Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
8,
No.
5,
October
2018,
pp.
3767
–
3777
ISSN:
2088-8708
3767
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Mark
o
vian
Queueing
Model
f
or
Thr
oughput
Maximization
in
D2D-Enabled
Cellular
Netw
orks
Abiodun
Gbenga-Ilori
1
and
Olufunmilay
o
Sanusi
2
1
Department
of
Electrical
and
Electronics
Engineering,
Uni
v
ersity
of
Lagos,
Lagos,
Nigeria.
2
Computer
and
Electrical
Engineering
Department,
Olabisi
Onabanjo
Uni
v
ersity
,
Ago-Iw
o
ye,
Ogun
State,
Nigeria.
Article
Inf
o
Article
history:
Recei
v
ed
July
21,
2017
Re
vised
May
19,
2018
Accepted
June
21,
2018
K
eyw
ord:
De
vice-to-De
vice
(D2D)
5G
cellular
netw
orks
continuous-time
Mark
o
v
chain
(CTMC)
queueing
model
spectrum
access
ABSTRA
CT
De
vice-to-De
vice
(D2D)
communication
has
been
considered
a
k
e
y
enabling
technol-
ogy
that
can
f
acilitate
spectrum
sharing
in
4
G
and
5
G
cellular
netw
orks.
In
order
to
meet
the
high
data
rate
demands
of
these
ne
w
generation
cellular
netw
orks,
this
paper
considers
the
optimization
of
a
v
ailable
spectrum
resource
through
dynamic
spectrum
access.
The
utilization
of
conti
nuous-time
Mark
o
v
chain
(CTMC)
model
for
ef
ficient
spectrum
access
in
D2D-enabled
cellular
netw
orks
is
in
v
estig
ated
for
the
purpose
of
de-
termining
the
impact
of
this
model
on
the
capacity
impro
v
ement
of
cellular
netw
orks.
The
paper
considers
the
use
of
CTMC
model
with
both
queueing
and
non-queueing
cases
called
13
-Q
CTMC
and
6
-NQ
CTMC
respecti
v
ely
with
the
aim
of
impro
ving
the
o
v
erall
capacity
of
the
c
ellular
netw
ork
under
a
f
airness
constrai
nt
among
all
users.
The
proposed
strate
gy
consequently
ensures
that
spectrum
access
for
cellular
and
D2D
users
is
optimally
coordinated
by
des
igning
optimal
spectrum
access
probabilities.
Numerical
simulations
are
performed
to
observ
e
the
impact
of
the
proposed
Mark
o
vian
queueing
model
on
spectrum
access
and
consequent
ly
on
the
capacity
of
D2D-enabled
cellular
netw
orks.
Results
sho
wed
tha
t
the
proposed
13
-Q
CTMC
pro
vide
a
more
spectrum-
ef
ficient
sharing
scheme,
thereby
enabling
better
netw
ork
performances
and
lar
ger
ca-
pabilities
to
accommodate
more
users.
Copyright
c
2018
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Abiodun
Gbeng
a-Ilori
Department
of
Electrical
and
Electronics
Engineering
Uni
v
ersity
of
Lagos,
Lagos,
Nigeria.
gbeng
ailori@unilag.edu.ng
1.
INTR
ODUCTION
Mobile
data
traf
fic,
especially
multimedia-rich
services,
are
becoming
a
v
ailable
to
more
mobile
users
in
recent
years
leading
to
an
e
v
er
-increasing
demand
for
higher
data
rate
wireless
access.
Examples
of
present
netw
orks
that
demand
higher
data
rates
are
t
h
e
Long
T
erm
Ev
olution-Adv
anced
(L
TE-A)
and
W
orldwide
Inter
-
operability
for
Micro
w
a
v
e
Access
(W
iMAX).
There
is
also
the
ne
xt
generation
5
G
netw
ork
which
will
require
e
v
en
higher
data
rates
in
order
to
pro
vide
services
to
users.
Due
to
bandwidth
limitation,
it
is
vital
to
utilize
tech-
niques
which
can
achie
v
e
higher
spectral
ef
ficienc
y
.
T
raditionally
,
the
cellular
netw
ork
operates
on
a
centralized
netw
ork
topology
which
is
not
spectral
ef
ficient
since
it
requires
that
mobi
le
de
vices
communicate
through
the
base
station
e
v
en
when
the
y
are
in
close
proximity
.
As
an
alternati
v
e,
D2D
communication
has
been
introduced
to
allo
w
peer
-to-peer
transmission
among
mobile
de
vices
in
close
proximity
,
[1–3].
The
adv
antages
of
allo
wing
D2D
communication
underlay
a
cellular
netw
ork
is
that
it
can
increase
area
spectral
ef
ficienc
y
,
impro
v
e
cellular
co
v
erage,
reduce
l
atenc
y
rate
and
also
reduce
ener
gy
consumption
by
mobile
de
vices
[4].
Ho
we
v
er
,
since
D2D
communi
cation
is
lightly
controlled
by
the
base
station,
it
poses
a
set
of
ne
w
challenges
such
as
interference
management
and
mode
sel
ection
coordination.
It
is,
therefore,
necessary
to
ef
ficiently
and
f
airl
y
share
the
spectrum
resource
among
cell
ular
users
(CUs)
and
D2D
users
i
n
order
to
tak
e
full
adv
antage
of
the
benefits
of
D2D
communication
and
increase
the
o
v
erall
capacity
of
the
netw
ork.
A
lot
of
research
has
been
done
in
controlling
interference
in
D2D
communication
underlaying
cellular
J
ournal
Homepage:
http://iaescor
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ns
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A
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ine
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i
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,
DOI:
10.11591/ijece.v8i5.pp3767-3777
Evaluation Warning : The document was created with Spire.PDF for Python.
