r
i
t
hm
.
T
h
e
y
a
s
s
i
g
n
e
d
t
h
e
Q
o
S
i
n
t
e
r
m
s
o
f
d
e
l
a
y
,
b
a
n
d
w
i
d
t
h
,
a
n
d
t
h
e
r
a
t
e
o
f
p
a
c
k
e
t
l
o
s
s
,
a
n
d
t
h
e
r
o
u
t
i
n
g
p
a
t
h
w
a
s
a
l
l
o
c
a
t
e
d
a
c
c
o
r
d
i
n
g
t
o
dy
n
a
m
i
c
e
n
v
i
r
o
n
m
e
n
t
s
.
A
n
o
v
e
l
j
o
i
n
t
r
o
u
t
i
n
g
a
n
d
w
i
r
e
l
e
s
s
a
l
l
o
c
a
t
i
o
n i
n
D
2
D
c
o
m
m
u
n
i
c
a
t
i
o
n
s
w
a
s
i
n
t
r
o
d
u
c
e
d
i
n
[
2
1
]
t
h
a
t
i
s
b
a
s
e
d
o
n
t
h
e
b
r
a
n
c
h
-
a
n
d
-
c
u
t
m
e
t
h
o
d
.
F
i
n
a
l
l
y
,
a
u
t
h
o
r
s
o
f
[
2
2
]
c
om
p
o
s
e
d
c
e
l
l
u
l
a
r
n
e
t
w
o
r
k
s
o
f
D
2
D
p
a
i
r
w
h
e
r
e
r
e
l
a
y
s
a
r
r
a
n
g
e
d
i
n
c
l
u
s
t
e
r
s
.
T
h
e
y
i
n
v
e
s
t
i
g
a
t
e
D
2
D
c
om
m
u
n
i
c
a
t
i
o
n
o
p
t
i
m
a
l
a
n
d
s
u
b
o
p
t
i
m
a
l
r
o
u
t
i
n
g
i
n
t
h
e
i
n
t
e
r
f
e
r
e
n
c
e
p
r
e
s
e
n
c
e
.
T
h
e
o
p
t
i
m
a
l
p
a
t
h
w
a
s
t
h
e
o
n
e
w
i
t
h
t
h
e
l
a
r
g
e
s
t
e
n
d
-
to
-
e
n
d
S
I
N
R
.
This
pap
e
r
pr
e
sents
a
propos
ed
op
ti
m
al
ro
ut
ing
al
gorithm
for
D
2D
netw
ork,
i
n
w
hic
h
the
bit
-
rate
is
m
axi
m
iz
ed
under
the
c
on
st
r
ai
nts
of
la
te
nc
y
and
pac
ket
loss.
T
his
al
go
rithm
is
fo
r
m
ula
te
d
based
on
the
desig
ne
d
m
ulti
-
ob
j
ect
ive
op
ti
m
iz
at
ion
f
orm
ula. T
his
form
ula is s
olv
e
d us
in
g Lag
range
m
ul
ti
plier
m
eth
od.
2.
RESEA
R
CH MET
HO
D
In this sect
io
n,
we prese
nt the
syst
e
m
m
od
el
an
d al
gorithm
s of the
prop
os
e
d
syst
em
.
2.
1
.
S
ystem
mod
el
Pr
ese
nting
the
m
at
he
m
at
ic
a
l
m
od
el
ing
an
d
form
ulati
on
of
the
pr
opos
e
d
syst
e
m
.
W
e
a
dopte
d
a
n
ad
-
ho
c
netw
ork
consi
st
of
nodes
that
are
co
nnect
ed
by
li
nk
s
ℒ
a
nd
represe
nts
a
dev
ic
e
-
to
-
dev
ic
e
com
m
un
ic
at
ion
en
vir
on
m
ent
[23]
.
