Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 3
,
Ju
n
e
201
6, p
p
. 1
122
~ 11
32
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
3.9
961
1
122
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Analysis
of
IEEE
802.15.4 Beacon-
E
nabled MAC Prot
ocol
Ng
a
Dinh
, S
a
ngs
o
o
n
Lim
Software R&D
Center
, Samsung El
ectron
i
cs, Seoul, South
Korea
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ma
r 5, 2016
Rev
i
sed
Mar
27
, 20
16
Accepted Apr 10, 2016
This paper
aims to develop sev
e
ral ma
th
ematical models to stu
d
y
medium
acc
ess control (MAC) protocol in the IEEE 802
.15.4 bea
c
on-en
abled m
ode
with star topolo
g
y
. In particular, the
MAC protocol which
employ
s a slotted
carri
er-sense m
u
ltipl
e
a
c
c
e
ss with co
ll
ision avo
i
d
a
nce
(CSMA/CA) algorithm
used in the contention
access period (C
AP) of a
superframe is modelled.
The
anal
ys
is
s
t
udies
the effe
ct
ivenes
s
of the CS
M
A
/
C
A algorithm
and provides
expli
c
it m
a
them
ati
cal
expres
s
i
on
s
for power con
s
um
ption, ac
ces
s
dela
y,
an
d
data fr
ame dr
op probability
. The proposed
models precisely
fo
llow
CSMA/CA algo
rithm in MAC
protocol
of beacon-enabled mode and differ
from those previously
published
in the
lit
erature
as 1) they
are d
e
rived based
on data
frame g
e
neration r
a
te o
f
end
devices, 2)
they
provid
e
a
completed
expression for fr
ame access delay
,
and 3)
lowpower states of
en
d devices are
cons
idered for
power effic
i
enc
y
ev
aluations. The paper shows how power
consumption of
end d
e
vices is
improve
d on
t
h
e ba
lan
ce wi
th
dat
a
fr
am
e
dela
y.
The v
a
lid
it
y
o
f
the propo
sed m
odels is confirmed and co
mplemented
b
y
ext
e
nsive
sim
u
lations
.
Keyword:
80
2.
1
5
.
4
Analy
s
is
Lo
w P
o
we
r
WP
AN
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Sang
soon
Lim
,
Soft
ware
R&
D
Center,
Sam
s
ung El
ect
ro
ni
cs,
56
,
Se
o
ngc
h
o
n
-
gi
l
,
Seoc
h
o
-
g
u, Seo
u
l
,
K
o
re
a.
Em
a
il: lssg
o
od8
0@g
m
ai
l.co
m
1.
INTRODUCTION
Int
e
re
st
i
n
l
o
w p
o
w
er
wi
re
l
e
ss pr
ot
oc
ol
has l
e
d t
o
w
o
rk
on t
h
e IE
E
E
80
2.
1
5
.
4
st
a
nda
r
d
w
h
i
c
h
specifies t
h
e
physical (PHY) and m
e
dium
access c
ontrol
(MAC
) layers of
networks
[1]. The
standard
is
devel
ope
d
fo
r
per
s
o
n
al
area
net
w
or
ks
(P
ANs
)
wi
t
h
l
o
w p
o
w
er
co
ns
um
pt
i
on, l
o
w
com
p
l
e
xi
t
y
, and
hi
g
h
reliability which ena
b
le PANs to be
widel
y
em
ployed in
m
a
ny industri
a
l
applications
such as E-hea
lthcare,
hom
e aut
o
m
a
tion
,
en
vi
r
onm
ent
a
l
m
oni
t
o
ri
n
g
, an
d i
n
du
st
ri
al
aut
o
m
a
ti
on [
2
]
.
A PA
N i
s
com
posed
of o
n
e
PA
N
co
ord
i
n
a
tor and
m
u
ltip
le en
d d
e
v
i
ces (h
ereafter
d
e
no
te
d
as d
e
v
i
ces)
which
transm
i
t
d
a
ta fram
e
s (h
ereafter
denoted as
fra
m
e
s) to the coordi
nat
o
r. Dependi
ng on
t
h
e
application
requirem
ents, an
IEEE 802.15.4 P
AN
can
o
p
e
r
a
te in eith
er
o
f
two
to
po
log
i
es: star
top
o
l
og
y and p
eer-
t
o-p
eer
t
o
po
log
y
.
I
n
the star
topo
logy, th
e
comm
unication is establishe
d bet
w
een
de
vices and the
PAN
coordi
na
tor. In pee
r-t
o-pee
r
topol
ogy, each
devi
ce i
s
capa
b
l
e
of c
o
m
m
u
n
i
cat
i
ng
wi
t
h
any
ot
he
r de
vi
ces wi
t
h
i
n
i
t
s
radi
o sp
here
o
f
i
n
fl
u
e
nce
.
Th
e IEE
E
80
2.
1
5
.
4
st
an
d
a
rd s
u
pp
o
r
t
s
t
w
o c
h
a
nnel
ac
cess al
go
ri
t
h
m
s
. A
beac
on
-e
nabl
e
d
P
AN
u
s
es a sl
ot
t
e
d c
a
rri
e
r
sense
m
u
ltiple
access
with c
o
llision a
v
oida
nce
(CSMA/
C
A
) algorithm
t
o
access radi
o channel. The
slot
bounda
ries
of
each
device a
r
e aligne
d with
the slot bounda
ries of the
PAN coordi
nato
r. On the
othe
r hand, if
beacons
are
not available (non-beac
on-ena
bled PAN),
a si
m
p
le unslotted CSMA/CA al
gorithm
is use
d
.
Th
er
e h
a
s
b
e
en d
i
v
e
r
s
e r
e
search
es
o
n
th
e IEEE 80
2.
15.
4
stan
d
a
rd
(
s
ee
[3
]–
[7
],
[9
],
[10
]
,
[
12
]–
[16
]
and
refe
rences
t
h
e
r
ei
n).
Per
f
o
rm
ance e
v
al
uat
i
o
n
o
f
t
h
e
IE
EE
80
2.
1
5
.
4
M
A
C
pr
ot
oc
ol
has
bee
n
ca
rri
e
d
out
by
sim
u
l
a
t
i
ons fo
r
sm
al
l and l
o
w
l
o
ad net
w
o
r
ks
i
n
[4]
and
fo
r
dense
net
w
or
ks i
n
[
5
]
.
It
s t
h
r
o
ug
h
put
an
d
del
a
y
were also
ev
al
u
a
ted
b
y
m
easu
r
em
en
ts and
si
m
u
latio
n
s
in
[6
].
