Overlay Secondary Spectrum Sharing with Independent Re-attempts in Cognitive Radios

Abstract

Opportunistic spectrum access (OSA) is a promising reform paradigm envisioned to address the issue of spectrum scarcity in cognitive radio networks (CRNs). While current models consider various aspects of the OSA scheme, the impact of retrial phenomenon in multi-channel CRNs has not yet been analyzed. In this work, we present a continuous-time Markov chain (CTMC) model in which the blocked/preempted secondary users (SUs) enter a finite retrial group (or orbit) and re-attempt independently for service in an exponentially distributed random manner. Taking into account the inherent retrial tendency of SUs, we numerically assess the performance of the proposed scheme in terms of dropping probability and throughput of SUs.

Full text

Overlay Secondary Spectrum Sharing with
Independent Re-attempts in Cognitive Radios
Muthukrishnan Senthil Kumar∗, Aresh Dadlani†, Kiseon Kim†and Richard O. Afolabi‡
∗Department of Applied Mathematics and Computational Science, PSG College of Technology, India
†School of Electrical Engineering and Computer Science,
Gwangju Institute of Science and Technology, Gwangju 61005, South Korea
‡Computer Science Department, University of Nevada - Las Vegas, NV 89119, USA
E-mail: msk@amc.psgtech.ac.in, {dadlani, kskim}@gist.ac.kr, ao.richard@me.com
Abstract—Opportunistic spectrum access (OSA) is a promising
reform paradigm envisioned to address the issue of spectrum
scarcity in cognitive radio networks (CRNs). While current
models consider various aspects of the OSA scheme, the impact
of retrial phenomenon in multi-channel CRNs has not yet been
analyzed. In this work, we present a continuous-time Markov
chain (CTMC) model in which the blocked/preempted secondary
users (SUs) enter a finite retrial group (or orbit) and re-attempt
independently for service in an exponentially distributed random
manner. Taking into account the inherent retrial tendency of SUs,
we numerically assess the performance of the proposed scheme
in terms of dropping probability and throughput of SUs.
I. INTRODUCTION
Proliferation of wireless services in recent years has stimu-
lated the need for improved spectrum management policies to
exploit the abundant spectrum holes in existing licensed bands.
Cognitive radio (CR) has emerged as a potential technology
that allows unlicensed or secondary users (SUs) to temporarily
access idle licensed bands exclusive to primary users (PUs)
[1]. To avoid interference with PUs, SUs continuously sense
the spectrum using artificial intelligent techniques and are pre-
empted when a newly arriving PU finds insufficient bandwidth
for its transmission. Therefore, the degree of flexibility in
spectrum sharing between PUs and SUs is regulated by the
opportunistic spectrum access (OSA) policy in use [2] [3].
Modelling OSA schemes for CRNs has been the focus of
many recent active research studies. In [4], an OSA model
with a single primary traffic for the PUs and two prioritized
secondary traffic classes for the SUs was studied. In this work,
the authors assumed that the blocked and preempted SUs
had no option other than to quit the system in absence of
vacant bands. In practical scenarios however, such SUs are
expected to retry for service after some random amount of
time. With regard to the retrial behavior of SUs, the authors
of [5] proposed a continuous-time Markov chain (CTMC)
with level-dependent quasi-birth-and-death (QBD) structure to
analyze the effect of retrying SUs on the performance of an
unslotted CRN. Nonetheless, they dealt with the carrier sense
multiple access (CSMA) protocol in a mixed environment of
dedicated licensed and unlicensed bands. In [6], an M/M/1
retrial queueing framework for OSA was proposed for single
channel CRNs. In this paper, we divulge the impact of the
retrial behavior of opportunistic SUs in multi-channel CRNs
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Arriving PU ൫ߣ௣൯Served PU ൫ߤ௣൯
Arriving SU ሺߣ௦ሻServed SU ሺߤ௦ሻ
Finite retrial buffer (orbit)
ߠ
Preempted/
Blocked SU
Fig. 1: The proposed OSA model with retrial phenomenon.
where all spectrum bands are licensed to PUs. We express the
state transitions of the proposed OSA model as a tri-variate
CTMC and investigate the system performance in terms of the
dropping probability and network throughput of SUs.
The rest of this paper is structured as follows. Section II de-
scribes and formulates the system model, followed by deriva-
tions of the performance measures in Section III. Analytical
and simulation results are extensively discussed in Section IV.
Finally, conclusive remarks are drawn in Section V.
II. SY ST EM MO DE L FORMULATION
We consider a multi-channel CRN comprising of Mli-
censed bands, each divided into Nsub-bands. Henceforth, we
use the terms ‘band’ and ‘sub-band’ to refer to a bandwidth
unit for PU and SU traffic sources, respectively. As shown
in Fig. 1, a PU requires one band (Bi)while an SU needs
one sub-band (bi,j )for transmission. Hence, when a given
band is exploited by a PU, the underlying sub-bands are made
unavailable to SUs. A newly arriving PU occupies a band if
vacant. Otherwise, it preempts the SUs using the sub-bands of
one of the primary bands. The preempted SUs then enter the
orbit of size Land retry again after some random time with
rate θ. On retrial, if a sub-band is idle, the SU opportunistically
utilizes it. Otherwise, it repeats the cycle. A preempted or
blocked SU is dropped only if the orbit is full. We assume
that PU and SU arrivals follow Poisson processes with rates λp
and λs, respectively. Moreover, let µpand µsdenote the mean
service rates of the exponentially distributed service times of
PU and SU, respectively. Let Np(t)and Ns(t)be the number
arXiv:1607.08450v1 [cs.PF] 28 Jul 2016

