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1
Performance Analysis of Cognitive Radio Spectrum
Access with Prioritized Traffic
Vamsi Krishna Tumuluru, Student Member, IEEE, Ping Wang, Member, IEEE, Dusit Niyato, Member, IEEE, and
Wei Song, Member, IEEE,
Abstract—Dynamic spectrum access (DSA) is an important
design aspect for the cognitive radio networks. Most of the
existing DSA schemes are to govern the unlicensed user (i.e.,
secondary user) traffic in a licensed spectrum without compromising the transmissions of the licensed users, in which all the
unlicensed users are typically treated equally. In this paper,
prioritized unlicensed user traffic is considered. Specifically,
the unlicensed user traffic is divided into two priority classes
(i.e., high and low priority). We consider a general setting in
which the licensed users’ transmissions can happen at any time
instant. Therefore, the DSA scheme should perform spectrum
handoff to protect the licensed user’s transmission. Different
DSA schemes (i.e., centralized and distributed) are considered
to manage the prioritized unlicensed user traffic. These DSA
schemes use different handoff mechanisms for the two classes
of unlicensed users. We also study the impact of sub-channel
reservation for the high priority secondary users in both DSA
schemes. Each of the proposed DSA schemes is analyzed using
a continuous time Markov chain. For performance measures,
we derive the blocking probability, the probability of forced
termination, the call completion rate and the mean handoff delay,
for both high and low priority unlicensed users. The numerical
results are verified using simulations.
Index Terms—Cognitive radio, spectrum handoff, quality-ofservice (QoS), Markov chain analysis, dynamic spectrum access.
I. I NTRODUCTION
In the recent years, there has been tremendous increase in
the demand for spectrum due to the rapid proliferation of
wireless technologies and wireless markets. For example, the
Internet broadband markets are expanding despite the limited
spectrum (around the 2.4 GHz band) due to the competition
between the 3G cellular networks and the WiFi networks [1].
Such trends endanger the quality-of-service (QoS) that must
be achieved for the future wireless services. According to the
recently published report [2] by the Federal Communications
Commission (FCC), the spectrum regulatory authority in the
United States, the traffic distribution across the radio spectrum is extremely uneven. It is observed that the unlicensed
portions of the spectrum (2.4GHz and 5GHz bands) in which
most wireless networks operate (e.g. WiFi and WiMAX),
Manuscript received Feb. 01, 2011, revised April 26, 2011, Aug. 05, 2011
and Nov. 03, 2011, accepted Jan. 06, 2012. V. K. Tumuluru, P. Wang and D.
Niyato are with the School of Computer Engineering, Nanyang Technological
University, Singapore (e-mail: {tumu0001, wangping, dniyato}@ntu.edu.sg).
W. Song is with the Department of Computer Science, University of New
Burnswick (e-mail: [email protected]). This paper was partially presented at
IEEE ICC 2011.
Copyright (c) 2012 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to [email protected].
are heavily occupied whereas the licensed portions of the
spectrum (e.g. UHF band) are sporadically used. The above
observation motivates the design of wireless networks in which
the unlicensed users can explore and exploit unused portions
of the licensed spectrum while safeguarding the transmissions
of the licensed users.1 Such wireless networks are referred to
as the cognitive radio networks (CRNs) [4]. Recently, the FCC
approved the deployment of CRNs in the TV spectrum, subject
to specific operating constraints which were determined based
on a series of experiments [3]. Similar experiments were
conducted to classify other portions of the licensed spectrum
for the deployment of CRNs (e.g. public safety bands [5] and
cellular bands [6]).
The channel2 availability for the unlicensed users varies
both temporally and spatially, due to the licensed user’s
activity. This phenomenon is called spectrum heterogeneity
[7]. Spectrum heterogeneity complicates coordination among
the unlicensed users during data transmission. In order to cope
with spectrum heterogeneity, the unlicensed users in the CRN
implement two basic functions, namely spectrum sensing and
dynamic spectrum access (DSA) [4]. While spectrum sensing
is responsible for identifying idle channels in the licensed
spectrum, the DSA scheme is used to facilitate the unlicensed
users’ transmissions over the detected idle channels. An important aspect of a DSA scheme is to give higher priority to
the licensed users during spectrum access compared to the
unlicensed users. Due to this reason, the licensed user is also
known as the primary user (PU) and the unlicensed user is
known as the secondary user (SU).