3768
ISSN:
2088-8708
netw
orks,
[5–11].
A
fe
w
papers
ha
v
e
addressed
this
interference
issue
by
controlling
D2D
access
to
the
spectrum
in
a
cellular
netw
ork
[12–15].
V
arious
methods
ha
v
e
also
been
used
in
the
past
for
the
analysis
and
design
of
D2D
spectrum
sharing.
In
[16],
the
authors
used
a
Poisson
point
process
(PPP)
to
design
a
spectrum
sharing
mode
for
D2D-enabled
cellular
netw
orks.
In
[17],
in
v
estig
ation
of
the
throughput
optimizat
ion
problem
in
D2D-
underlaid
cellular
netw
ork
while
prioritizing
cellular
services
w
as
done.
In
[18],
a
mode
selection
algorithm
to
minimize
outage
probability
and
manage
interference
w
as
proposed.
In
[11],
a
technique
for
determining
the
minimum
distance
between
simultaneously
operating
D2D
links
in
order
to
determine
the
minimum
required
signal-to-interference-plus-noise
ratio
(SINR)
at
all
recei
v
ers
in
the
netw
ork
w
as
introduced.
A
similar
method
w
as
used
in
[7].
Some
other
papers
used
po
wer
control
schemes
for
interference
a
v
oidance
in
the
netw
orks,
[7,
8,
13,
19–21].
Game
theoretical
approaches
ha
v
e
also
been
used
to
control
interference
and
for
ef
ficient
resource
allocation,
[5],
[22–25].
Although
the
e
xisting
dynamic
spectrum
access
schemes
ha
v
e
achie
v
ed
some
successes
in
enhancing
spectrum
ef
ficienc
y
,
most
of
them
do
not
address
f
airness
in
heterogeneous
netw
orks,
[21].
Besides
maximizing
the
o
v
erall
spectrum
utilization,
a
good
spectrum-sharing
scheme
should
also
be
able
to
achie
v
e
f
airness
among
dissimilar
users.
The
consequence
of
unf
air
resource
allocation
between
dissimilar
user
s
may
result
in
spectrum
resource
w
astage
or
redundant
allocation,
[26].
CTM
C-based
models
ha
v
e
been
used
before
no
w
for
analyzing
the
performance
of
cogniti
v
e
radio
netw
orks
(CRNs).
Most
importantly
,
it
has
been
used
to
model
the
spectrum
access
of
primary
and
secondary
users
in
the
CRN
in
order
to
achie
v
e
an
ef
ficient,
f
air
and
fle
xible
spectrum
sharing,
[27–33].
In
[32],
an
M/D/1
priority
queueing
scheme
w
as
applied
to
e
v
aluate
the
performance
of
CRNs.
In
[33],
a
primary-prioritized
Mark
o
v
approach
w
as
also
used
for
dynamic
spectrum
access
between
secondary
and
primary
users
in
CRNs.
T
o
the
best
of
our
kno
wledge,
dynamic
spectrum
access
schemes
that
can
be
used
to
impro
v
e
the
spectral
ef
ficienc
y
of
D2D-enabled
cellular
netw
orks
has
not
been
well
in
v
estig
ated.
Moti
v
ated
by
the
successes
of
CTMC
models
for
ef
ficient
and
f
air
spectrum
sharing
among
dissimilar
users
in
CRNs,
this
paper
proposes
an
optimized
spectrum
access
strate
gy
for
combining
CUs
and
D2D
users
in
a
cellular
netw
ork.
CTMC
model
is
use
d
with
the
aim
of
impro
ving
the
o
v
erall
capacity
of
the
cellular
netw
ork
under
a
f
airness
constraint
among
users.
The
proposed
strate
gy
consequently
ensures
that
there
is
no
redundant
allocation
to
a
user
while
other
users
are
in
need
of
spectrum
resource.
Unlik
e
pre
vious
approaches,
spectrum
access
for
D2D
users
is
optimally
coordinated
by
designing
optimal
spectrum
access
probabilities.
Consequently
,
Mark
o
vian
queueing
and
non-queueing
models
are
used
for
dynamic
spectrum
access
where
the
cellular
spectrum
sub-band
is
shared
by
a
CU
and
2
D2D
users
and
later
e
xtended
to
the
analysis
of
a
ge
n
e
ral
case
with
N
D2D
users.
The
quality
of
service
(QoS)
constraint
is
defined
by
an
SINR
threshold
that
the
CU
should
absolutely
achie
v
e.
Hence
depending
on
the
channel
state
information
recei
v
ed,
the
CU,
D2D
users
or
all
N
+
1
users
can
transmit
on
the
same
frequenc
y
band.
The
computation
time
of
this
comple
x
CTMC
model
consisting
of
one
CU
and
N
D2D
users
is
also
quite
lo
w
.
The
k
e
y
contrib
utions
of
this
paper
can
be
summarized
as
follo
ws:
formulation
of
ef
ficient
spectrum
access
6
-NQ
CTMC
and
13
-Q
CTMC
models
to
sho
w
t
h
e
throughput
g
ain
possible
in
D2D-enabled
cellular
netw
orks,
proposal
of
a
13
-Q
CTMC
model
that
ensures
ef
ficient
and
optimal
spectrum
access
scheme
for
D2D
users
while
protecting
cellular
users
from
intolerably
high
interference
from
D2D
users,
proposal
of
a
13
-Q
CTMC
model
that
reduces
the
connection
set-up
time
and
thereby
reducing
the
o
v
erall
latenc
y
in
the
cellular
netw
ork.
The
remaining
part
of
the
paper
is
or
g
anized
as
follo
ws.
Section
2
presents
the
system
model
and
as
-
sumptions.
Section
3
presents
the
proposed
Mark
o
vian
non-queueing
model
and
computation
of
the
probability
of
co-transmission
for
multiple
D2Ds
and
CU
ha
ving
SINR
constraint.