The
m
ai
n
assig
nm
ent
of
our
pr
e
s
ented
al
go
rith
m
is
to
identify
the
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Op
ti
mize
d
r
outi
ng
algorit
hm f
or
ma
xi
mizin
g t
ra
nsmissi
on r
ate in D
2D n
et
work
(
Marw
a K
. Farha
n)
577
op
ti
m
u
m
path
in
a
net
work
th
at
m
axi
m
iz
es
t
he
bi
t
rate
a
nd
m
ini
m
iz
es
the
total
netw
ork
l
at
ency
as
well
as
the
pack
et
l
os
s.
T
he
m
ai
n
obj
ect
ive fu
nction
is
bit rate m
axi
m
i
zat
ion
[2
4]
-
[
25]
f
or
num
ber
of av
ai
la
ble
paths i
n
a n
et
w
ork
and
can
be
e
xpress
ed
m
at
he
m
at
icall
y by;
ma
x
∑
Ʀ
i
=
1
That
s
ubj
ect
t
o
the
c
onstrai
nts
of
total
delay
m
ini
m
iz
at
ion
a
nd
pac
ket
l
os
s
m
ini
m
iz
at
ion
f
or
each
paths
and ca
n be c
har
act
e
rized
by:
min
∑
δ
i
+
min
∑
ψ
i
=
1
=
1
By
util
iz
ing
th
e
m
ulti
-
obj
ect
ive
ap
proac
h
t
o
m
od
el
this
ide
a
and
ap
plyi
ng
the
Lag
ra
ng
e
Mult
ipl
ie
rs
Op
ti
m
iz
ation
m
et
ho
d
t
o
t
he a
bove
m
od
el
,
we
c
onstruct t
he
obj
ect
i
ve
f
un
ct
ion
as
sho
wn in th
e
equati
on:
ℒ
ℱ
=
∇
bit
rate
−
∇
tot
al
delay
−
∇
pa
c
ket
los
s
In
(1)
an
d
(2)
sho
wn
belo
w,
re
present
t
he
La
gr
a
ng
ia
n
-
ob
j
ect
ive
f
unct
ion
with
res
pect
to
th
e
transm
issi
on
pow
e
r.
.
ꝓ
=
∑
Ʀ
ꝓ
=
−
∑
ꝓ
=
−
∑
ꝓ
=
(
1
)
=
∑
[
×
(
+
(
ꝓ
×
)
)
×
×
]
=
+
∑
[
ᴌ
×
(
+
)
×
×
×
(
+
(
ꝓ
×
)
)
(
(
+
(
ꝓ
×
)
)
)
]
=
+
∑
[
[
(
ꝓ
×
×
(
(
+
(
ꝓ
×
)
)
)
−
ꝓ
×
)
]
×
[
(
(
+
(
ꝓ
×
)
)
)
ꝓ
(
+
(
ꝓ
×
)
)
−
=
×
(
(
+
(
ꝓ
×
)
)
)
ꝓ
×
+
ꝓ
×
]
]
(
2
)
Wh
il
e
(3)
a
nd (4) re
pr
ese
nt th
e Lag
rangia
n
-
obj
ect
iv
e f
unct
ion wit
h res
pect
to
c
hannel
fade.
=
∑
Ʀ
=
−
∑
=
−
∑
=
(
3
)
=
∑
[
×
ꝓ
(
+
(
ꝓ
×
)
)
×
×
]
=
+
∑
[
ᴌ
×
ꝓ
(
+
)
×
×
×
(
+
(
ꝓ
×
)
)
(
(
+
(
ꝓ
×
)
)
)
]
=
+
∑
[
[
(
ꝓ
×
×
(
(
+
(
ꝓ
×
)
)
)
−
ꝓ
×
)
]
×
[
(
(
+
(
ꝓ
×
)
)
)
(
+
(
ꝓ
×
)
)
−
=
×
(
(
+
(
ꝓ
×
)
)
)
×
ꝓ
+
×
ꝓ
]
]
(4)
By
evaluati
ng
μ
an
d
λ
from
the
previ
ous
e
qua
ti
on
s
a
nd
t
hen
pl
ugging
th
ose
val
ues
bac
k
into
t
he
obj
ect
ive
funct
ion
.