In the following, we give an overview of how DSA is
addressed for different CRN architectures, namely centralized
and distributed, from the literature.
A. Related Work
1) DSA in Centralized CRN: In a centralized CRN, a
central controller manages the spectrum sensing and DSA for
the SUs associated with it. The DSA can be implemented
either as frame-level scheme (e.g., [9], [10]) or as call-level
scheme (e.g., [11]-[15]).
In the frame-level DSA schemes, a central controller implements medium access control (e.g., MAC protocol) on every
vacant licensed channel on a frame-by-frame basis to handle
the packet transmissions of the SUs associated with it. In the
1 A licensed user is a device which can legitimately operates in a licensed
spectrum.
2 A licensed spectrum can be divided into several channels (i.e., frequency
bands) which can be specified by their center frequency and bandwidth.
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IEEE 802.22 network [9], expected to provide DSA for SUs
in the TV spectrum, the MAC protocol is divided into uplink
(i.e, SUs to central controller) and downlink (central controller
to SUs) subframes. In each frame, the central controller
broadcasts the uplink and downlink schedules. The central
controller assigns exclusive bandwidth (portions of an idle TV
channel) to the SUs based on their bandwidth requests for
the uplink transmission. In [10], the central controller uses a
scheduling algorithm to assign SUs to the licensed channels at
the beginning of each frame such that the aggregate throughput
is maximized. In [10], the channel status varies within the
frame duration.
In the call-level DSA schemes ([11]-[15]), the SU and
PU transmissions are treated as calls which are assigned
dedicated frequency bands. However, an SU should relinquish
its frequency band when a PU call claims it, because the PU
call assignment is oblivious of any ongoing SU calls. The
central controller admits an SU call if the requested bandwidth
is available, and performs spectrum handoff (i.e., reassigning
an SU call to another vacant frequency band when it interferes
with a new PU call). According to the DSA scheme in [11],
an incoming SU call was queued till a new transmission
opportunity was found. Also, the SUs which experienced
handoff failure were dropped. In [12], the effect of a buffer
for SU call arrivals was considered. SUs which experienced
handoff failure were dropped. In [13], the SUs were queued
upon handoff failure and reassigned to channels when they
are available. Thus, the SU transmissions were prevented from
forced termination due to a PU arrival in [13]. In [14], Zhu
et al. proposed a DSA scheme which considered channel
reservation for SU handoff. According to [14], an incoming
SU call was assigned a channel only when the number of
idle channels in the licensed spectrum exceeds the number
of channels reserved for SU handoff. According to the DSA
scheme in [15], the central controller assigned as much as
possible bandwidth to the SUs to improve the spectrum utilization. This bandwidth assignment was performed whenever
the system state changed.
In all the above call-level DSA schemes, the performance
was analyzed using continuous time Markov chain (CTMC).
The performance was evaluated in terms of the blocking
probability and probability of forced termination for the SU
calls.
2) DSA in Distributed CRN: Most distributed CRNs have
also used frame-level DSA approach [16]-[22]. However, the
MAC protocol is managed by the SUs as there is no central
controller. A frame may be further divided into several slots.
During a frame, multiple SUs sharing the same idle channel
use contention mechanisms to transmit their packets (e.g.,
using CSMA/CA). Most distributed CRNs assume a common
control channel for coordination among the SUs (e.g., [17],
[18]). The MAC protocol in a distributed CRN is expected to
address issues including spectrum sensing, synchronization,
hidden/exposed nodes and group coordination.