of bands and sub-bands used by PUs and SUs, respectively,
at time t. Also, let Nr(t)denote the number of SUs in the
orbit at time t. Hence, {(Np(t), Ns(t), Nr(t))|t≥0}is a
three-dimensional CTMC with state space Ω = {(i, j, k)|i=
0, . . . , M ;j= 0,...,min(MN , (M−i)N); k= 0, . . . , L}.
Assuming the elements of Ωto be ordered lexicographically,
the infinitesimal generator Qof the above process is a finite
level-dependent QBD type (LDQBD) given as follows:
Q=











A0D10 0 · · · 0 0
C1A1D20· · · 0 0
0C2A2D3· · · 0 0
0 0 C3A3· · · 0 0
.
.
..
.
..
.
........
.
..
.
.
0 0 0 0 · · · AM−1DM
0 0 0 0 · · · CMAM











,(1)
where the block matrices Ai,Di, and Ciare of order X(L+1),
X(L+1)×(X−N)(L+1), and (X+N)(L+1)×X(L+1),
respectively, with Xdefined as (M−i)N+1. Matrix Aiis the
transition rate matrix in level iwith the following structure:
Ai=











A0,0A0,10· · · 0 0
A1,0A1,1A1,2· · · 0 0
0A2,1A2,2· · · 0 0
0 0 A3,2· · · 0 0
.
.
..
.
..
.
.....
.
..
.
.
0 0 0 · · · AX−2,X −2AX−2,X−1
0 0 0 · · · AX−1,X −2AX−1,X−1











.
(2)
In (2), Aj,j−1is the transition rate sub-matrix for SU service
completion and Aj,j+1 indicates the service/retrial requests of
SUs. With the Kronecker delta function and identity matrix of
order Ydenoted as δi,j and IY, respectively, the elements of
Aiare given as below, where each element is a square matrix:













































Aj,j =−[λs+1−δi,M λp+(1−δj,M N )kθ]IL+1
−jµsIL+1 −iµpIL+1 ,
Aj,j−1=jµsIL+1,
Aj,j+1 =











λs0 0 · · · 0 0
θ λs0· · · 0 0
0 2θ λs· · · 0 0
0 0 3θ· · · 0 0
.
.
..
.
..
.
.....
.
..
.
.
000· · · λs0
000· · · Lθ λs