In
ad
d
ition
,
Wan
g
et al. [7
] co
m
p
ared po
wer
con
s
um
pt
i
on,
t
h
r
o
ug
h
put
, a
n
d
en
d-t
o
en
d
del
a
y
bet
w
ee
n sl
o
t
t
e
d an
d
unsl
o
t
t
e
d C
S
M
A
/
C
A
al
go
ri
t
h
m
s
by
us
i
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ana
l
ysis o
f
I
E
EE 802
.1
5.4 Bea
c
on
Enab
led MAC Pro
t
o
c
o
l
(Ng
a
D
i
nh
)
1
123
OPNET sim
u
lations. More
recently,
the authors
[8] carried
out a
n
extensi
v
e anal
ysis based on bot
h
si
m
u
latio
n
s
and
exp
e
rim
e
n
t
s to
inv
e
stig
ate en
erg
y
efficien
cy, scalab
ility, reliab
ility, an
d
t
i
m
e
l
i
n
e
ss
p
r
o
b
le
m
s
of IEEE 802.15.4. MAC pa
ra
m
e
ters were set to increas
e
delivery ratio but with th
e
cost of a
n
inc
r
eased
l
a
t
e
ncy
.
Fu
rt
he
rm
ore, som
e
studi
es
ha
ve ana
l
y
t
i
call
y
eval
uat
e
d t
h
e be
ha
v
i
or
of sl
ot
t
e
d
C
S
M
A
/
C
A al
g
o
ri
t
h
m
in IEEE
802.15.4 MAC protoc
ols. In [9], the aut
h
ors
deri
ved t
h
e
proba
b
ility distribution of access
delay and
throughput of IEEE
80
2.15.4
beacon-e
n
a
b
led PAN
with uplink t
r
ans
m
ission in
non-sat
u
ration m
ode
.
In
an
o
t
h
e
r stud
y [1
0
]
,
Po
llin
et al. p
r
esen
ted
an an
alytical
m
o
d
e
l fo
r MA
C l
a
yer and
ev
aluated
throug
hput an
d
energy for sl
otted CSMA/
C
A algor
ith
m
.
Th
e
k
e
y approx
im
at
io
n
in th
e m
o
d
e
l is th
at carrier
sen
s
ing
probability is
constant and inde
pe
nde
nt. Delay anal
ysis for
IEEE
802.15.4
CSMA/
C
A algorithm with
het
e
r
oge
ne
ous
bu
ffe
red t
r
a
f
f
i
c was anal
y
zed i
n
[
11]
. T
h
e aut
h
o
r
s he
r
e
used a M
a
r
k
o
v
ch
ai
n t
o
prese
n
t
CSMA/CA
p
r
ocess and
M/G/
1
/
K
qu
eu
es to
ch
aracter th
e
bu
ffered
con
d
itio
n. Th
ose
work
s
[9
]–[1
1
]
are b
a
sed
on
m
odel
i
n
[
12]
a
n
d
use
d
a M
a
rk
o
v
chai
n t
o
desc
ri
be
devi
ce st
at
es.
Ho
we
ver
,
t
h
e
st
at
us o
f
back
of
f t
i
m
e
cou
n
t
e
r i
s
not
M
a
rko
v
i
a
n a
s
i
t
s
val
u
e depen
d
s o
n
t
h
e past
hi
st
ory
(i
.e., h
o
w
m
a
ny
t
i
m
e
s a devi
ce has
atte
m
p
ted to access radi
o channel and
found it busy; af
ter each ti
m
e
, the backoff
exponent is in
creased by
one
). T
h
r
o
ug
h
put
a
nd e
n
er
gy
were al
so a
n
al
y
zed i
n
[1
3]
w
i
t
h
t
h
e assum
p
t
i
on t
h
at
t
h
e
uni
fo
rm
di
st
ri
but
i
on
of
back
o
ff co
u
n
ter is geom
etrical so
that the backoff algorith
m becom
e
s
me
m
o
ryless. The evaluation of IEE
E
80
2.
1
5
.
4
M
A
C
prot
ocol
i
s
furt
her st
udi
e
d
i
n
[
14]
. T
h
e aut
h
or he
re
pr
op
ose
d
a m
odel
t
o
descri
be t
h
e
probability of
packet succes
sful tra
n
sm
ission rece
ption and m
ean
delay statistic for both contention
access
peri
od
(C
AP)
and
co
nt
e
n
t
i
o
n
free
pe
ri
o
d
(C
FP) i
n
a
su
pe
rf
ram
e
i
n
st
ar an
d t
r
ee
t
o
pol
ogi
es. T
h
e m
odel
use
d
Markov chai
n assum
i
ng tha
t
each
device
always ha
s
one fram
e to transm
it. Th
roughput a
n
d
delay of
unsl
o
t
t
e
d I
EEE
80
2.
1
5
.
4
we
re
add
r
esse
d i
n
[
15]
but
wi
t
h
si
m
p
l
e
net
w
or
k
con
d
i
t
i
on:
t
h
e
PA
N co
nsi
s
t
s
of
o
n
l
y
one
c
o
o
r
di
nat
o
r
a
n
d
one
de
vi
ce.
M
o
re rece
nt
l
y
,
t
h
e
a
u
t
h
o
r
s
i
n
[1
6]
pr
o
pos
ed a n
ovel
adapt
i
v
e d
u
t
y
cy
cl
e
al
go
ri
t
h
m
whi
c
h m
a
kes
m
a
xim
u
m
use of ne
t
w
o
r
k t
r
a
ffi
c f
o
r a
u
t
o
m
a
t
i
c
al
ly
adju
st
i
ng
dut
y
cy
cl
e t
o
m
i
n
i
m
i
ze
po
we
r c
ons
um
pt
i
o
n
.
Power con
s
u
m
p
tio
n is on
e
of th
e
forem
o
st con
cer
ns fo
r t
h
e
IE
EE 80
2.
15
.4 connected
devices
.
Ho
we
ver
,
m
o
st
pre
v
i
o
us
res
earch
di
d
not
suf
f
i
c
i
e
nt
l
y
st
u
d
y
p
o
w
er
co
n
s
um
pt
i
on.
In
p
a
rt
i
c
ul
ar,
l
o
w-
po
we
r
st
at
es whi
c
h c
a
n si
g
n
i
f
i
c
a
n
t
l
y
im
prove
p
o
w
er e
ffi
ci
ency
were
n
o
t
wel
l
-
st
u
d
i
e
d e
v
en t
h
e IE
EE 8
0
2
.
1
5.
4 ha
s
i
n
act
i
v
e pe
ri
o
d
d
u
ri
ng
whi
c
h de
vi
ces t
o
e
n
t
e
r l
o
w p
o
w
er m
ode fo
r p
o
we
r savi
n
g
.
Thi
s
pa
per t
h
eref
ore
considers diffe
r
ent power
sta
t
es while
m
o
deling powe
r c
ons
um
pti
on for IEEE
802.15.4 connected devices.
Besid
e
s power con
s
u
m
p
tio
n,
d
e
lay and
frame d
r
op
p
r
ob
ab
i
lity wh
ich
would
d
e
grad
e qu
ality o
f
serv
ice (QoS)
fo
r m
a
ny
ap
pl
i
cat
i
ons al
s
o
ne
ed t
o
be c
onsi
d
ered
seri
ousl
y
.