According to the MAC protocol for the ECMA-392 standard
[16], proposed for providing DSA for SUs in TV spectrum,
an SU can transmit on a frame shared by several SUs using
two methods, namely PCA (prioritized contention access) or
2
CRP (channel reservation protocol). Under the PCA, an SU
transmits its packets on a channel based on its random backoff
time. The higher an SU’s priority, the shorter is the interval
from which it chooses the backoff value randomly. Under the
CRP, an SU reserves a few slots of the frame for contentionfree access. In [16], SUs perform handoff when they detect
a PU activity during the frame. In [17], all SUs participate
in detecting the idle channels in the current frame. However,
in [17], the winner of the contention phase in the previous
frame transmits on the detected idle channels in the current
frame. For analysis, the packet arrival and channel availability
at an SU were modeled as a M/G/1 queue in [17]. In [18],
the SUs form clusters or groups and each group is headed
by a leader. The leaders took responsibility for scheduling the
contention process and data transmissions within the respective
groups during the MAC frame. In [19], an SU modeled the PU
occupancy within a frame using a partially observable Markov
decision process (POMDP). Based on the state of the POMDP,
the expected rate of transmission for the winning SU pair
was analyzed. In [20]-[22], the IEEE 802.11 DCF (distributed
coordination function) mechanism [26] was adopted for the
contention process. For analysis, the saturation throughput of
the secondary user was calculated in [20]-[22].
In few works [23]-[25], the DSA was implemented without
SU coordination (i.e., no MAC protocol was considered). The
SU used slotted transmission. In these works, whenever the
SU sensed and accessed a channel successfully for a slot
(i.e., SU transmits data without causing collisions to the PU
transmissions) a reward was accrued. The objective of these
works was to maximize the expected reward over a finite
number of slots subject to the constraint on the interference
permissible to the PUs. This objective was achieved in [23][25] using constrained partially observable Markov decision
process (CPOMDP).
B. Contribution of the Paper
The major contributions of this paper are summarized
below:
In a real scenario, the SU traffic can be prioritized based on
QoS requirements (e.g., real-time traffic has higher priority
than non real-time traffic). To date, very few works [16],
[27]-[29] considered SU traffic prioritization. In these works,
the SUs’ priorities are used for packet transmission during
a frame. However, the SU priority does not affect spectrum
handoff. On the other hand, in our paper, SUs’ priorities play
an important role during spectrum handoff (e.g., a high priority
SU gets handoff before a low priority SU, in a two priority
class case). Our DSA schemes are particularly helpful when
multiple SU transmissions (ongoing or those on hold) require
handoff simultaneously.
Our DSA schemes work at a call-level, similar to other
existing call-level DSA schemes [11]-[15]. However, there are
several key differences with [11]-[15]: 1) we consider prioritybased spectrum handoff, 2) we propose distributed call-level
DSA schemes, and 3) we analyze the effect of handoff buffer
under both the centralized and distributed CRNs.
The rest of the paper is organized as follows. In Section
II, we present the system model and the proposed call-level
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DSA schemes for the centralized and distributed CRNs. In
Section III, we provide analytical models based on continuous
time Markov chain (CTMC) for the centralized and distributed
CRNs with respect to the proposed DSA schemes. The performance measures including the blocking probability, the probability of forced termination, the successful call completion
rate and mean handoff delay, for both high and low priority
SUs are derived. In Section IV, we present the numerical and
simulation results under the proposed DSA schemes. Finally,
Section V gives the concluding remarks.
II. S YSTEM M ODEL
The system (Fig. 1) is composed of M licensed channels,
each of which is further divided into N sub-channels (this
system model was also considered in [11], [12], [14], [15]).
The PU and SU transmissions are treated as calls which
use dedicated sub-channels. A PU call requires one channel
whereas an SU call requires one sub-channel3 . A PU call
assignment depends on the number of ongoing PU calls
(denoted by k) in the system (i.e., a PU call is admitted if
k < M ). A PU call assignment is oblivious of the ongoing SU
calls. Therefore, an ongoing SU call interfering the new PU
call should be handed-off to another vacant sub-channel. The
SUs are classified into two priority classes. The high priority
SUs are denoted as SU1 while the low priority SUs are denoted
as SU2 . We assume a fully connected CRN, i.e., all SUs
observe the same channel status (i.e., PU/SU activity). Perfect
sensing is assumed to detect the PU activity. A common
control channel is assumed to exist for the coordination among
the SUs.
sub-channel
1
N
N(M-1)+1
1
MN
M
channel
Fig. 1.