This
proc
edure
is
ap
plie
d
f
or
e
ve
ry
av
ai
la
ble
node
c
onnecti
on
an
d
even
t
ually
sel
ect
the
op
ti
m
u
m
path
that
m
axi
m
iz
e
the
obj
ect
ive
f
un
ct
io
n
Ta
ble
1.
S
umm
arize
a
li
s
t
of
no
ta
ti
on
s
us
e
d
in
m
od
el
in
g
equ
at
io
ns an
d al
gorithm
s.
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l.
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, N
o.
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,
Ju
ly
2021
:
5
7
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-
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578
Table
1.
List
of
no
ta
ti
ons
Sym
bol
Sem
ant
i
cs
ꝓ
Pow
er
avai
l
abl
e
f
or data tr
ansm
i
ss
i
on
ω
Band
w
i
dt
h
al
l
oca
t
ed
for
t
he
net
w
or
k
σ
N
oi
se ge
nerat
ed
b
y
t
he
c
hannel
H
Random
vari
abl
e
repr
esent
t
he
cha
nnel
fadi
ng
Eucli
dean dist
anc
e
ℒ
N
um
ber
of avail
a
bl
e
l
i
nks
ℒ
.
ℱ
Lagrangi
an
ob
j
ec
t
i
ve
funct
i
on
Ʀ
Bit
rat
e
cal
cul
at
ed
for
t
rans
m
i
ss
i
on
δ
Total
del
ay
cal
cul
at
ed
ψ
Probabi
l
i
t
y
of pac
ket
s los
s calcul
at
ed
λ
,
μ
Lagrange
m
ul
t
i
pl
i
ers
α
Packet
avera
ge
ar
ri
val
rat
e
N
um
ber
of
N
odes
i
n
t
he
ad
-
hoc
net
w
ork
2.2.
LO
R
DP
algorithm
Aim
ing
to
for
ward
tra
ff
ic
be
tween
tw
o
node
s
in
a
m
ob
il
e
ad
-
hoc
net
work,
a
r
ou
ti
ng
t
able
m
us
t
be
issued.
A
r
ou
t
e
request/
re
ply
procedure
de
li
ver
s
s
uch
a
n
assignm
ent.
Firstl
y,
al
l
avail
able
path
co
nne
ct
ion
s
from
so
ur
ce
end
to
destinat
ion
e
nd
m
us
t
be
co
ns
ide
red
and
a
routin
g
ta
ble
is
const
ru
ct
ed
acc
ordin
gly
.
Algorithm
1
s
hows
the
buil
di
ng steps
of t
he LORD
P syste
m
.
This
im
plies
bu
il
ding
up
a
ta
ble
of
al
l
node
s
co
nn
ect
e
d
to
the
source
a
nd
le
ading
t
o
the
destinat
io
n.
The
c
os
t
of
a
ll
avail
able
paths
is
cal
culat
ed
us
i
ng
a
m
ulti
-
obj
ect
ive
op
ti
m
iz
ation
m
et
ho
d.
Algo
r
it
h
m
2
determ
ines
path
c
onnecti
vity
.
Finall
y,
the
optim
u
m
route
for
re
quest
a
nd
re
ply
is
sel
e
ct
ed
acco
r
ding
to
the
route
with the
highest
obj
ect
ive that is
b
ei
ng served
. Alg
or
i
thm
3
d
et
ai
ls
la
gr
a
nge
op
ti
m
izati
on
calc
ulati
on
s
.
Algorithm 1
LORDP
Input
: SrcN, DestN
Output
: the optimum path from SrcN to DestN
Read Node's
Information (SrcN, DestN, node spacing, node speed)
determine path connectivity
using Euclidean distance
go to
route request
algorithm to acquire routing list
go to
route reply
algorithm to fulfill routing table
go to
Lagrange Optimization Calculations
algorithm to optimize routing table
Algorithm 2
path connectivity
Input
: distance spaces, packets, number of nodes
Output
: line
identify global variables (distance spaces, packets, number of nodes)
for i = 1 to number of nodes
for j = 1 to number of nodes
if i = j then it’s the same node
obf = 0
connection matrix = 0
continue
end if
Calculate Euclidean
distance
If
Euclidean
distance
< =
distance
spaces
Plot a path line
Store connection matrix = j
End if
end for
end for
2.3.