,
AX−1,X−1=−[λs+(1−δi,M )λp+(X−1)µs]IL+1
−iµpIL+1 +λsZ,
(3)
and Z= [0|IL|0T]is an augmented matrix of order L+ 1.
Transitions associated with PU service completion from level
ito (i−1) are given in sub-matrix Ci=iµp[IX(L+1)|0]. The
block matrix Diholds the transition rates from level (i−1)
to ifor PU requests. The rate from state (i−1, j, k)to state
(i, j, k)is λpif j≤X+N. The transition from state (i−
1, j, k)to (i, j −l, k +l)occurs with rate λpif j > X +N,
l= 1,2, . . . , N , and k≤L−1. The loss of SUs due to
PU preemption from state (i−1, j, L)to (i, j −l, L)takes
place at rate λpfor l= 1,2, . . . , N and j > X +N. Now, let
Πbe the steady-state probability vector satisfying equations
ΠQ= 0 and Πe= 1, where erepresents a unit column vector.
Furthermore, we partition Πinto (Π0,Π1,...,ΠM), where
vector Πi=Πi,0,Πi,1,...,Πi,min(MN ,(M−i)N)and vector
Πi,j = (πi,j,0, πi,j,1, . . . , πi,j,L). Thus, πi,j,k is the steady-
state probability that the system is in state (i, j, k). The mth
πi,j,k element of Πcan be acquired as follows:
m="i
X
l=1
((M−i+1)N+1)#(L+1)+j(L+1)+(k+1).(4)
Undertaking the same approach of [7], Πican be obtained in
following matrix geometric form, where RM=−DMA−1
Mand
Ri=−Di[Ai+Ri+1Ci+1 ]−1for 1≤i≤M−1:
Πi= Π1
i
Y
j=1
Rj;i= 1,2, . . . , M, (5)
with the normalization Π1R0e0+PM
i=1 Qi
j=1 Rjei= 1,
where eidenotes the unit column vector.
III. PERFORMANCE MEASURES
In this section, we derive the dropping probability (PSU
drop)
and throughput (TSU )of SUs using the steady-state distribu-
tion obtained earlier. An SU is said to be dropped from the
system in any one of the following mutually-exclusive events:
•When an SU finds all bands occupied on arrival and the
retrial orbit full, it gives up its service with rate λsπM,0,L.
•When an arriving SU finds all sub-bands already taken
by other SUs and the orbit full, it leaves with rate
λsPM−1
i=0 πi,(M−i)N,L .
•When an SU in service is preempted by an arriving PU
and finds the orbit full, it quits the system with rate
λpPM
i=0 PN
l=1 πi,(M−i)N−l,L.
Consequently, (PSU
drop), defined as the ratio of the dropping
rate of SUs to their arrival rate, is derived to be:
PSU
drop =
M
X
i=0
πi,(M−i)N,L +λp
λs"M
X
i=0
N
X
l=1
πi,(M−i)N−l,L#.
(6)
The achievable throughput of SUs is the number of SUs
that succeed in accessing sub-bands per unit time and is [5]:
TSU =λs(1 −PSU
drop).(7)
IV. NUMERICAL AND SIMULATION RESULTS
We merely focus on the impact of SU retrials on the system
performance in this section. Without loss of generality, we set
λs= 1.5,λp= 0.1,µs= 0.4, and µp= 0.2in all scenarios.
Also, all simulation results have been averaged over 100 runs.
Fig. 2 depicts PSU
drop as functions of the user arrival rates for
varying (M, N )values with L=10 and θ= 2. To highlight the
retrial effect, our scheme is compared with a non-retrial system

Fig. 2: SU dropping probability with respect to arrival rates.
Fig. 3: SU throughput with respect to arrival rates.
(i.e. L= 0). We observe that PSU
drop increases with the arrival
rate of PUs. This probability however, reduces substantially
with increase in bands and sub-bands. In comparison to the
non-retrial system, the proposed model yields lower PSU
drop
values. For instance, at λp=0.4,PS U
drop reduces by almost 30%
as Mincreases to 3 and further by about 40% as Nrises to
3 in presence of retrying SUs. Similarly, PSU
drop increases with
the arrival rate of SUs. However, as λsincreases, PSU
drop in our
scheme converges to that of the non-retrial system accounting
for unavailable sub-bands and full orbit size.
For the same system parameters, the effect of λpand λson
the throughput of SUs are shown in Fig. 3. It is evident that for
any given (M, N ),TSU decreases as λpincreases, whereas it
interestingly rises with increase in λs. This is because of the
retrial action of SUs that result in higher sub-band utilization
as the number of SUs entering the system increases. For M=3
and λp=0.5,TSU steeply falls by almost 30% as Ndecreases
to 2, while this difference is less than 0.37% for λs= 0.5. This
clearly justifies the fact that more number of bands increases
the spectrum utilization opportunity for SUs.
Finally, Fig. 4 signifies the impact of SU retrial rate on their
dropping probability and throughput for (M, N ) = (3,2). We
see that the dropping probability of SUs in the system can
be reduced if the preempted/blocked SUs try to access idle
sub-bands more frequently. In other words, the chances of
SUs finding vacant sub-bands is higher if they keep retrying
for service at higher rates. Likewise, increasing Lallows for
the accommodation of more SUs and thus, further alleviates
their probability of being forced to leave the system. The
dropping probabilities for all Lvalues eventually stabilize for
high retrial rates. The opposite impact however, is anticipated
Fig. 4: SU dropping probability and throughput with respect
to retrial rate for varying Lvalues.
for SU throughput, i.e. with increase in θ, more SUs are able
to access the sub-bands. The higher SU throughput for orbits
with larger capacities is also apparent in this figure.
V. CONCLUSION
An OSA scheme for multi-band CRNs was investigated
in this paper, wherein the retrial behavior of blocked and
pre-empted SUs was considered. The proposed scheme was
modeled as a three-variate Markov chain and the steady-
state probability distribution was obtained using matrix ge-
ometric method. Measures such as SU dropping probability
and throughput were derived analytically and justified through
simulation results. Results revealed the evident impact of
retrial phenomenon with respect to PU and SU arrival rates,
the orbit size, and retrial rate of SUs in the orbit. A possible
extension to this work is considering general distributions for
the inter-arrival time, service time, and retrial time.
ACKNOWLEDGMENT
This research was a part of the project titled “Development
of Ocean Acoustic Echo Sounders and Hydro-Physical Prop-
erties Monitoring Systems”, funded by the ministry of Oceans
and Fisheries, Korea.
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