System model.
Licensed spectrum
In this paper, we propose various DSA schemes for the
centralized and the distributed CRN scenarios. For the centralized CRN, four novel DSA schemes are presented. These
centralized DSA schemes are denoted as DSA-C1, DSA-C2,
DSA-C3 and DSA-C4.4 For the distributed CRN, two novel
DSA schemes denoted as DSA-D1 and DSA-D2 are presented.
Each proposed DSA scheme performs handoff differently,
based on the SUs’ priorities. The schemes DSA-C1, DSAC2, and DSA-D1 will be referred to as DSA schemes without
buffer. In these schemes, the SU calls which experience
handoff failures are dropped. The schemes DSA-C3, DSA-C4
and DSA-D2 will be referred to as DSA schemes with buffer
because when an SU call experiences unsuccessful handoff,
it is placed on hold till further transmission opportunity is
available. Such on hold SU calls can be viewed as waiting in
a handoff buffer.
3 Note that this assumption is made for the simplicity of presentation. Our
DSA schemes can be applied to handle SU calls having different bandwidth
requirements.
4 Note that these are simply the names of our proposed DSA schemes which
will be explained later.
3
Under all the proposed DSA schemes, a number of subchannels are reserved for new high priority SU calls (SU1 ).
That is, if the total number of idle sub-channels is less than
ζ which is the number of sub-channels reserved for SU1 , the
new SU2 call will be rejected. In this way, we provide higher
priority for the SU1 calls over the SU2 calls.5
Call arrivals occur independently as Poisson processes with
mean arrival rates λp , λ1 and λ2 for PU, SU1 and SU2 , respectively. The service times independently follow exponential
distributions with mean service rates of µp , µ1 and µ2 for PU,
SU1 and SU2 calls, respectively. During a call (PU or SU),
the data traffic is disassembled into packets and the packet
transmissions are slotted. We assume the slot duration (Ts )
to be very small compared to a call duration. We assume
the packet delivery mechanism exists for each call (e.g.,
modulation and packet acknowledgement).
A. DSA Schemes for Centralized CRN
For the centralized CRN, we assume that a central controller performs spectrum sensing, sub-channel assignment and
spectrum handoff for the SU calls. The central controller
tracks all the ongoing calls (i.e., PU, SU1 and SU2 calls). Let
Y denote the total number of busy sub-channels at a given
time instant. New SU1 , SU2 and PU calls are dropped when
Y = M N , Y = M N − ζ and k = M , respectively. When a PU
starts transmission on a given channel, the central controller
performs handoff for any ongoing SU calls associated with the
sub-channels corresponding to this channel. These displaced
SU calls can belong to different priorities (SU1 and SU2 ), and
the central controller does handoff for displaced SU1 calls
followed by handoff for displaced SU2 calls (i.e., due to the
priority). Our centralized DSA schemes only differ in their
handoff mechanism (explained below).
1) Handoff Mechanism for DSA-C1: Handoff for DSA-C1
is done according to the following steps.
1) Randomly assign a displaced SU1 call to a unique idle
sub-channel (if available).
2) For the remaining displaced SU1 calls, terminate the
required number of ongoing SU2 calls and assign each
resulting idle sub-channel to a displaced SU1 call.
3) If there are no ongoing SU2 calls, terminate the remaining displaced SU1 calls.
4) After handoff for all the displaced SU1 calls, if there are
still idle sub-channels, randomly assign a displaced SU2
call to a unique idle sub-channel.
5) When there is no idle sub-channel, terminate the remaining displaced SU2 calls.
2) Handoff Mechanism for DSA-C2: The handoff in DSAC2 is the same as DSA-C1 except for steps (2) and (3). No
ongoing SU2 calls are terminated for the sake of SU1 handoff.
When there is no idle sub-channel, the displaced SU1 calls are
terminated.
3) Handoff Mechanism for DSA-C3: For DSA-C3, handoff
is done according to the following steps.
1) Randomly assign a displaced SU1 call to a unique idle
sub-channel (if available).
5 Note that the PU calls are not affected by such sub-channel reservation
due to the highest priority of PU.