Route
re
quest al
go
ri
thm
Af
te
r
bein
g
s
upplied
by
the
s
ource
a
nd
dest
inati
on
nodes
’
identific
at
ions.
A
re
quest
pro
cedure
f
r
om
the
source
side
is
e
m
it
te
d
to
exp
l
or
e
the
nei
ghbor
hood.
Algorithm
4
cl
ari
fies
the
Rou
te
Re
qu
est
pr
oce
dure
.
This
proce
dure
is d
el
ive
red in
stages:
a)
At
the
first
sta
ge,
al
l
li
nke
d
neig
hbor
node
s
of
t
he
s
our
ce
are
li
ste
d
a
long
with
t
heir
c
orrespo
nd
i
ng
obj
ect
i
ve
fun
ct
ion
s
.
b)
Wh
il
e
the
sec
ond
sta
ge
incl
ud
e
s
the
li
nke
d
neig
hbors
f
r
om
the
first
sta
ge
ass
ociat
ed
with
al
l
of
th
ei
r
li
nk
ed
no
des
a
nd their
corres
pondin
g object
ive fu
nctions a
nd so on.
c)
Last
ly
, th
e re
quest
li
st i
s con
du
ct
e
d wh
e
re a
p
at
h t
o
t
he des
ti
nation
is al
lo
cat
ed.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
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c Eng &
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IS
S
N:
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02
-
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Op
ti
mize
d
r
outi
ng
algorit
hm f
or
ma
xi
mizin
g t
ra
nsmissi
on r
ate in D
2D n
et
work
(
Marw
a K
. Farha
n)
579
If
m
ulti
ple
pat
hs
are
m
anifested,
the
n
the
op
tim
u
m
req
uest
path
is
chosen
base
d
on
the
hig
he
st
value
of the
obj
ect
iv
e f
un
ct
io
n
t
hat
sat
isfie
s b
it
r
at
e m
axi
m
iz
at
io
n,
lat
ency,
a
nd
pack
et
l
os
s m
inim
iz
at
ion
.
Algorithm 3
Lagrange Optimization
Calculations
Input: nextNode, currentNode
Output: Optimum Lagrangian path
Identify global variables (packets, pktLength, avgArrvRate, w, p, No, dT, PL)
For i = 1 to number of paths to the destination
If nextNode = currentNode
then it’s the same node
Set Euclidean distance
,
Ʀ
,
,
, and
= 0
Else
Calculate bit rate
Ʀ
Calculate transmission, queuing, propagation delay, and total nodal delay
Calculate packet loss pro
bability
Determine Lagrange Multipliers λ, μ
Calculate the Lagrange objective function
End if
End for
If values of Lagrange objective function
are the same
Choose optimum path = min
Else
Choose op
timum path = max
.
End if
Algorithm 4
Route Request
Input: SrcN, DestN
Output: obfNodesTable
Identify variables (packets, pktLength, avgArrvRate, w, p, No, dT, PL)
Starting node = 0
While route discovery request is true
Starting node = starting node +1
Get connection matrix (starting node)
For i = repeated DestN entries
For j = number of occurrences entries
Go to Lagrange Optimization algorithm
Delete repeated DestN entries but the optimum path
End for
End for
For k = number of entries in the route discovery list
Calculate Euclidean distance
If Euclidean distance
= 0 then it’s the same node
Set
Ʀ
,
,
, and
= 0
Else
Calculate bit rate
Ʀ
Calculate transmission, queuing, propagation delay, and total nodal delay
Calculate packet loss probability
Determine Lagrange Multipliers λ, μ
Calculate the Lagrange objective function
End if
End for
Set route discovery list (obfNodesTable)
End while
Go to RouteReply function and pass the DestN as the initial node
2.4.