For
e
x
am
pl
e, i
n
hom
e aut
o
m
a
t
i
on,
use
r
s e
x
pect
t
o
o
p
e
rate and
mo
n
itor th
eir homes re
m
o
tely
at an
y ti
me. Th
ey also need their hom
es
real-tim
e inform
ation
,
fo
r
instance, whe
n
te
m
p
erature re
aches a
certain th
resho
l
d. Ev
en
app
licatio
n
s
with
string
en
t ti
m
i
n
g
requ
iremen
ts
can be s
o
l
v
e
d
by
usi
n
g c
ont
e
n
t
i
on
free
pe
ri
od
(C
FP
) o
f
a
sup
e
r
fram
e
, t
h
e num
ber o
f
g
u
ara
n
t
eed t
i
m
e sl
ot
s
(GT
S
s)
i
n
t
h
e
C
FP i
s
l
i
m
it
ed
t
o
se
ven
[
1
4]
.
M
ean
del
a
y
o
f
a fr
am
e was al
so m
e
nt
i
one
d i
n
[1
4]
but
t
h
e
m
odel
here starte
d from
the reception
of the be
ac
on fram
e.
In fact, access delay is calculate
d from
the point the
fram
e
is g
e
n
e
rated
u
n
til th
e p
o
i
n
t
it is
actu
a
lly sen
t
. Un
lik
e th
e app
r
o
a
ch
in
[14
]
, we
p
r
op
o
s
e a co
m
p
lete
m
odel for
fra
me access delay. In
addition to delay,
we
propose m
odel
s
for
po
we
r consum
ption a
nd fram
e
d
r
op
prob
ab
ility wh
ile con
s
idering
th
e limit
atio
n
s
o
f
p
r
ev
i
o
u
s
research. Th
e p
r
o
p
o
s
ed
m
o
d
e
ls
are
d
e
riv
e
d
fram
e
generat
i
on
rat
e
o
f
de
vi
ces and t
h
u
s
t
h
ey
are m
o
re
r
eal
i
s
t
i
c
and no
vel
ap
pr
oac
h
com
p
ared t
o
pr
evi
o
u
s
st
udi
es.
The re
st
o
f
t
h
i
s
pa
per
pr
ocee
ds as
fol
l
o
ws.
Sect
i
on
II
desc
ri
bes t
h
e
sl
ot
t
e
d C
S
M
A
/
C
A a
l
go
ri
t
h
m
i
n
IEEE
802.15.4. Analytical
m
odels a
r
e prese
n
ted in
Sec
tion
III. Next, Section IV
provide
s
sim
u
lation re
sults
t
o
val
i
d
at
e
o
u
r
m
odel
s
. Fi
nal
l
y
, Sect
i
o
n
V
c
oncl
ude
s
ou
r
p
a
per
.
2.
SLOTTED CSMA/CA ALGORITHM
Acco
r
d
i
n
g t
o
t
h
e IE
EE 8
0
2
.
1
5.
4 M
A
C
p
r
ot
ocol
[
1
]
,
t
h
e ac
cess t
o
t
h
e c
h
a
nnel
i
s
m
a
nage
d t
h
r
o
ug
h a
sup
e
r
fram
e
, st
art
i
ng
wi
t
h
a
be
acon
fr
am
e t
r
ansm
i
t
t
e
d by
t
h
e PA
N co
o
r
di
n
a
t
o
r.
The s
u
per
fram
e
i
s
di
vi
de
d i
n
t
o
16 e
q
ual
l
y
si
ze sl
ot
s. O
p
t
i
o
n
a
l
l
y
, t
h
e supe
r
fram
e
can ha
v
e
an act
i
v
e
per
i
od a
nd
an i
n
a
c
t
i
v
e peri
od
. I
n
act
i
v
e
peri
od i
s
use
d
fo
r p
o
we
r sa
vi
ng as
devi
ces
can swi
t
c
h
of
f
du
ri
n
g
t
h
i
s
pe
r
i
od. T
h
e act
i
v
e
po
rt
i
on m
a
y
consi
s
t
of a CAP a
n
d a
CFP, a
s
s
h
own in Figure
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
11
2
2
– 11
32
1
124
Fi
gu
re
1.
S
upe
rf
ram
e
st
ruct
ur
e co
nsi
s
t
i
n
g
o
f
an active
pe
riod a
n
d an inacti
v
e
peri
od
Any
devi
ce
w
i
shi
n
g t
o
c
o
m
m
uni
cat
e duri
ng C
A
P c
o
m
p
et
es wi
t
h
ot
he
r de
vi
ces
usi
n
g a sl
ot
t
e
d
C
S
M
A
/
C
A al
go
ri
t
h
m
.
In C
FP,
GTS
p
o
rt
i
ons
are
de
di
ca
t
e
d by
t
h
e P
A
N c
o
o
r
di
nat
o
r
t
o
a
ppl
i
cat
i
o
n
s
t
h
at
require speci
fic
data ba
ndwi
dth [1].
T
h
e
le
ngt
h of
th
e
superfram
e
(called the
beacon
interval, BI) a
n
d the
l
e
ngt
h
of ac
t
i
v
e peri
o
d
(
cal
l
e
d supe
rf
r
a
m
e
durat
i
o
n,
SD) a
r
e d
e
fi
ne
d as f
o
l
l
o
ws [
1
]
:
B
I
=
aB
aseS
u
p
erf
r
a
m
eD
ur
at
i
o
n
ⅹ
2
BO
and S
D
=
aBase
S
u
p
erf
r
ame
D
u
r
at
i
o
n
ⅹ
2
SO
w
h
er
e
aB
aseS
u
p
erf
r
a
m
eD
ur
at
i
o
n
= 96
0 sy
m
bol
s or
15
.3
6 m
s
[1
4]
;
BO
and
SO
d
e
no
te th
e b
eacon
or
der
and
superfram
e
order, res
p
ectivel
y. These value
s
ar
e det
e
rm
i
n
ed by
t
h
e co
or
di
nat
o
r an
d sat
i
sfi
e
d 2
≤
SO
≤
BO
≤
1
4
. Th
e ratio
o
f
activ
e p
e
riod
to
th
e wh
o
l
e su
p
e
rfram
e
d
u
ration
,
wh
ich is eq
u
a
l to
2
-(BO-SO
)
, is ca
lle
d
du
ty
cycle.
CSMA/CA al
go
rith
m
is u
s
ed
b
e
fo
re tran
sm
i
ssio
n
of a
d
a
ta fram
e
. In
sl
o
tted
CSM
A
/CA
alg
o
rith
m
,
the bac
k
off sl
ot boundaries
of each de
vi
ce are aligned
with the superfram
e
sl
ot bounda
ries of
the c
o
ordinator.
The
begi
nni
ng
of t
h
e fi
r
s
t
b
ack o
ff
pe
ri
o
d
of eac
h
devi
c
e
i
s
al
i
gned
w
i
t
h
t
h
e be
gi
n
n
i
ng
o
f
beac
o
n
fram
e
t
r
ansm
i
ssi
on.