In
Section
4,
the
Mark
o
vian
queue-
ing
model
is
presented
while
the
simulation
studies
are
pro
vided
in
Section
5.
Finally
,
concluding
remarks
are
pro
vided
in
Section
6.
2.
SYSTEM
MODEL
In
this
paper
,
a
dynamic
spectrum
access
model
is
used
in
a
cellular
netw
ork
where
multiple
D2D
users
are
allo
wed
to
underlay
licensed
CUs.
A
netw
ork
consisting
of
N
D2D
links
and
1
CU
de
vice
with
licensed
sub-band
is
considered.
A
sub-band
is
a
frequenc
y
spectrum
sub-allocated
to
a
licensed
cellular
user
.
A
cellular
user
o
wns
a
licensed
sub-band
which
it
can
share
with
a
number
of
D2D
links.
Figure
1
sho
ws
the
system
diagram.
The
CU
communicates
solely
t
hrough
the
base
station
using
link
l
while
the
tw
o
sets
of
D2D
users
communicate
directly
without
the
base
station
using
links
D
1
and
D
2
.
It
is
IJECE
V
ol.
8,
No.
5,
October
2018:
3767
–
3777
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
I
SSN:
2088-8708
3769
Figure
1.
D2D-Enabled
Cellular
Netw
ork
assumed
that
all
communication
occurs
in
the
same
cell
within
the
same
channel.
The
paper
also
assumed
that
the
D2D
links
share
the
uplink
resource
with
the
cellular
user
equipment.
D2D
communication
is
allo
wed
as
long
as
it
does
not
cause
SINR
of
the
cellular
link
to
drop
belo
w
the
required
minimum.
The
SINR
of
the
cellular
link
tak
es
a
higher
priority
.
The
paper
aims
at
determining
the
optimal
spectrum
access
probabilities
for
each
D2D
link
in
the
cellular
netw
ork.
If
optimal
coordination
of
D2D
spectrum
access
can
be
guaranteed,
then
it
is
possible
to
achie
v
e
a
good
trade-of
f
between
spect
rum
ef
ficienc
y
and
interference
reduction.
First,
the
spectrum
access
is
modelled
as
a
CTMC
without
queueing.
In
this
case,
if
a
D2D
link
does
not
meet
the
minimum
requirement
to
underlay
a
cellular
sub-band,
it
is
dropped
and
has
to
start
the
process
of
spectrum
search
all
o
v
er
ag
ain.
The
disadv
antage
of
this
is
that
the
D2D
users
spend
more
time
and
battery
po
wer
is
lost
while
searching
for
ne
w
spectrum.
The
spectrum
access
is
later
modelled
as
a
CTMC
with
queueing
where
D2D
links
that
do
not
meet
present
spectrum
use
requirements
h
a
v
e
the
opportunity
to
queue
up
for
a
future
time
to
access
the
spectrum
instead
of
being
dropped.
This
hopefully
impro
v
es
the
netw
ork
throughput
while
reducing
communication
set-
up
time
and
battery
po
wer
consumption.
The
non-queueing
CTMC
spectrum
access
is
modelled
as
a
si
x-state
CTMC
while
the
queueing
CTMC
spectrum
access
is
modelled
as
a
thirteen-state
CTMC.
The
se
state
diagrams
are
used
to
compute
the
spectrum
access
probabilities
(
)
of
being
in
each
state.
The
a
v
erage
throughput
U
for
each
user
in
the
cellular
netw
ork
is
therefore
computed
as:
U
=
c
r
c
+
d
1
r
d
1
+
+
d
n
r
d
n
;
(1)
where
the
set
=
f
c
;
d
1
;
;
d
n
g
is
the
spectrum
access
probabilities
of
the
cellular
user
C
and
set
of
N
D2D
users
D
=
[
d
1
;
d
2
;
;
d
n
]
and
U
is
a
function
of
and
the
channel
capacity
of
each
user
r
=
f
r
c
;
r
d
1
;
;
r
d
n
g
.
The
channel
capacity
for
a
user
A
operating
in
the
spectrum
band
alone
is
r
1
A
=
W
l
og
2
(1
+
P
A
G
AA
n
0
)
;
(2)
and
the
channel
capacity
for
user
A
when
it
coe
xists
with
another
user
B
in
the
same
spectrum
band
is
r
2
A
=
W
l
og
2
(1
+
P
A
G
AA
n
0
+
P
A
6
=
B
P
B
G
B
A
)
;
(3)
where
W
is
the
communication
bandwidth,
n
0
is
the
thermal
noise
po
wer
,
P
A
and
P
B
are
the
transmission
po
wer
for
users
A
and
B
respecti
v
ely
,
and
G
AA
is
the
channel
g
ain
for
user
A
while
G
B
A
is
the
channel
g
ain
from
user
B’
s
transmitter
to
user
A
’
s
recei
v
er
.
Using
the
channel
state
information
(CSI)
g
athered,
the
base
station
e
v
aluates
the
spectrum
utilization,
computes
the
opti
mal
access
probabilities
in
dif
ferent
states
and
sends
the
results
to
the
D2D
link.
The
queueing
model
helps
to
determine
the
w
aiting
period,
if
necessary
,
for
each
D2D
link.
Of
course,
if
the
w
aiting
period
is
unacceptably
long,
the
D2D
link
may
choose
to
use
another
cellular
link
or
e
v
en
an
unlicensed
band.
If
a
D2D
user
is
transmitting
and
a
CU
arri
v
es
requesting
the
use
of
the
channel
and
the
minimum
requirement
is
not
met,
the
CU
queue
up
and
w
ait
for
the
D2D
user
to
complete
transmission.