Route
re
ply
algorithm
The
desti
natio
n
node
i
den
ti
f
ic
at
ion
is
al
locat
ed
as
the
init
ia
l
no
de
in
the
rep
ly
-
obj
e
ct
ive
li
st.
A
rep
ly
in
g proce
dure
from
the d
est
inati
on si
de
is
ex
hib
it
ed
in Alg
or
it
hm
5
.
a)
The
fi
rst
sta
ge
is
achieve
d
by
search
a
nd
m
at
ch
fo
r
t
he
destinat
io
n
na
m
e
in
the
first
sta
ge
of
the
re
qu
e
st
li
st.
If
no
m
at
c
h
occ
urs,
the
n
a
rep
ly
-
obj
ect
ive
li
st
is
create
d
an
d
the
destinat
ion
nam
e
is
add
e
d
an
d
al
l
Ʀ
,
φ
.
δ
.
ψ
.
ℒ
ℱ
is na
ught sin
ce it
’s
the
no
de
it
sel
f.
b)
The
n
procee
din
g
to
the
sec
ond
sta
ge
of
the
rep
ly
procedu
re,
the
seco
nd
sta
ge
of
the
re
qu
e
st
procedu
r
e
is
now
unde
r
c
on
siderati
on.
I
nspect
ing
wh
ic
h
nodes
are
li
nked
t
o
the
destinat
ion
nam
e
a
nd
a
dd
them
to
th
e
rep
ly
-
obj
ect
ive
li
st al
ong wit
h t
heir
c
orres
pond
i
ng
Ʀ
,
φ
.
δ
.
ψ
.
ℒ
ℱ
.
c)
Con
ti
nuin
g
the
pr
ece
ding
ste
ps
unti
l
the
source
nam
e
con
diti
on
is
m
e
t.
Breakin
g
off
t
he
re
ply
proce
dure
and
passi
ng
ba
ck
the
rep
ly
-
obj
ect
iv
e
li
st
to
the
re
qu
est
procedu
re
to
c
om
bin
e
bo
th
li
s
ts
an
d
form
ing
the
Evaluation Warning : The document was created with Spire.PDF for Python.
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on
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n
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E
le
c Eng &
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m
p
Sci,
Vo
l.
23
, N
o.
1
,
Ju
ly
2021
:
5
7
5
-
582
580
Objecti
ve
-
Ro
ut
e
ta
ble
based
on
t
he
highest
obj
ect
ive
a
nd
achieve
bit
rate
m
axi
m
iz
a
ti
on
,
total
delay
,
and
pack
et
l
os
s m
inim
iz
at
ion
.
Algorithm 5
Route Reply
Input: SrcN, DestN
Output: replyObjTable
Set starting node = SrcN
Set dedicated reply destination of (starting node) in obfNodesTable = DestN
Se
tu
p
ca
lc
ul
at
io
n
of
re
p
ly
Ob
jT
ab
le
(F
ro
mN
od
e,
To
No
de
,
Ob
je
ct
iv
eV
al
ue
,
No
de
sD
is
ta
nc
e
,
Rate, Delay, packetLoss)
Add SrcN to replyObjTable
set
Ʀ
,
.
.
.
= zeros
While route
reply is true
Assign nextObvNode of (starting node) = obfNodesTable.FromNode
If more than one element responded as reply destination, then
go to Lagrange optimization function and choose accordingly
End if
Set
values of replyObjTable (starting node)
Insert
Ʀ
,
.
.
.
correspondingly
Set starting node = nextObvNode
If DestN = starting node
Re
tu
rn
to
Ro
ut
e
Re
qu
es
t
al
go
ri
th
m
to
fo
rm
th
e
ob
fR
ou
te
Ta
bl
e
(r
eq
ue
st
&
repl
y list)
End for
End while
3.
RESU
LT
S
A
ND AN
ALYSIS
It
is
ver
y
be
ne
fit
to
m
ention
so
m
e
of
resear
ch
so
far
that
bu
il
t
a
strong
m
et
ho
dolo
gy
f
or
desig
ning
syst
e
m
,
su
ch
a
s
[26]
-
[
32]
.