Ho
we
ver
,
t
r
a
n
sm
i
ssi
ons m
a
y st
art
o
n
t
h
e
b
o
u
n
d
ary
of
ba
cko
f
f
sl
ot
s.
Ea
ch
devi
ce m
a
int
a
i
n
s
th
ree v
a
riab
les fo
r tran
sm
issi
o
n
attem
p
t:
NB
,
CW
, and
BE
.
NB
is th
e n
u
m
b
e
r o
f
ti
m
e
s CSMA/CA alg
o
rith
m
was re
qui
r
e
d t
o
bac
k
of
f w
h
i
l
e
att
e
m
p
t
i
ng t
h
e curre
nt
t
r
ansm
i
ssi
on.
CW
i
s
t
h
e num
ber o
f
bac
k
of
f
sl
ot
s,
d
e
no
ted as t
b-slot
, th
at n
e
ed
t
o
b
e
clear of chan
n
e
l activ
ity
b
e
fo
re tran
sm
i
ssio
n
.
NB
i
s
t
h
e bac
k
o
f
f
ex
p
one
nt
related
to how
man
y
t
b-slot
a device s
h
all wait
before
attem
p
ting to acce
ss c
h
annel
[1].
In
beac
on
-ena
bl
ed P
A
Ns,
w
h
en a
de
vi
ce wi
shes t
o
t
r
a
n
s
f
er
dat
a
t
o
a c
o
o
r
di
nat
o
r, i
t
f
i
rst
l
i
s
t
e
ns fo
r
the
net
w
ork beacon. Whe
n
beacon
is found,
t
h
e device s
y
nchronizes to the s
upe
r
fra
me structure.
The
n
, it
t
r
ansm
i
t
s
dat
a
fram
e
t
o
t
h
e coo
r
di
nat
o
r usi
ng sl
ot
t
e
d C
S
M
A
/
C
A al
go
ri
t
h
m
,
as expl
ained i
n
Fi
gu
re
2. Fi
rst
,
NB
,
CW
, and
BE
are in
itialized
to
0, 2, an
d
BE
min
, res
p
ect
i
v
el
y
,
and
devi
ce l
o
cat
es
t
h
e bo
u
nda
ry
of
next
b
ackof
f
p
e
r
i
od
(
S
tep 1)
.
Up
on r
ecep
tio
n of
t
h
e b
eaco
n
,
d
e
v
i
ce d
e
lays for
a
r
a
ndo
m
n
u
m
b
e
r
of
t
b-slot
slots i
n
the
r
a
ng
e fro
m
0
t
o
2
BE
-1
(Step
2
)
. T
h
en
, the P
HY lay
e
r
per
f
o
rm
s cl
ear channel assessm
ent (CCA)
(Ste
p
3). The
carri
er se
nsi
n
g
st
art
s
on a b
acko
ff
peri
od
bo
u
nda
ry
. The
M
A
C
l
a
y
e
r then
pr
ocee
ds,
pro
v
i
d
e
d
t
h
at
t
h
e
rem
a
in
in
g
CSMA/CA algo
ri
th
m
step
s includi
ng
fram
e tr
ansm
ission and any ac
knowl
e
dgm
ent are c
o
m
p
leted
before t
h
e end of a CAP sl
ot
. If the M
A
C layer cannot
proceed, it
m
u
st wait until the start of CAP in ne
xt
sup
e
r
fram
e
and t
h
e
n
re
peat
a
g
ai
n.
I
f
t
h
e c
h
a
nnel
i
s
assessed
bu
sy
(Step
4), th
e M
A
C layer in
creases bo
th
NB
and
BE
by
one
, ensu
ri
n
g
t
h
at
BE
is n
o
t
m
o
re th
an
aMA
XBE
, and
CW
is set to
2
.
If
NB
is less th
an
or equal to
mac
M
axC
S
MA
Back
offs
, th
e C
S
MA/CA al
g
o
rith
m
retu
rn
s
Step
2
,
el
se it termin
ates with
T
r
ansm
ission Fa
ilure
status. If t
h
e c
h
annel is
assess
ed to be
free (Step 5),
t
h
e M
A
C layer m
u
st en
sure t
h
at th
e co
n
t
en
tio
n wi
n
d
o
w
is
expi
red
before data transm
ission. For this, t
h
e MAC layer decreases
CW
by 1
.
I
f
CW
is
greater th
an
0, it
m
u
st
go
t
o
St
ep
3,
el
se i
t
st
art
s
t
o
t
r
ansm
i
t
on t
h
e
b
o
u
n
d
ary
of
t
h
e
next
sl
ot
peri
o
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ana
l
ysis o
f
I
E
EE 802
.1
5.4 Bea
c
on
Enab
led MAC Pro
t
o
c
o
l
(Ng
a
D
i
nh
)
1
125
Fi
gu
re
2.
Sl
ot
t
e
d C
S
M
A
/
C
A
Al
g
o
ri
t
h
m
3.
AN
ALYTI
C
A
L
MO
DELS
The a
n
alysis is restricted t
o
upstream
traffic
from
devi
ces t
o
t
h
e PA
N
c
o
or
di
nat
o
r.
W
e
assum
e
t
h
at
t
h
ere i
s
o
n
e
P
A
N
co
o
r
di
nat
o
r a
n
d
t
w
o
de
vi
ces i
n
IEE
E
80
2.
15
.4
st
ar
t
o
p
o
l
o
gy
. F
r
am
e generat
i
o
n
rat
e
of
eac
h
devi
ce
i
s
ass
u
m
e
d t
o
fol
l
o
w
Poi
s
s
o
n
di
st
ri
b
u
t
i
o
n
wi
t
h
a
ra
t
e
(
n
um
ber
of
f
r
am
es per
seco
nd
).
I
n
a
d
di
t
i
on,
C
A
P sl
ot
o
f
a
sup
e
r
fram
e
i
s
assum
e
d t
o
be
l
o
n
g
e
n
ou
g
h
so t
h
at
fr
am
e transm
i
ssi
on i
s
fi
ni
s
h
ed
wi
t
h
i
n
one
CAP sl
ot. In addition, since ack
nowledgm
ent is optional i
n
the
IEEE 802.15.4 standa
rd [1]
,
no
acknowledgm
e
nt is im
ple
m
ented for sim
p
lic
ity. The IEEE
802.15.4 standard lim
its
the
num
ber of tim
e
s that
a d
e
v
i
ce tries
to
attem
p
t cu
rren
t tran
sm
issi
o
n
to
3
.
Th
is
p
a
p
e
r t
h
erefore set
NB
to
3
.
If
a
fram
e
cann
o
t
be
tran
sm
it
ted
aft
e
r three attem
p
ts, it will b
e
dro
p
p
e
d
.