Ho
we
v
er
,
if
on
arri
v
al
of
the
CU,
there
are
D2D
users
on
the
queue
for
spectrum
use,
the
CU
tak
es
priority
o
v
er
the
D2D
users
in
the
queue.
Mark
o
vian
Queueing
Model
for
Thr
oughput
Maximization
in
D2D-Enabled
...
(Abiodun
Gbenga-Ilori)
Evaluation Warning : The document was created with Spire.PDF for Python.
3770
ISSN:
2088-8708
T
able
1.
The
Six
States
of
the
6
-NQ
CTMC.
S
tate
D
escr
ipti
on
0
No
user
in
the
spectrum
C
CU
in
the
spectrum
D
One
D2D
user
in
the
spectrum
1
CU
and
one
D2D
user
in
the
spectrum
2
Both
D2D
users
in
the
spectrum
3
All
users
in
the
spectrum
3.
CELLULAR-PRIORITIZED
NON-Q
UEUEING
CTMC
In
this
section,
the
dynamics
of
the
system
consisting
of
a
CU
and
tw
o
D2D
users
is
first
modell
ed
using
a
CTMC
without
queueing
and
later
generalized
to
multiple
D2D
users.
The
probabilities
in
v
olv
ed
in
these
transitions
are
also
computed
and
used
to
deri
v
e
the
throughput
that
can
be
achie
v
ed
in
the
cellular
netw
ork.
3.1.
6
-NQ
CTMC
In
this
section,
it
is
assumed
that
when
a
D2D
user
requesting
spectrum
access
appears,
the
base
stati
on
determines
if
the
D2D
meet
the
minimum
spectrum
access
requirements
needed
in
the
cellular
netw
ork
using
the
CSI.
Otherwise,
the
D2D
user
is
dropped
and
can
either
w
ait
for
a
later
time
to
try
ag
ain,
request
for
another
cellular
band
or
use
an
unlicensed
spectrum
band.
The
scenario
is
therefore
modelle
d
as
a
six-state
non-queueing
CTMC.
First,
it
is
assumed
that
a
maximum
of
three
users
can
use
t
he
single
uplink
frequenc
y
channel
of
the
cellular
user;
1
CU
and
2
D2D
users.
The
paper
later
e
xtends
to
a
more
general
case
of
N
-D2D
users.
In
the
non-queueing
CTMC
model,
the
CU’
s
priority
,
in
terms
of
spectrum
access,
is
not
so
ob
vious.
Ho
we
v
er
,
the
base
station
gi
v
es
the
CU
higher
data
rates
compared
to
the
D2D
users.
The
spectrum
access
of
the
cellular
and
D2D
users
are
modelled
as
independent
Poisson
process
with
arri
v
al
rates
c
and
d
respecti
v
ely
.
The
servi
ce
times
are
assumed
to
be
e
xponentially
distrib
uted
with
departure
rates
for
cellular
and
D2D
users
denoted
as
c
and
d
respecti
v
ely
.
The
six
states
of
the
non-queueing
CTMC
are
described
in
T
able
1.
This
six-state
Mark
o
v
chain
is
denoted
by
6
-NQ
CTMC
for
short.
The
spectrum
access
process
is
sho
wn
in
Figure
2
.
Assume
at
first
that
cellular
band
is
idle,
in
which
case
t
he
6
-NQ
CTMC
is
in
state
0
.
In
this
case,
there
can
be
either
an
arri
v
al
of
a
cellular
user
C
or
a
D2D
user
d
.
If
an
y
of
these
2
users
arri
v
e,
the
6
-NQ
CTMC
transit
to
either
state
C
or
D
with
transition
rates
c
and
d
respecti
v
ely
.
If
user
C
or
d
complete
service
before
an
y
other
user
requests
spectrum
access,
6
-NQ
CTMC
then
transits
to
state
0
with
departure
rate
c
and
d
accordingly
.
Ho
we
v
er
,
if
a
second
D2D
arri
v
es
while
the
CU
or
the
first
D2D
are
in
the
spectrum,
the
6
-NQ
CTMC
transits
to
either
1
or
2
accordingly
with
rate
d
.
Once
the
CU
or
one
of
the
D2D
complete
transmission,
there
is
a
transition
to
either
state
C
or
D
with
the
departure
rate
of
d
.
If
both
the
CU
and
a
D2D
are
in
the
spectrum
and
the
second
D2D
requests
a
spectrum
band,
then
the
6
-NQ
CTMC
can
either
transit
to
state
3
from
2
with
an
arri
v
al
rate
of
c
or
transit
to
state
3
from
state
1
with
an
arri
v
al
rate
of
d
.
In
all
of
the
transitions
described
abo
v
e,
it
has
been
assumed
that
no
tw
o
D2D
users
can
arri
v
e
or
depart
at
e
xactly
the
same
time.
This
assumption
is
justified
for
independent
Poisson
processes.
0
D
C
1
2
3
d
c
d
c
d
d
c
d
c
d
c
d
c
d
Figure
2.
The
Rate
Diagram
of
6-NQ
CTMC
IJECE
V
ol.
8,
No.
5,
October
2018:
3767
–
3777
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
I
SSN:
2088-8708
3771
The
CTMC
model
is
represented
by
(
,
Q
)
where
=
f
1
;
2
;
;
n
g
is
the
state
space
while
Q
is
the
transition
rate
matrix
and
in
our
6
-NQ
CTMC,
=
f
0
;
C
;
D
;
1
;
2
;
3
g
.
Q
=
[
q
ij
]
;
(4)
where
Q
in
our
6
-NQ
CTMC
is
gi
v
en
as
the
matrix:
Q
=
2
6
6
6
6
6
4
(
c
+
d
)
c
d
0
0
0
c
(
c
+
d
)
0
d
0
0
d
0
(
d
+
c
+
d
)
c
d
0
0
d
c
(
d
+
c
+
d
)
0
d
0
0
d
0
(
d
+
c
)
c
0
0
0
d
c
(
d
+
c
)
3
7
7
7
7
7
5
From
the
matrix
sho
wn
abo
v
e,
q
ii
=
P
j
6
=
i
q
ij
and
0
q
ij
<
1
8
i
6
=
j
.