T
his
sect
ion
is
ded
ic
at
e
d
to
th
e
netw
ork
set
up
an
d
nu
m
erical
cal
culat
ion
of
t
he
routin
g
ta
ble
f
or
the
desig
ne
d
sc
hem
es.
Th
e
node
distri
buti
on
s
how
n
i
n
Fi
gure
1
is
base
d
on
the
r
andom
wayp
oin
t
m
od
el
that
is
us
ed
to
evaluate
m
ob
il
e
ad
hoc
netw
ork
routin
g
prot
oco
ls.
N
od
e
s
co
nn
ect
i
vity
is
placed
within
a
pre
-
def
i
ned
com
m
un
ic
at
ion
ra
nge
a
nd
a
set
of
pe
rfor
m
ance
cal
culat
io
ns
is
a
ppli
ed
f
or
e
ach
path.
T
hese
cal
culat
ion
s
a
re
im
ple
m
ented
for
al
l
avail
able
paths
.
In
our
s
ce
nar
i
o,
f
ro
m
t
he
sourc
e
node
(1
)
t
o
the
destinat
io
n
node
(
6).
Each
pat
h
identi
fies
four
par
a
m
et
ers,
that
is,
the
obj
ect
ive
functi
on
valu
e,
the
distance
betwe
en
en
d
nodes
,
the
tra
ns
m
issi
o
n
bit
rate,
a
nd
finall
y
the
tota
l
nodal
delay
.
More
ov
e
r,
t
he
pack
et
los
s
rate
is
ass
um
ed
to
be
fi
xe
d
in
this
sta
ge
at
0.1
.
Ta
ble
2
sho
w
al
l
av
ai
la
ble
paths
be
tween
node
(
1)
an
d
node
(6)
a
nd
their
c
orres
pondin
g
cal
culat
io
ns
.
By
e
xam
ini
ng
Table
2,
on
e
can
no
ti
ce
th
at
m
or
e
tha
n
one
pat
h
can
le
a
d
to
the
sam
e
no
de
.
T
hat’s
w
hen
pat
h
op
ti
m
iz
ation
an
d
sel
ect
io
n
com
e
in
ha
nd
y
.
Im
ple
m
entat
i
on
of
the
path
opti
m
iz
at
ion
pr
oc
edure
is
base
d
on
ch
oo
si
ng
the
path
that
achieves
the
m
axi
m
u
m
ca
lc
ulate
d
obj
ect
ive
funct
ion
in
te
rm
s
of
bit
rate,
tota
l
la
te
ncy,
and
pack
et
los
s
rat
e,
an
d
discar
di
ng
al
l
othe
rs.
This
proce
dure
is
pe
rfor
m
ed
in
sev
eral
sta
ges
for
ever
y
pat
h
le
ad
ing
to
the
sam
e
node
res
ulti
ng
in
the
final
routing
ta
ble as s
how
n i
n
Ta
ble 3.
Figure
1.
N
ode
d
ist
rib
utio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Op
ti
mize
d
r
outi
ng
algorit
hm f
or
ma
xi
mizin
g t
ra
nsmissi
on r
ate in D
2D n
et
work
(
Marw
a K
. Farha
n)
581
Table
2.