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2) For the remaining displaced SU1 calls, place the required
number of ongoing SU2 calls on hold and assign each
resulting idle sub-channel to a displaced SU1 call.
3) If there are no ongoing SU2 calls, place the remaining
displaced SU1 calls on hold.
4) After handoff for all the displaced SU1 calls, if there are
still idle sub-channels, randomly assign a displaced SU2
call to a unique idle sub-channel.
5) When there is no idle sub-channel, place the remaining
displaced SU2 calls on hold.
When an ongoing SU call is placed on hold, new SU calls
(i.e., SU1 and SU2 ) are not accepted. When an ongoing call
(SU1 /SU2 /PU) completes service, the SU calls put on hold are
reassigned to the resulting idle sub-channels according to their
priority. These reassigned SU calls resume transmissions for
their remaining service times. The act of the central controller
placing a SU call on hold and reassigning an idle sub-channel
can be viewed as putting the displaced SU call in a virtual
buffer till transmission opportunity is available.
4) Handoff Mechanism for DSA-C4: For DSA-C4, handoff
is the same as DSA-C3 except for steps (2) and (3). No
ongoing SU2 calls are put on hold for the sake of SU1 handoff,
when there is no idle sub-channel the displaced SU1 calls are
put on hold.
B. DSA Schemes for Distributed CRN
In a distributed CRN, the SU calls independently perform
spectrum sensing, sub-channel selection and spectrum handoff.
During an SU call, the sender and destination exchange control messages on the common control channel (e.g., handoff
messages). A new SU call performs full spectrum sensing at
the beginning of the slot which occurs after its arrival time.
Then, the new SU call randomly picks an idle sub-channel
for transmission. New SU calls are dropped depending on the
number of detected busy sub-channels (e.g., a new SU2 call is
dropped if it sensed less than ζ idle sub-channels). An ongoing
SU call senses its own sub-channel in every slot to avoid
interference to the PU. If a PU call is detected, the ongoing SU
call must perform spectrum handoff. The handoff mechanisms
of the distributed DSA schemes are discussed below.
1) Handoff Mechanism for DSA-D1: Having detected the
PU call, at the commencement of the next slot, a displaced
SU (i.e., sender) determines the idle sub-channels through
full spectrum sensing. If idle sub-channels are found, the
displaced SU randomly selects only one idle sub-channel
and claims it using a contention process because there could
be other displaced SU calls also choosing the same subchannel. As the displaced SU calls can have different priorities,
we adopt the idea of contention resolution from the EDCF
(enhanced distributed coordination function) protocol in IEEE
802.11e network [30]. Note that unlike in the IEEE 802.11e
network [30] we allow only the winner of the contention
process (explained later) to stay on the sub-channel. In other
words, at most one displaced SU gets successful handoff on
a chosen idle sub-channel. The duration of the contention
process (Tc ) is smaller compared to the slot period.
During the contention process, the displaced SUs use an
arbitration inter-frame space (AIFS) and contention window
4
(CW) depending on their priority class (similar to [30]). A
displaced SU1 call uses shorter AIFS and CW than those
of a displaced SU2 call, as SU1 calls have higher priority
than SU2 calls. We denote the AIFS corresponding to the
SU1 calls and SU2 calls as AIF S1 and AIF S2 , respectively.
The CW corresponding to the SU1 calls and SU2 calls are
denoted as [1, W1 ] and [1, W2 ], respectively. Each displaced
SU senses its chosen idle sub-channel for a duration equal
to AIF Sx + backof fx depending on its priority x ∈ {1, 2},
where backof fx is the time spent for backoff based on the
random integer number chosen from the corresponding CW.
The handoff for a displaced SU is treated as successful if
it chose the lowest AIF Sx + backof fx among all displaced
SUs contending for the same idle sub-channel. An SU call
which achieves successful handoff resumes its transmission for
the remaining service time. A displaced SU call experiences
handoff failure under two scenarios: 1) the chosen sub-channel
becomes busy before its AIF Sx + backof fx expires (i.e., other
SU access the sub-channel first or a collision occurs), 2) if
idle sub-channels are not available. The displaced SU calls
experiencing handoff failure are dropped (i.e., treated as force
terminated by the incoming PU call).