Ot
herwise, th
e
d
e
v
i
ce
tran
sm
its th
at fram
e
fo
r a
d
u
ratio
n
T
T
. This section de
rive
s num
e
rical
m
o
d
e
ls for
1)
m
e
an access del
a
y of data fra
m
es 2) m
ean
powe
r
co
nsu
m
p
tio
n
of a
d
e
v
i
ce, an
d
3
)
d
a
ta
fram
e
drop
p
r
ob
ab
ility du
ri
n
g
CAP of sup
e
rfram
e
.
3.
1.
Aver
age Acce
ss
Del
a
y
Befo
re sen
d
in
g a fram
e
to the PA
N co
or
d
i
nator
,
th
e d
e
vice first waits
for th
e n
e
twork
b
eaco
n
[1
].
We let T
W
d
e
no
te th
is waiting
ti
m
e
. As th
e
au
tho
r
s are aware, m
o
st p
r
ev
io
u
s
wo
rk
s
d
i
d
n
o
t
co
nsid
er T
W
but
T
W
can
sig
n
i
fican
tly i
m
p
act o
v
erall d
e
lay as we will see in
Sectio
n
IV.
Access d
e
lay refers to
th
e in
terval th
e
fram
e
is generated up to t
h
e poi
nt that the fram
e
is a
c
tually sent. Only access delay for s
u
cce
ssfully
tran
sm
it
ted
frames is con
s
id
ered, i.e.,
d
e
la
y
cause
d
by
dr
op
ped
f
r
am
es i
s
i
g
n
o
r
ed
. Let
T
S
d
e
no
te th
e du
ration
of a superfram
e
. To calculate T
W
, we di
vi
de
t
h
e supe
rf
ram
e
i
n
t
o
M
sm
all subi
nt
e
r
val
s
whe
r
e M
i
s
suffi
ci
ent
larg
e. Let
m
den
o
t
e th
e
waitin
g tim
e fo
r
b
e
aco
n
fram
e o
f
a
d
a
ta fram
e g
e
nerated
du
ri
n
g
th
e
m
th sub-in
t
e
rv
al,
m
i
s
gi
ven
by
(1
)
Because Poisson
process is me
m
o
ryless, t
h
e proba
b
ilitie
s
of fram
e generated duri
ng e
ach subinterval
are the
sam
e
. Triv
ially
th
en, T
W
is d
e
t
e
rm
in
ed
as:
(2
)
Since
, T
W
can
b
e
sim
p
ly re-written
as:
(3
)
Sin
ce th
e nu
m
b
er of attem
p
ts
to
d
a
ta tran
smissio
n
is
li
m
ite
d
to 3,
we co
nsid
er t
h
ree
fo
llowing
cases.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
11
2
2
– 11
32
1
126
C
a
se 1:
A devi
ce t
r
ansm
it
s dat
a
aft
e
r onl
y
on
e at
t
e
m
p
t
,
as sho
w
n i
n
Fi
g
u
r
e
3. Let
T
1
, T
1
B
, and T
1
CCA
be the m
ean ac
cess delay,
bac
k
off du
rat
i
o
n,
and
car
ri
er se
n
s
i
ng
d
u
rat
i
o
ns,
res
p
ect
i
v
el
y
.
At
t
h
e
begi
nni
ng
o
f
a
sup
e
r
fram
e
, t
h
e devi
ce bac
k
s
off a
n
d bac
k
o
ff d
u
r
at
i
on i
s
u
n
i
f
orm
l
y
di
st
ribut
e
d
f
r
om
0 t
o
2
BE
-1
,
T
1
B
i
s
gi
ve
n
by
(4
)
Fig
u
re
3
.
CSM
A
/CA
o
p
eration
wh
en
a d
e
v
i
ce tran
sm
its d
a
ta after
on
ly one atte
m
p
t
Next
,
P
H
Y
l
a
y
e
r pe
rf
o
r
m
s
carri
er
se
nsi
n
g
d
u
ri
ng
t
w
o c
ons
ecut
i
v
e
t
b-slot
sl
ot
s.
Si
nce
t
h
e
de
vi
ce
tran
sm
its d
a
ta in
th
e
first attem
p
t, ch
an
n
e
l is free
du
ri
n
g
carrier
sen
s
i
n
g. Let
p
b
e
t
h
e
p
r
ob
ab
ility th
at chan
n
e
l
is free
d
u
ri
ng
one
t
b-slot
sl
ot
.
Si
nce P
o
i
s
s
o
n
pr
ocess
i
s
m
e
m
o
ry
l
e
ss and
b
acko
f
f
pe
ri
o
d
i
s
u
n
i
f
orm
di
st
r
i
but
i
o
n,
p
is also
th
e pro
b
a
b
ility th
at no
fram
e
is g
e
n
e
rated
du
ring
t
b-
slot
. Acc
o
rding
to P
o
isson
process,
p
i
s
gi
ve
n
by
(5
)
Let
P
1
b
e
th
e
prob
ab
ility o
f
case 1, we th
en
hav
e
(6
)
The m
ean acce
ss delay
of cas
e 1 is
there
f
ore
determ
ined as
(7
)
Case 2
:
A d
e
vice tran
smits d
a
ta after two
atte
m
p
ts, as sh
o
w
n
in
Fi
g
u
re 4
.
Th
is m
ean
s th
at d
u
ring
carrier sen
s
ing
o
f
th
e first atte
m
p
t,
th
e ch
annel is b
u
s
y eith
er in
th
e first t
b-s
l
ot
(subcase
2-
1
)
or i
n
t
h
e sec
o
nd t
b-
slot
gi
ve
n t
h
at
t
h
e
fi
rst
t
b-slot
is
free (s
ubca
s
e 2-2). In
the second
atte
m
p
t, chan
n
e
l is free
du
ri
n
g
two
co
n
s
ecu
tiv
e
t
b-slot
of sensi
n
g
process. These two subca
s
es are t
h
e sa
me, except t
o
tal num
ber
of
t
b-slot
slots for
carrie
r
sensi
n
g.
Let
P
1
2
d
e
n
o
t
e t
h
e
p
r
o
b
a
b
ility o
f
sub
case
2
-
1
,
P
1
2
i
s
gi
ven
by
(8
)
Si
m
ilarly, let P
2
2
d
e
no
te th
e
p
r
o
b
a
b
ility o
f
sub
case
2
-
2
,
P
2
2
i
s
gi
ven
by
(9
)
Fig
u
re
4
.