All av
ai
la
ble p
at
hs b
et
ween
node
(1
)
a
nd no
de
(
6)
Fro
m
No
d
e
ToNo
d
e
Ob
jectiv
eValue
No
d
esDis
tan
ce
Rate (bp
s)
Delay (
m
)
Pack
etLos
sR
ate
1
5
-
2
.76
E+24
4
.72
0
1
6
9
4
8
8
1
6
2
4
1
9
9
.7
8
8
0
.01
1
3
4
8
3
7
3
0
.1
1
8
-
6
.52
E+06
6
.66
2
0
1
9
2
1
3
1
2
4
7
2
2
2
.7
5
9
0
.01
4
7
7
8
4
5
7
0
.1
1
9
-
1
9
9
6
0
9
8
3
8
.6
4
.49
2
2
1
5
4
8
9
1
3
0
5
5
4
1
.6
8
2
0
.01
4
1
1
8
2
9
3
0
.1
1
10
-
1
.34
E+19
2
.91
2
0
4
3
9
5
6
1
5
5
3
4
0
0
.5
3
1
0
.01
1
8
6
5
5
9
1
0
.1
5
2
-
1
.23
E+17
6
.70
8
2
0
3
9
3
2
1
5
2
0
6
8
4
.5
9
0
.01
2
1
2
0
8
7
9
0
.1
5
3
-
1
.98
E+15
6
.57
6
4
7
3
2
1
9
1
4
8
8
3
1
4
.0
1
5
0
.01
2
3
8
4
5
0
5
0
.1
5
4
1
1
0
4
2
1
6
.0
1
4
5
.31
5
0
7
2
9
0
6
1
1
0
7
3
7
8
.3
6
3
0
.01
6
6
4
4
7
3
5
0
.1
5
7
1
1
0
3
7
9
3
.4
1
7
5
.7
1
0
9
7
0
5
2
.2
4
6
0
.01
6
8
0
1
4
0
7
0
.1
5
11
1
.09
E+06
5
.90
5
2
9
4
2
3
5
1
1
2
8
2
4
7
.9
4
0
.01
6
3
3
6
8
5
4
0
.1
5
12
-
3
.02
0
9
8
E+12
3
.25
7
2
9
9
4
9
5
1
4
2
8
4
5
6
.3
7
0
.01
2
9
0
3
4
5
0
.1
8
4
1
1
0
4
2
1
6
.0
1
4
6
.43
2
9
2
3
1
3
1
1
0
7
3
7
8
.3
6
3
0
.01
6
6
4
4
7
3
9
0
.1
8
7
1
1
0
3
7
9
3
.4
1
7
3
.72
5
9
2
2
7
0
5
1
0
9
7
0
5
2
.2
4
6
0
.01
6
8
0
1
4
0
.1
8
12
-
3
.02
0
9
8
E+12
3
.40
9
1
7
8
7
8
7
1
4
2
8
4
5
6
.3
7
0
.01
2
9
0
3
4
5
1
0
.1
9
2
-
1
.23
E+17
4
.52
7
6
9
2
5
6
9
1
5
2
0
6
8
4
.5
9
0
.01
2
1
2
0
8
7
2
0
.1
9
3
-
1
.98
E+15
6
.10
3
2
7
7
8
0
8
1
4
8
8
3
1
4
.0
1
5
0
.01
2
3
8
4
5
0
4
0
.1
9
4
1
1
0
4
2
1
6
.0
1
4
6
.5
1
1
0
7
3
7
8
.3
6
3
0
.01
6
6
4
4
7
3
9
0
.1
9
11
1
.09
E+06
4
.01
5
2
8
3
3
0
3
1
1
2
8
2
4
7
.9
4
0
.01
6
3
3
6
8
4
8
0
.1
9
12
-
3
.02
0
9
8
E+12
5
.62
2
2
7
7
1
1
9
1
4
2
8
4
5
6
.3
7
0
.01
2
9
0
3
4
5
8
0
.1
10
7
1
1
0
3
7
9
3
.4
1
7
6
.99
2
1
3
8
4
4
3
1
0
9
7
0
5
2
.2
4
6
0
.01
6
8
0
1
4
1
1
0
.1
10
12
-
3
.02
0
9
8
E+12
5
.08
0
3
5
4
3
1
8
1
4
2
8
4
5
6
.3
7
0
.01
2
9
0
3
4
5
6
0
.1
Table
3
.