The
balance
equation
to
be
solv
ed
is
Q
=
0
and
P
n
=
1
.
Therefore
the
analysis
of
Figure
2
consists
of
the
follo
wing
system
of
equations;
8
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
:
0
(
c
+
d
)
=
C
c
+
D
d
;
C
(
c
+
d
)
=
0
c
+
1
d
;
D
(
d
+
c
+
d
)
=
0
d
+
1
c
+
2
d
;
1
(
d
+
c
+
d
)
=
C
d
+
D
c
+
3
d
;
2
(
d
+
c
)
=
D
d
+
3
c
;
3
(
c
+
d
)
=
1
d
+
2
c
;
(5)
0
+
C
+
D
+
1
+
2
+
3
=
1
:
(6)
Equation
(5)
represents
the
flo
w-balance
at
each
of
the
six
states
and
equation
(6)
represents
the
nor
-
malization
equation
that
should
satisfy
a
Mark
o
v
chain
with
n
being
the
steady
state
probabilities
of
being
in
a
particular
place
where
n
2
f
0
;
C
;
D
;
1
;
2
;
3
g
.
From
these
equations,
the
a
v
erage
throughput
for
the
cellular
(
U
c
)
and
each
of
the
tw
o
D2D
users
U
d
1
and
U
d
2
can
be
deduced
as
follo
ws:
U
c
=
C
r
c
+
1
r
1
+
3
r
3
;
(7)
U
d
1
=
U
d
2
=
D
r
d
+
1
r
1
+
2
r
2
+
3
r
3
:
(8)
T
otal
a
v
erage
throughput
is
therefore
U
=
U
c
+
U
d
1
+
U
d
2
:
(9)
3.2.
Generalized-NQ
CTMC
Our
CTMC
can
be
generalized
to
model
the
scenario
with
1
CU
and
N
D2D
users
as
sho
wn
in
the
rate
diagram
of
Figure
3
.
In
this
case,
the
state
space
S
N
Q
has
2(
N
+
1)
states.
S
N
Q
consists
of
a
combination
of
the
status
of
the
CU
and
the
N
D2D
users
and
can
be
written
as:
(
s
N
Q
C
U
;
s
N
Q
D
2
D
)
2
S
N
Q
,
(
idl
e
C
U
;
idl
e
D
2
D
)
[
(
C
U
;
idl
e
D
2
D
)
[
f
(
C
U
;
D
2
D
)
g
[
f
(
idl
e
C
U
;
D
2
D
)
g
;
(10)
where
(
idl
e
C
U
;
idl
e
D
2
D
)
is
a
state
(0
;
[0
;
;
0])
,
in
which
there
is
no
user
re
qu
e
sting
the
spectrum.
(
C
U
;
idl
e
D
2
D
)
is
a
state
(1
;
[0
;
;
0])
in
which
only
the
CU
is
using
the
spectrum.
The
set
of
states
f
(
C
U
;
D
2
D
)
g
represent
all
the
states
where
a
combination
of
1
CU
and
one
or
up
to
N
D2D
users
are
in
the
spectrum.
The
set
of
states
f
(
idl
e
C
U
;
D
2
D
)
g
represent
all
the
states
where
there
is
no
CU
b
ut
one
or
up
to
N
D2D
users
are
in
the
spectrum.
If
q
ij
,
f
s
i
!
s
j
g
denotes
the
transition
from
state
s
i
to
state
s
j
,
then
we
can
construct
the
matrix
Q
=
[
q
ij
]
.
F
or
the
state
space
S
N
Q
=
[
n
0
;
n
1
;
;
n
g
;
;
n
N
+1
]
where
N
+
1
is
the
number
of
users
in
the
spectrum;
CU
or
(and)
D2D
users,
the
number
of
transition
states
is
gi
v
en
as
n
=
2(
N
+
1)
for
N
D2D
users.
Therefore,
q
f
[
n
0
;
n
1
;
;
n
g
;
;
n
N
+1
]
!
[
n
0
;
n
1
;
;
1
n
g
;
;
n
N
+1
]
g
=
g
.
W
e
can
also
solv
e
the
stationary
probability:
s
n
=
[
s
1
;
;
s
(2(
N
+1))
]
using
Q
=
0
and
P
2(
N
+1)
n
=1
s
n
=
1
.
W
e
can
re
wri
te
this
as:
Q
T
1
1
(2(
N
+1))
T
=
0
(2(
N
+1))
1
1
:
(11)
Mark
o
vian
Queueing
Model
for
Thr
oughput
Maximization
in
D2D-Enabled
...
(Abiodun
Gbenga-Ilori)
Evaluation Warning : The document was created with Spire.PDF for Python.
3772
ISSN:
2088-8708
0
C
D
0
D
1
C
D
1
D
N
1
C
D
(
N
1)
D
N
C
D
N
c
d
1
c
d
1
d
2
d
1
c
d
1
d
2
c
d
2
d
N
1
d
2
d
N
1
d
N
1
d
N
d
N
1
d
N
d
N
c
d
N
c
Figure
3.
The
Rate
Diagram
of
the
Generalized-NQ
CTMC
4.
CELLULAR-PRIORITIZED
Q
UEUEING
CTMC
In
the
pre
vious
section,
D2D
link
that
is
unable
to
meet
the
QoS
requirement
of
the
netw
ork
is
dropped
by
the
base
station.
This
means
that
the
D2D
link
is
compelled
to
seek
alternati
v
e
means
of
communication.