2) Handoff Mechanism for DSA-D2: Unlike the DSA-D1
scheme, in the DSA-D2 scheme, displaced SU calls experiencing handoff failures are not terminated, but allowed to
retry in the subsequent slots till they get successful handoff.
Therefore, in the subsequent slot, such displaced SU calls perform spectrum sensing and repeat the contention process. The
displaced SU calls can be viewed as being in a virtual buffer
and contending for the idle sub-channels to get successful
handoff.
Additionally, in the DSA-D2 scheme, the displaced SU
calls are given higher priority over the new SU arrivals. A
new SU call (SU1 /SU2 ) must sense all idle sub-channels at
the beginning of the slot to ascertain any ongoing contention
process. Only when handoff SUs are not present (i.e., no
contention process is detected), the new SU call will be
admitted. This is accomplished by letting the handoff SUs
transmit a jamming signal at the beginning of the slot on their
selected idle sub-channels before the commencement of the
contention process.
III. P ERFORMANCE A NALYSIS
A. Analytical Models for Centralized CRN
In this section, we develop analytical models for the centralized CRN under each DSA scheme using a continuous time
Markov chain (CTMC). A CTMC can be described by its state
transition characteristics.
1) Centralized DSA Schemes without Buffer: The state
of the CTMC for the centralized DSA schemes without
buffer (DSA-C1 and DSA-C2) is denoted as [i, j, k], where
i ∈ {0, 1, . . . , M N }, j ∈ {0, 1, . . . , M N − ζ} and k ∈ {0, 1, . . . , M }
represent the number of ongoing SU1 , SU2 , and PU calls in the
system, respectively. For a valid state [i, j, k], Y (= i + j + kN )
should not exceed M N .
Let l (where l ∈ {0, 1, . . . , N }) and m (where m ∈ {0, 1, . . . , N })
respectively denote the number of SU1 call and SU2 calls
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displaced by an incoming PU call when the state is
l and m should satisfy the following conditions:
l ≤ i, m ≤ j
and
5
[i, j, k].
l + m ∈ {0, 1, . . . , N }
r := M N − Y − (N − (l + m))
and
r≥0
s := (l + m) − min(r, l + m) .
value 1 when the condition given inside the parenthesis is
true and returns 0 otherwise. In Fig. 2, δ2 = 1(i+j+kN <M N −ζ)
(condition for sub-channel reservation in state [i, j, k]) and
δ3 = 1(i+j+(k−1)N ≤N (M −1)) .
i, j , k − 1
(1)
iµ1
δ 2 ⋅ λ2
jµ 2
i
j
k
Y = i + j + kN
l and m
r
lq and mq
l′ and m′
s = l′ + m′
ls and ms
Number of ongoing SU1 calls
Number of ongoing SU2 calls
Number of ongoing PU calls
Number of busy sub-channels
Number of displaced SU1 and SU2 calls
Number of sub-channels available for handoff
Number of SU1 and SU2 calls in buffer
Number of unsuccessful SU1 and SU2 handoff calls
Total number of unsuccessful handoff calls
Number of successful SU1 and SU2 handoff calls
The evolution of the state [i, j, k] of the CTMC is presented
under three cases of Y :
1) Y ≤ N (M − 1): The system has at least N idle subchannels.
2) N (M − 1) < Y < M N : The number of idle sub-channels
in the system is in the range {1, . . . , N − 1}.
3) Y = M N : The system has no idle sub-channel.
For the case Y ≤ N (M − 1), all displaced SU1 and SU2 calls
get successful handoff (i.e., s = 0) when displaced by a PU call
arrival. In other words, no calls are terminated (under DSAC1 and DSA-C2) due to an incoming PU call. For the case
N (M − 1) ≤ Y < M N , s = {1, . . . , N − 1} number of SU calls
experience unsuccessful handoff whereas, when Y = M N , s =
N SU calls experience unsuccessful handoff. The exact number
of terminated SU1 and SU2 calls under each centralized DSA
scheme are explained later. Let l′ and m′ denote the number
of terminated SU1 and SU2 calls, respectively. Thus, l′ + m′ =
s. For convenience, a quick reference of the symbols with
descriptions frequently used in this paper is given in Table I.
a) State Transitions under DSA-C1 Scheme: Under the
DSA-C1 scheme, the transitions for the state [i, j, k] for different cases of Y are explained using Fig. 2. State transitions
from/to the state [i, j, k] occur due to any of the six possible
events, namely PU call arrival, SU1 call arrival, SU2 call arrival,
PU call departure, SU1 call departure and SU2 call departure.