O
pti
m
iz
at
ion
of a
vaila
ble p
at
hs
bet
ween n
ode
(1) a
nd no
de (6
)
Fro
m
No
d
e
ToNo
d
e
Ob
jectiv
eValue
No
d
esDis
tan
ce (
m
)
Rate (bp
s) (
b
p
s)
Delay (sec
)
Pack
etLos
sR
ate
1
5
-
2
.76
E+24
4
.72
0
1
6
9
4
8
8
1
6
2
4
1
9
9
.7
8
8
0
.01
1
3
4
8
3
7
3
0
.1
1
8
-
6
5
1
7
5
8
3
.249
6
.66
2
0
1
9
2
1
3
1
2
4
7
2
2
2
.7
5
9
0
.01
4
7
7
8
4
5
7
0
.1
1
9
-
1
9
9
6
0
9
8
3
8
.6
4
.49
2
2
1
5
4
8
9
1
3
0
5
5
4
1
.6
8
2
0
.01
4
1
1
8
2
9
3
0
.1
1
10
-
1
.34
E+19
2
.91
2
0
4
3
9
5
6
1
5
5
3
4
0
0
.5
3
1
0
.01
1
8
6
5
5
9
1
0
.1
5
4
1
1
0
4
2
1
6
.0
1
4
5
.31
5
0
7
2
9
0
6
1
1
0
7
3
7
8
.3
6
3
0
.01
6
6
4
4
7
3
5
0
.1
8
7
1
1
0
3
7
9
3
.4
1
7
3
.72
5
9
2
2
7
0
5
1
0
9
7
0
5
2
.2
4
6
0
.01
6
8
0
1
4
0
.1
9
2
-
1
.23
E+17
4
.52
7
6
9
2
5
6
9
1
5
2
0
6
8
4
.5
9
0
.01
2
1
2
0
8
7
2
0
.1
9
3
-
1
.98
E+15
6
.10
3
2
7
7
8
0
8
1
4
8
8
3
1
4
.0
1
5
0
.01
2
3
8
4
5
0
4
0
.1
9
11
1
0
9
2
4
0
4
.9
8
4
.01
5
2
8
3
3
0
3
1
1
2
8
2
4
7
.9
4
0
.01
6
3
3
6
8
4
8
0
.1
9
12
-
3
.02
0
9
8
E+12
5
.62
2
2
7
7
1
1
9
1
4
2
8
4
5
6
.3
7
0
.01
2
9
0
3
4
5
8
0
.1
11
6
-
7
5
8
5
9
2
8
8
6
2
6
.85
0
7
2
9
8
8
8
1
3
5
8
6
1
3
.6
4
3
0
.01
3
5
6
6
7
9
4
0
.1
4.
CONCL
US
I
O
N
This
pa
pe
r
a
ddresse
d
r
outi
ng
opti
m
iz
at
i
on
pro
blem
s
ov
e
r
a
d
hoc
connecti
on
t
hat
pe
rfor
m
m
axi
m
iz
ation
of
the
bit
rate
under
t
he
tot
al
nodal
delay
and
pro
bab
il
i
ty
of
pac
ket
loss
c
on
st
raints
.
we
pro
po
se
d
a
n
optim
al
ro
utin
g
proce
dure
a
nd
their
c
orrespo
ndin
g
al
go
rithm
s
that
are
ap
plied
in
bet
ween
nodes
to
sat
isfy
the
desig
ne
d
ob
j
ec
ti
ve
sta
rting
from
the
so
urce
node
a
nd
reac
hing
the
destin
at
ion
no
de
us
ing
t
he
Lagr
a
nge
Mult
ipli
er
op
ti
m
iz
a
ti
on
.
T
he
opti
m
al
path
rep
re
sented
the
bes
t
fit
m
easur
em
ent
that
ver
ifie
s
the
obj
ect
ive
f
unc
ti
on
over
an
a
dd
it
ive
w
hite
Gau
s
sia
n
nois
e
cha
nnel
.
R
e
su
lt
s
s
how
t
he
ef
fecti
ven
e
ss
of
the
pro
po
se
d
s
che
m
e
in m
axi
m
izing
t
he object
i
ve fu
nctio
n
.
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a
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h
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u
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t
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t
u
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f
e
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c
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m
ult
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