CSM
A
/CA
o
p
eration
wh
en
a d
e
v
i
ce tran
sm
its d
a
ta after t
w
o attem
p
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
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I
S
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0
8
Ana
l
ysis o
f
I
E
EE 802
.1
5.4 Bea
c
on
Enab
led MAC Pro
t
o
c
o
l
(Ng
a
D
i
nh
)
1
127
In
add
itio
n, let T
1
2
and T
2
2
be
the m
ean access delay
of s
ubcase
2-1 and
2-2, res
p
ectivel
y. The
n
T
1
2
and T
2
2
are
det
e
rm
ined as follows:
(1
0)
(1
1)
In
(
1
0
)
a
n
d
(1
1)
, t
h
e
m
i
ddl
e t
e
rm
i
s
m
ean b
acko
f
f
du
rat
i
o
n,
de
n
o
t
e
d a
s
T
2
B
,
and
th
e la
s
t
te
r
m
s
a
r
e
th
e to
tal carrier sen
s
ing
du
ratio
n
s
fo
r subcases 2
-
i
, de
n
o
t
e
d as T
i
CCA2
with
(
i
= 1,2
)
. C
a
se 3:
A devi
ce
tran
sm
its d
a
ta after three attem
p
ts. Th
is m
e
an
s that rad
i
o
ch
ann
e
l is
bu
sy d
u
ring
carrier sen
s
ing
in first two
at
t
e
m
p
t
s
but
f
r
ee i
n
t
h
e l
a
st
at
t
e
m
p
t
.
C
a
se 3 i
s
fu
rt
he
r
di
vi
d
e
d i
n
t
o
f
o
ur s
u
bcases
3-
j
(
j
= 1, 2, 3, 4
)
,
as
s
h
o
w
n
in Fig. 5. T
h
es
e subcases a
r
e
th
e sam
e
, except total num
b
er of t
b-slot
slots for ca
rrie
r
se
nsing. Let P
j
3
a
nd
T
j
3
be
the proba
bility and m
ean access delay in subcase 3-
j
, we h
a
v
e
th
e
fo
llowing
s:
(1
2)
(1
3)
(1
4)
(1
5)
(1
6)
(1
7)
(1
8)
(1
9)
Fig
u
re
5
.
CSM
A
/CA
o
p
eration
wh
en
a d
e
v
i
ce tran
sm
its d
a
ta after t
h
ree atte
m
p
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
11
2
2
– 11
32
1
128
I
n
(1
3)
, (1
5)
, (1
7)
, and
(
19)
, t
h
e m
i
d
d
l
e term
is th
e m
ean
b
ackof
f
du
r
a
ti
o
n
,
d
e
no
ted as T
3
B
; th
e last
term
s
are the total carrier sens
in
g
dur
atio
ns f
o
r
sub
cases 3-
j
and are de
not
ed as T
j
CCA2
with (
j
= 1, 2, 3
,
4)
. Let
T
D
be t
h
e
final
mean fram
e
access delay.
The
n
,
T
D
is determin
ed
su
ch
t
h
at:
(2
0)
whe
r
e T
1
, T
i
2
, P
i
2
(
i
=
1,
2),
T
j
2
, a
n
d P
j
2
(
j
=
1, 2,
3
,
4)
are d
e
t
e
rm
i
n
ed by
(
7
)
-
(
1
9).
3.
2.
Power Consu
m
ption
We con
s
ider a co
m
p
leted
cy
cle fro
m
th
e po
in
t a fram
e is
g
e
n
e
rated
u
n
t
i
l
th
e p
o
i
n
t
it is
co
m
p
letel
y
transm
itted. Since in b
eac
on-ena
b
le PANs
, each de
vice knows whe
n
the ne
xt beac
on fram
e arrives, we
assu
m
e
th
at the d
e
v
i
ce is swi
t
ch
ed
off wh
ile it is waitin
g
fo
r th
e
b
eaco
n
fram
e to
redu
ce po
wer con
s
um
p
t
io
n.
In
ad
d
ition
,
we co
n
s
i
d
er th
e
Ch
ip
co
n
8
0
2
.
15
.4
co
m
p
lian
t
RF tran
sceiv
e
r, CC2
42
0
[15
]
. Th
e Ch
i
p
con rad
i
o
sup
p
o
rts
t
h
e fo
llowin
g
fo
ur
st
ates:
•
Sleep:
whe
n
device is waiting for a
beacon
fram
e
.
•
Idle:
whe
n
de
vice is
backi
n
g off.
•
Receive:
whe
n
device is
doi
n
g carrier se
nsi
n
g.
•
Tran
smit:
when
device is
tra
n
sm
itting frame.
Let W
S
, W
I
,
W
R
, a
n
d
W
T
be the
powe
r t
h
at device
cons
um
es in
Sleep
,
Id
le
,
Receive
, an
d
Tr
ansmit
states, res
p
ectively. The
n
W
S
< W
I
< W
T
< W
R
[15
]
. In
add
itio
n
,
let
W
1
, W
i
2
(
i
= 1
,
2)
, an
d W
j
3
(
j
= 1
,
2,
3,
4
)
be t
h
e
po
we
r
con
s
um
pt
i
on
o
f
case
1
,
s
u
bc
ase 2
-
i
, subca
s
e
3-
j
, res
p
ectively.
The
n
W
1
, W
i
2
, an
d
W
j
3
are
d
e
term
in
ed
as
fo
llows:
(2
1)
(2
2)
(2
3)
Assu
m
e
th
at po
wer and
tim
e
wh
en th
e device tran
s
ition
s
fro
m
o
n
e
po
wer state to an
oth
e
r can be
i
g
n
o
re
d a
n
d l
e
t
W
de
not
e t
h
e
fi
nal
po
wer
co
nsum
pt
i
o
n
o
f
t
h
e
devi
ce,
t
h
e
n
W
i
s
ap
pr
o
x
i
m
at
ely
exp
r
ess
e
d as
(2
4)
whe
r
e W
1
,W
i
2
, an
d
W
j
3
a
r
e c
a
l
c
ul
at
ed by
(2
1)
, (
2
2
)
, a
n
d (
2
3
)
,
res
p
ect
i
v
e
l
y
.
P
i
2
and
P
j
3
are
calculated in
sub-
section II
I-
A.
3.
3.
Dro
p
Pr
ob
abi
l
i
t
y
Let P
drop
d
e
note th
e fram
e
drop
p
r
ob
ab
ility du
ring
C
A
P.
A fram
e is d
r
o
p
p
e
d
if ch
ann
e
l is bu
sy
d
u
ring
carrier sen
s
ing
i
n
all three attem
p
ts. P
drop
is d
e
term
in
ed
in th
e
fo
llowing
way:
(2
5)
In
t
u
itiv
ely, h
i
gh
er d
a
ta
fram
e
g
e
n
e
ration
rat
e
or
larg
er num
b
e
r o
f
end
dev
i
ces in th
e
network wou
l
d
in
crease co
llisio
n pro
b
a
b
ility. As a
resu
lt, th
ere
will b
e
an
increase in fram
e
drop
p
r
ob
ab
ility.
4.