This
has
some
disadv
antages
especially
with
respect
to
ef
ficient
usage
of
spectrum
resources
and
delays
in
the
netw
ork.
In
order
to
maximize
the
ef
ficient
use
of
these
cellular
channels,
a
concept
w
as
introduced
where
spectrum
requests
by
D2D
links
that
do
not
meet
QoS
of
the
netw
ork
are
queued
in
a
b
uf
fer
at
the
base
station
and
the
spectrum
is
immediately
made
a
v
ailable
to
D2D
links
on
the
queue
without
an
y
time
lapse
in
the
usage
of
the
licensed
cellular
bands.
This
w
ay
the
o
v
erall
communi
cation
set-up
time
for
de
vices
in
the
netw
ork
is
greatly
reduced
and
the
D2D
user
can
conserv
e
battery
ener
gy
.
First,
this
is
modelled
as
a
thirteen-state
CTMC
with
queueing
kno
wn
as
13-Q
CTMC
and
then
later
generalized
in
what
is
called
the
Generalized-Q
CTMC.
4.1.
13
-Q
CTMC
In
this
sub-section,
the
netw
ork
is
modelled
to
depict
a
situation
where
a
D2D
link
request
the
use
of
a
cellular
spectrum
and
the
base
station,
using
the
CSI,
determines
if
the
D2D
link
meets
the
minimum
QoS
requirement
of
the
netw
ork.
If
it
does,
the
D2D
link
is
admitted
into
the
channel.
Ho
we
v
er
,
if
it
does
not
meet
this
requirement,
it
is
admitted
into
a
queue
and
can
access
the
spectrum
at
a
later
time.
The
thi
rteen
states
of
the
13-Q
CTMC
are
described
in
T
able
2
and
the
rate
diagram
is
gi
v
en
in
Figure
4
.
Then
the
equation
array
go
v
erning
the
abo
v
e
system
is
gi
v
en
by:
8
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
:
0
(
c
+
d
)
=
1
c
+
2
d
;
1
(
c
+
2
d
)
=
0
c
+
3
d
+
6
d
;
2
(
d
+
c
+
2
d
)
=
0
d
+
4
d
+
8
c
+
12
d
;
3
(
d
+
2
d
)
=
1
d
+
5
d
+
11
d
;
4
(
d
+
2
c
)
=
2
d
+
5
c
+
9
c
;
5
(
d
+
c
)
=
3
d
+
4
c
;
6
(
d
+
d
)
=
1
d
+
7
c
;
7
(
d
)
=
6
d
;
8
(
c
)
=
2
c
;
9
(
c
)
=
2
c
;
10
(
c
)
=
12
c
;
11
(
d
)
=
3
d
;
12
(
d
+
c
)
=
2
d
+
10
c
;
(12)
0
+
1
+
2
+
3
+
4
+
5
+
6
+
7
+
8
+
9
+
10
+
11
+
12
=
1
:
(13)
Ag
ain
the
stationary
probabilities
can
be
solv
ed
by
using
Q
=
0
and
P
n
=
1
as
sho
wn
in
equations
(12)
and
(13),
and
the
total
a
v
erage
throughput
in
the
netw
ork
can
be
determined
from
these
equations.
IJECE
V
ol.
8,
No.
5,
October
2018:
3767
–
3777
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
I
SSN:
2088-8708
3773
T
able
2.
The
Thirteen
States
of
the
13
-Q
CTMC.
S
tate
D
escr
ipti
on
0
(0
;
0)
No
user
in
the
spectrum
1
(
C
;
0)
CU
in
the
spectrum
2
(
D
;
0)
1
D2D
user
in
the
spectrum
3
(1
;
0)
CU
and
1
D2D
user
in
the
spectrum
4
(2
;
0)
Both
D2D
users
in
the
spectrum
5
(3
;
0)
All
3
users
in
the
spectrum
6
(
C
;
D
w
)
CU
in
the
spectrum,
1
D2D
user
w
aiting
7
(
C
;
2)
CU
in
the
spectrum,
2
D2D
users
w
aiting
8
(
D
;
C
w
)
1
D2D
user
in
the
spectrum,
CU
w
aiting
9
(2
;
C
w
)
Both
D2D
users
in
the
spectrum,
CU
w
aiting
10
(
D
;
1
w
)
1
D2D
user
in
the
spectrum,
1
D2D
and
CU
w
aiting
11
(
D
;
D
w
)
1
D2D
user
in
the
spectrum,
1
D2D
w
aiting
12
(1
;
D
w
)
CU
and
1
D2D
user
in
the
spectrum,
1
D2D
w
aiting
4.2.
Generalized-Q
CTMC
W
e
can
generalize
the
CTMC
with
queueing
model
as:
(
s
Q
C
U
;
s
Q
D
2
D
)
2
S
Q
,
S
N
Q
[
S
W
;
(14)
where
S
Q
is
the
state
space
for
the
queueing
model,
S
N
Q
is
as
gi
v
en
in
equation
(10).
The
state
space
for
the
w
aiting
incorporated
is
denoted
by
S
W
and
it
is
gi
v
en
as:
S
W
=
[
f
(
in
1
user
;
W
1
user
)
g
[
f
(
in
1
user
;
W
2
user
s
)
g
[
[
f
(
in
1
user
;
W
k
1
user
s
)
g
[
[
f
(
in
2
user
s
;
W
k
2
user
s
)
g
[
[
f
(
in
k
1
user
s
;
W
1
user
)
g
]
;
(15)
where
k
is
the
number
of
users
in
the
spectrum;
CU
and
D2D
users
inclusi
v
e.
(
in
1
user
;
W
k
1
user
s
)
means
that
1
user
is
occup
ying
the
spectrum,
CU
or
D2D,
and
the
other
(
k
1)
users
are
w
aiting
in
the
queue
to
use
the
spectrum.