PERFO
R
MA
NCE E
V
ALU
A
TIO
N
To
supp
lem
e
n
t
th
e an
alytical resu
lts and to
d
e
term
in
e th
e
p
e
rfo
r
m
a
n
ce i
n
term
s of
p
o
wer
consum
ption,
access delay, a
n
d fram
e
drop
probability, C
programming i
s
us
e
d
t
o
sim
u
late upstream
t
r
affic
fr
om
devi
ces t
o
t
h
e P
A
N c
o
o
r
di
nat
o
r. T
h
i
s
sect
i
on
als
o
com
p
ares m
a
them
atical
resu
lts ob
tain
ed fro
m
anal
y
s
i
s
i
n
sec
t
i
on I
I
I
wi
t
h
s
i
m
u
l
a
t
i
on res
u
l
t
s
obt
ai
ne
d f
r
o
m
C
pro
g
ra
m
m
i
ng. Fram
e ge
nerat
i
o
n rat
e
s are
m
odel
e
d as a Poi
s
s
on
pr
oces
s;
t
h
e perf
o
r
m
a
nces o
f
ot
her
t
r
affi
c m
odel
s
are cur
r
e
n
t
l
y
bei
n
g i
nvest
i
g
at
ed.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ana
l
ysis o
f
I
E
EE 802
.1
5.4 Bea
c
on
Enab
led MAC Pro
t
o
c
o
l
(Ng
a
D
i
nh
)
1
129
Si
nce a dat
a
fr
am
e has 6 by
t
e
s for sy
nch
r
o
n
i
zat
i
on an
d PH
Y hea
d
ers
,
0-
1
27
by
t
e
s for
pa
y
l
oad, t
h
e f
r
am
e si
ze
v
a
ries
fro
m
6
t
o
1
3
3
b
y
tes [1]. In add
ition
,
th
e d
a
ta
rate
of th
e IEEE
8
0
2
.
1
5
.4 is
2
0
kbp
s, 40
kb
p
s
, an
d 250
kb
ps,
ca
n b
e
vari
ed i
n
t
h
e
ran
g
e [
1
9;
5
2
0
8
]
(f
ram
e
s/
secon
d
)
. Let
D
be
t
h
e num
ber
of
t
b-slot
slots that each
fram
e
occupi
es
whi
l
e
bei
n
g t
r
ansm
i
t
t
e
d, t
h
en
D i
s
an i
n
t
e
ge
r i
n
t
h
e ra
n
g
e [
2
]
,
[
13]
de
pe
nd
i
ng
on t
h
e m
i
ni
m
u
m
an
d
m
a
x
i
m
u
m
p
o
s
sib
l
e fram
e
size [1
],[12
]
. In
our sim
u
lati
o
n
, D is fix
e
d
at 3
resu
ltin
g
T
T
, wh
ich
is eq
u
a
l t
o
D. t
b-slot
, is 0.96 m
s
. The supe
rfra
m
e
length is de
fine
d by
the IEEE
802.15.4 standard as
aB
aseS
u
p
erf
r
a
m
eD
ur
at
i
o
n
ⅹ
2
BO
where
aB
a
s
eS
uperf
r
a
me
Dur
a
t
i
o
n
is 15.36
m
s
an
d
0
<
BO
<
14
. T
h
e
r
ef
ore
ou
r si
m
u
l
a
t
i
on,
B
I
i
s
va
ri
ed
fr
om
100
m
s
t
o
10
0
0
m
s
. The
sim
u
l
a
t
i
ons r
u
n
fo
r
1,
00
0,
0
0
0
t
i
m
e uni
t
s
an
d t
h
e
resul
t
s
a
r
e t
h
e
m
ean val
u
es f
r
o
m
100
di
ffe
re
nt
r
u
ns
wi
t
h
10
0
di
ffe
re
nt
see
d
val
u
es
.
Figure
6 illustrates how m
ean access delay
T
D
de
pen
d
s
o
n
su
per
fram
e
l
e
ngt
h T
S
whe
n
i
s
fi
xed
at
10
(f
ram
e
s/secon
d
)
. I
n
this f
i
gu
re, T
D
seem
s
to
b
e
lin
early in
creased with
T
S
. Thi
s
can be e
xpl
ai
ned as
follows: from
equation
(20) a
nd
related e
q
uati
ons for m
e
a
n
access
delay, we obse
rve t
h
at T
D
is co
m
p
osed of
T
S
/2 which is
m
u
ch larger
than rem
a
ining term
s because
a superfram
e
is m
u
ch longe
r than a CAP sl
ot and
back
o
ff
d
u
rat
i
on
. I
n
fact
, f
r
o
m
bot
h si
m
u
l
a
ti
on a
n
d num
e
rical analysis, we see that T
D
sl
ig
h
tly in
creases with
. T
h
at is because a hi
ghe
r
in
creases th
e
p
r
ob
ab
ility th
at th
e rad
i
o
ch
an
n
e
l is bu
sy du
ri
n
g
carrier sen
s
ing,
whic
h m
a
kes the de
vice try other attem
p
ts to access ra
di
o
channel. T
h
us,
access delay is increase
d
.
Howeve
r,
since
ju
st
h
a
s a sm
all i
m
p
a
c
t
on
T
D
, we
om
it the effects
of
in th
e
figu
re.
Fi
gu
re
7 eval
uat
e
s p
o
w
er c
ons
um
pt
i
on
of
a de
vi
ce w
h
i
l
e
l
o
wp
o
w
er
s
t
at
es are em
ploy
ed.
Th
e
param
e
t
e
rs are chose
n
base
d
on
[1
5]
as fol
l
o
ws:
W
S
= 144
mW
, W
I
= 7
12
W,
W
R
=
35
.2
8
mW
. W
T
can be
ch
ang
e
d
b
a
sed o
n
setting
,
w
e
th
erefore choose tran
sm
it
m
o
d
e
at 0
d
B
m
o
r
W
T
= 1
mW
.
Th
e fi
g
u
re illustrates
ho
w
p
o
we
r c
o
nsum
pt
i
o
n
de
p
e
nd
s
on
T
S
wh
en
i
s
fi
xe
d 10
an
d 1
0
0
(
f
r
a
m
e
s/
second
).
As
T
S
increa
se
s, the
po
we
r c
ons
um
pt
i
o
n
dy
nam
i
cal
l
y
decreases
. The
reas
on is
that a
higher T
S
m
a
kes a de
vice sleep
for a l
o
nge
r
ti
m
e
. In
fact, th
is sleep ti
m
e
is d
o
m
in
an
t in on
e
o
p
e
ra
tion cycle of t
h
e
device. T
h
e fi
gure als
o
s
h
ows tha
t
em
pl
oy
i
n
g
l
o
w
p
o
w
e
r
st
at
es si
gni
fi
cant
l
y
im
pr
o
v
es
po
we
r
efficiency. Power cons
um
pt
ion in the
worst
case
of
o
u
r sim
u
latio
n
is lo
wer th
an
th
at in
Id
le
state and is m
u
ch m
o
re lower t
h
a
n
power c
o
ns
um
ption in
Transm
i
t
or
Receive
states. Furt
herm
ore, it
can be i
n
fe
rre
d from
Figur
e 6 and Fi
gure 7
that po
we
r consum
ption and a
ccess
del
a
y
have a
t
r
ade
o
f
f
rel
a
t
i
ons
hi
p
.