The
generator
matrix
Q
=
[
q
ij
]
is
ag
ain
constructed
for
s
n
=
[
n
0
;
n
1
;
;
n
g
;
;
n
k
]
where
n
=
N
2
+
4
N
+
1
for
N
D2D
users.
q
f
s
n
!
s
w
n
g
denote
transition
that
oc
curs
when
a
user
j
arri
v
es
gi
v
en
that
the
CSI
does
not
support
spectrum
sharing
with
user
j
at
that
time.
The
transition
goes
to
q
f
s
w
n
!
s
n
g
with
the
departure
of
some
users
and
the
accommodation
of
user
j
.
The
follo
wing
equation
array
is
then
solv
ed
to
obtain
our
stationary
probabilities:
Q
T
1
1
(
N
2
+4
N
+1)
T
=
0
(
N
2
+4
N
+1)
1
1
:
(16)
5.
NUMERICAL
RESUL
TS
In
this
section,
the
system
performance
of
the
6
-NQ
CTMC
and
13
-Q
CTMC
spectrum
access
schemes
are
e
v
aluated
and
analyzed
in
terms
of
the
total
throughput
that
can
be
achie
v
ed
using
each
of
them.
The
paper
simulates
a
system
with
a
cellular
user
and
multiple
D2D
users
arri
ving
according
to
Poisson
process
with
arri
v
al
rates
c
and
d
respecti
v
ely
.
MA
TLAB
is
used
to
conduct
the
simulation
e
xperiments
in
order
to
determine
the
throughput
in
a
cell
using
each
of
the
tw
o
schemes
discussed
in
sections
III
and
IV
.
The
goal
is
to
compare
the
performance
of
the
6
-NQ
CTMC
model
with
that
of
the
13
-Q
CTMC
model
in
order
to
sho
w
the
better
performance
of
the
proposed
Mark
o
vian
queueing
model.
The
follo
wing
parameters
were
used:
channel
bandwidth
=
5
M
H
z
,
UE
transmitter
po
wer
=
24
dB
m
,
thermal
noise
per
MHz
=
114
dB
,
recei
v
er
g
ain
=
0
dB
i
,
c
=
1
20
s
1
,
d
=
1
20
s
1
,
c
=
20
s
1
,
d
=
25
s
1
.
The
base
station
is
located
at
the
center
of
the
300
m
radius
cell
and
the
CU
and
D2D
users
are
distrib
uted
randomly
around
it.
D2D
links
ha
v
e
a
maximum
distance
of
20
m
.
Mark
o
vian
Queueing
Model
for
Thr
oughput
Maximization
in
D2D-Enabled
...
(Abiodun
Gbenga-Ilori)
Evaluation Warning : The document was created with Spire.PDF for Python.
3774
ISSN:
2088-8708
2
;
C
w
2
;
0
3
;
0
1
;
0
1
;
D
w
D
;
0
D
;
D
w
D
;
1
w
D
;
C
w
0
;
0
C
;
0
C
;
D
w
C
;
2
w
c
c
d
c
c
d
d
d
d
d
d
c
d
d
c
d
c
c
c
d
d
c
d
d
d
d
Figure
4.
The
Rate
Diagram
of
13-Q
CTMC
Figure
5.
A
v
erage
Throughput
Achie
v
able
in
Cell
for
6
-NQ
CTMC
and
13
-Q
CTMC
Figure
6.
Optimal
Access
Probability
for
CU
and
D2D
Users
The
simulation
is
also
used
to
determine
the
a
v
erage
w
aiting
time
in
the
entire
system
for
both
models.
It
is
also
used
to
determine
the
w
aiting
time
in
the
queue
for
the
13
-Q
CTMC
model.
This
part
of
the
simulation
pro
vides
a
w
ay
to
assess
the
connection
set-up
time
a
nd
o
v
erall
latenc
y
in
the
system
usi
ng
the
proposed
queueing
model.
F
or
determination
of
the
w
aiting
time
in
the
systems
and
queue,
the
con
v
entional
method
discussed
in
[34]
is
adopted.
The
performance
of
the
proposed
13
-Q
CTMC
model
is
also
v
alidated
by
comparing
it
with
the
e
xisting
non-persistent
carrier
sense
multiple
access
(CSMA)
spectrum
access
model
reported
in
[35]
to
further
sho
w
its
superiority
.
Figure
5
compares
the
throughput
achi
e
v
able
by
the
proposed
13
-Q
CTMC
model
with
that
of
the
6
-NQ
CTMC
model
and
the
e
xisting
non-persistent
CSMA
spectrum
access
technique.
It
can
be
sho
wn,
by
comparing
throughput
achie
v
able
from
the
three
spectrum
access
schemes,
that
13
-Q
CTMC
has
the
highest
throughput
while
CSMA
has
the
lo
west
throughput.
The
poor
performance
of
CSMA
is
due
to
the
collision
rate
and
inef
fic
ient
random
w
aiting
time
of
this
scheme.
Ho
we
v
er
,
by
controlling
the
access
probabilities
of
D2D
users
in
both
CTMC
schemes,
it
w
as
possible
to
accommodat
e
more
traf
fic
and
greatly
increase
the
throughput.
The
13
-Q
CTMC
model
w
as
able
to
achie
v
e
further
increase
in
throughput
becaus
e
queueing
UEs,
instead
of
rejecting
requests,
impro
v
ed
the
o
v
erall
throughput
of
the
netw
ork.
Generally
,
there
is
a
throughput
de
gradation
for
all
models
as
increases.
This
is
as
a
result
of
interference
that
may
occur
in
the
netw
ork.
Though
there
is
a
general
de
gradation
in
throughput
as
increases,
yet
a
slo
wer
rate
of
de
gradation
w
as
noticed
in
the
proposed
13
-Q
CTMC
model
with
a
de
gradation
of
0
:
58%
in
throughput
when
w
as
increased
from
1
to
4
and
5
:
53%
de
gradation
in
throughput
when
w
as
increased
from
1
to
20
.
In
the
6
-NQ
CTMC
model,
when
w
as
increased
from
1
to
4
,
the
netw
ork
e
xperienced
a
1
:
9%
de
gradation
in
throughput
and
when
w
as
increased
from
1
to
20
,
11
:
43%
de
gradation
in
throughput
w
as
e
xperienced
in
the
netw
ork.
The
CSMA
performed
v
ery
poorly
with
de
gradation
of
10
:
7%
as
increased
from
1
to
4
and
de
gradat
ion
of
65%
as
increased
from
1
to
20
.
Therefore
the
13
-Q
CTMC
w
as
able
to
achie
v
e
the
highest
throughput
and
also
has
the
best
access
scheme
because
it
performed
best
with
an
increase
in
arri
v
al
rate.
IJECE
V
ol.
8,
No.
5,
October
2018:
3767
–
3777
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
I
SSN:
2088-8708
3775
Figure
7.
W
aiting
T
ime
in
the
System
for
6
-NQ
CTMC
and
13
-Q
CTMC
Figure
8.
W
aiting
T
ime
on
the
Queue
for
13
-Q
CTMC
Figure
6
sho
ws
the
a
v
erage
access
probability
of
D2D
and
cellular
users.
The
access
probability
of
the
cellular
user
decreases
as
arri
v
al
r
ate
of
cellular
users
increases.
The
arri
v
al
rate
of
the
cellular
user
also
causes
a
reduced
access
probability
f
o
r
the
D2D
user
.
Ho
we
v
er
,
the
access
probability
of
the
cellular
user
is
still
more
than
that
of
the
D2D
user
because
of
the
priority
gi
v
en
to
the
cellular
user
since
its
arri
v
al
rate
is
fix
ed
at
20
s
1
.
The
service
time
in
the
netw
ork
for
our
6
-NQ
CTMC
w
as
also
compared
with
that
of
the
13
-Q
CTMC.
It
can
be
sho
wn
from
Figure
7
that
the
w
aiting
time
in
both
models
is
comparably
close
when
the
number
of
arri
v
als,
,
is
less
than
4
users
per
seconds
with
13
-Q
CTMC
model
slightly
better
than
the
6
-NQ
CTMC
model.
Ho
we
v
er
,
as
the
number
of
arri
v
als
per
second
increases,
the
w
aiting
time
in
the
system
increases
e
xponentially
in
the
6
-NQ
CTMC
model.
It
is
seen
that
the
13
-Q
CTMC
w
as
able
to
perform
better
in
that
it
is
able
to
toler
ate
interference
in
the
system
despite
the
inclusion
of
queueing
time
in
this
model.
Figure
8
sho
ws
the
w
aiting
time
on
the
queue
for
the
13
-Q
CTMC.
W
e
see
that
e
v
en
with
the
queue,
users
will
still
ha
v
e
access
to
the
system
f
aster
than
using
the
6
-NQ
CTMC.
The
proposed
13
-Q
CTMC,
therefore,
sho
wed
better
performances
and
lar
ger
capabilities
to
accommodate
more
users.
It
also
of
fers
a
more
ef
ficient
spectrum
utilization
compared
to
6
-NQ
CTMC.
6.
CONCLUSION
In
the
paper
,
a
Mark
o
vian-queueing
approach
is
proposed
for
optimizing
the
use
of
cellular
spectrum
resource
through
dynamic
spectrum
access.
This
is
highly
necessary
in
order
to
meet
the
high
data
rate
demands
of
4
G
and
5
G
cellular
netw
orks.
The
use
of
a
Mark
o
vian-queueing
model
kno
wn
as
13
-Q
CTMC
is
proposed
for
underlaying
D2D
users
in
a
cellular
bandwidth
in
order
to
optimize
the
use
of
spectrum
resource
and
increase
throughput
in
the
netw
ork.
A
Mark
o
vian-queueing
model
is
chosen
because
of
the
successes
of
CTMC
models
in
achie
ving
ef
ficient
and
f
air
spectrum
sharing
in
heterogeneous
netw
orks.
The
proposed
13
-Q
CTMC
queueing
model
is
compared
with
the
6
-NQ
CTMC
model
that
does
not
support
queueing
and
the
e
xisting
non-persistent
CSMA
spectrum
access
scheme.
Simulation
results
sho
wed
that
the
proposed
Mark
o
vian-queueing
model
is
more
ef
ficient
in
the
use
of
limited
spectrum
resource
and
also
yielded
better
throughput
in
the
netw
ork
compared
to
the
other
tw
o
spectrum
access
techniques.
The
13
-Q
CTMC
model
ensures
ef
ficient
and
optimal
spectrum
access
scheme
for
D2D
users
while
protecting
cellular
us
ers
from
intolerably
high
interference
from
D2D
users.
Compared
with
the
other
spectrum
access
techniques,
the
13
-Q
CTMC
model
sho
wed
a
considerable
reduction
in
the
connection
set-up
time
and
thereby
reducing
the
o
v
erall
latenc
y
in
the
cellular
netw
ork.
A
CKNO
WLEDGMENT
The
first
author
will
lik
e
to
ackno
wledge
the
support
of
the
Ale
xander
v
on
Humboldt
F
oundation
for
financing
her
post-doctoral
research
stay
at
the
Ruhr
-Uni
v
ersit
¨
at
Bochum,
German
y
.
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for
Thr
oughput
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D2D-Enabled
...
(Abiodun
Gbenga-Ilori)
Evaluation Warning : The document was created with Spire.PDF for Python.
3776
ISSN:
2088-8708
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