I
n
cre
a
sed s
upe
rf
ra
m
e
l
e
ngt
h res
u
l
t
s
i
n
a bet
t
er p
o
w
e
r sa
vi
ng
b
u
t
sim
u
l
t
a
neousl
y
res
u
l
t
s
i
n
a
w
o
rse
del
a
y
per
f
o
r
m
a
nce. The
r
ef
ore
,
s
upe
rf
r
a
m
e
du
rat
i
o
n
can
be a
p
p
r
op
ri
at
el
y
cho
s
en
o
n
t
h
e
bal
a
nce
bet
w
ee
n
po
we
r c
ons
u
m
pti
on a
n
d
acc
ess del
a
y
.
Figure
6. Mean access
delay T
D
with
respect to
th
e
sup
e
r
fram
e
l
e
ngt
h
T
S
Fi
gu
re 7.
P
o
we
r
c
ons
um
pt
i
on W wi
t
h
respect
t
o
sup
e
r
fram
e
l
e
ngt
h
T
S
Fig
u
re 8
illu
strates h
o
w fram
e
d
r
o
p
p
r
ob
ab
ility Pd
rop
d
e
p
e
nd
s on
. As
ob
serve
d
f
r
o
m
the figu
re, a
s
increases
, P
drop
dyna
m
i
cally increases. T
h
at is because increase in
resu
lts in
h
i
gh
er p
r
ob
ab
ility t
h
at th
e
radi
o c
h
an
nel
i
s
b
u
sy
du
ri
n
g
carri
er
sen
s
i
n
g
.
Si
nce
t
h
e
num
b
e
r o
f
attemp
ts to curren
t
t
r
an
sm
issio
n
is
li
mited
to
th
ree, th
e frame d
r
o
p
p
r
o
b
a
b
ility
is in
creased
. In
add
itio
n
,
it
can
b
e
in
ferred
fro
m
Fig
u
r
e 8
th
at
has strong
i
m
pact on
frame drop
probab
il
ity; howe
v
er, it has little i
m
pa
ct on m
ean access delay.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
11
2
2
– 11
32
1
130
Fi
gu
re
8.
Fram
e d
r
o
p
pr
o
b
abi
l
i
t
y
P
drop
with
resp
ect to fram
e
g
e
n
e
ration
rat
e
of
en
d de
vi
ce
Figure
9
determines the a
ffe
ct of fram
e size on
P
drop
.
He
r
e
,
we
c
onsi
d
er
2.
45
G
h
z ba
nd
wi
t
h
dat
a
rat
e
of
2
5
0
k
b
p
s.
P
acket
si
ze
vari
es f
r
om
40
by
t
e
s t
o
1
3
0
by
tes. As
ca
n be s
een from
the
figure,
a
s
packet
size
increases
, P
drop
dec
r
eases. T
h
is is beca
use
a l
a
rge
r
packet si
ze re
duces
t
h
e
num
ber
of
f
r
a
m
es gene
rat
e
d
wi
t
h
i
n
a g
i
v
e
n
ti
m
e
d
u
r
ation
,
wh
ich redu
ces th
e
p
r
o
b
a
b
ility o
f
the rad
i
o
ch
an
n
e
l b
e
in
g
b
u
sy du
ri
n
g
carrier sen
s
ing
.
Not
e
t
h
at
t
h
e
s
upe
rf
ram
e
l
e
ngt
h
d
o
es
n
o
t
a
ffect
P
drop
. In
ad
d
ition
,
it can
b
e
seen from
fig
u
r
es i
n
sectio
n
IV
th
at nu
m
e
rical
resu
lts are
v
e
ry
clo
s
e
with
simu
latio
n
resu
lts,
an
d th
is
v
e
ri
fies ou
r propo
sed
m
o
d
e
l.
Fi
gu
re
9.
Fram
e d
r
o
p
pr
o
b
abi
l
i
t
y
P
drop
with respect to data
fram
e size.
Fin
a
lly, Figu
r
e
10
pr
esen
ts
ho
w MA
C av
erag
e
d
e
lay d
e
pen
d
s on
Beacon
O
r
d
e
r
(
B
O)
. A
s
can
b
e
seen from
the
figure, t
h
e del
a
y dynam
i
cally increases
wh
en B
O
inc
r
ea
ses, in
othe
r
words, BO
ha
s strong
im
pact
s on
t
h
e
del
a
y
pe
rf
orm
a
nce.
Thi
s
i
s
d
u
e
t
o
t
h
e f
act that the inc
r
ease
d
B
O
m
a
kes superfram
e
longe
r
a
n
d
t
hus
M
A
C
del
a
y
i
n
creases
as
wel
l
.
T
h
e
st
r
o
ng
de
pe
nd
ance
of
th
e delay on
B
O
is
du
e to lo
ng b
eacon
i
n
terv
al
(BI =
aB
ase
S
u
p
erf
r
a
m
e
D
ur
at
i
o
n
ⅹ
2
BO
).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Ana
l
ysis o
f
I
E
EE 802
.1
5.4 Bea
c
on
Enab
led MAC Pro
t
o
c
o
l
(Ng
a
D
i
nh
)
1
131
Figure
10. Mea
n
access
delay
T
D
with
resp
ect to
th
e
b
eacon
o
r
d
e
r
5.
CO
NCL
USI
O
N
Th
is pap
e
r
pr
esen
ts a m
a
th
ematical an
alysi
s
o
f
I
E
EE 802.15
.4
b
e
acon
-
en
ab
led
MA
C
p
r
o
t
o
c
o
l
and
pr
o
v
i
d
es e
xpl
i
c
i
t
m
a
t
h
em
at
ical
exp
r
essi
o
n
s
fo
r p
o
w
er c
ons
um
pt
i
on, a
ccess del
a
y
,
a
nd
dat
a
f
r
am
e dr
o
p
probability. The wait for the next beac
on fram
e before
ba
cking off in be
acon-e
n
able
d PAN in fact induce
s
a
significa
nt pa
rt
on access
dela
y. Taki
ng
a
d
va
ntage of
this operation, we
le
t IEEE
802.15.4 c
o
nnected de
vices
enter
Sleep state to
reduce t
h
eir power
co
ns
um
pt
i
on. T
h
e
po
we
r m
odel
u
s
es di
ffe
rent
l
o
w-
po
we
r st
at
es
o
f
t
h
e
d
e
v
i
ces and
due to
tho
s
e states, power co
nsum
p
t
io
n
is
sign
i
f
ican
tly i
m
p
r
ov
ed. In
ad
d
ition
,
th
e
propo
sed
d
e
lay
m
o
d
e
l is m
o
re co
m
p
leted
in
co
m
p
ariso
n
to
ex
istin
g research
.
Th
e m
a
th
ematical
m
o
d
e
l
s
in
t
h
is
p
a
p
e
r allo
w
t
h
e ap
pl
i
cat
i
o
n
desi
gne
rs t
o
d
eci
de o
n
t
h
e
ba
l
a
nce bet
w
ee
n
po
we
r c
ons
um
pt
i
o
n
an
d m
e
ssage
del
a
y
.
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