Each state transition is represented by its corresponding rate.
Taking as an example, a SU2 call arrival in state [i, j − 1, k]
causes a transition to state [i, j, k] with a rate δ1 · λ2 , where
δ1 = 1(i+(j−1)+kN <M N −ζ) specifies the condition for subchannel reservation (i.e., a new SU2 call is accepted by the
system only when the condition i + (j − 1) + kN < M N − ζ
holds), where 1(·) is the indicator function which returns the
( j + 1) µ 2
γ li′,,mj , k′
Q UICK REFERENCE OF FREQUENTLY USED SYMBOLS WITH
DESCRIPTIONS .
i − l ′, j − m ′, k + 1
Fig. 2.
(i + 1) µ1
i, j , k
δ1 ⋅ λ2
i, j − 1, k
Description
i + 1, j , k
λ1
TABLE I
Symbols
δ3 ⋅λ p
kµ p
λ1
i − 1, j , k
In Eq. (1), the first condition defines the maximum number
of SU calls that can be displaced upon a PU call arrival.
The second condition defines the number of sub-channels
available for handoff (denoted as r) for the displaced SU calls.
Accordingly, the total number of unsuccessful handoff calls
(denoted as s) is calculated in the third condition.
i, j + 1, k
(k + 1) µ p
i, j , k + 1
State transitions for centralized DSA schemes without buffer.
′
The transition rate γli,j,k
′ ,m′ from state [i, j, k] to state [i − l , j −
m′ , k + 1] is calculated as follows.
1) Let Nl′ ,m′ denote the set containing the valid combinations of (l′ , m′ ).
2) For every valid pair of (l′ , m′ ) in the set Nl′ ,m′ , find Rl′ ,m′
which represents the number of valid combinations of l,
m, r and s = l′ + m′ . Valid l, m, r and s for given [i, j, k]
can be found using Eq. (1).
3) Then, the transition rate γli,j,k
′ ,m′ is given by
γli,j,k
′ ,m′ =
Rl′ ,m′
∑
Rl′ ,m′
λp .
(2)
(l′ ,m′ )∈Nl′ ,m′
Taking into consideration the handoff mechanism explained in
Section II-A1, the variables l′ and m′ in Eq. (2) are given by
l′ = s−min(j, s) and m′ = min(j, s). The value of s is determined
by Eq. (1).
For the cases Y ≤ N (M − 1) and N (M − 1) < Y < M N , all the
transitions shown in Fig. 2 are valid. For the case Y = M N ,
the transitions between the states [i, j, k] and [i + 1, j, k], and
[i, j, k] and [i, j + 1, k] are not considered as the system is full
(i.e., idle sub-channels not available). Apart from the state
transitions shown in Fig. 2, when Y = M N , few transitions
occur from the states in which the number of ongoing calls
is greater than N (M − 1) to the state [i, j, k] due to a PU call
arrival. These transitions are described below.
• Transition from state [i, j + j ′ , k − 1] to state [i, j, k] occurs
i,j+j ′ ,k−1
with rate γ0,j
, where j > 0 and 0 < j ′ < N . The
′
i,j+j ′ ,k−1
rate γ0,j ′
is calculated using Eq. (2) corresponding
to the state [i, j + j ′ , k − 1]. During this state transition, j ′
SU2 calls are terminated.
• Transition from state [i + (s′ − j ′ ), j + j ′ , k − 1] to state
i+(s′ −j ′ ),j+j ′ ,k−1
, where j = 0,
[i, j, k] occurs with rate γs′ −j ′ ,j ′
i+(s′ −j ′ ),j+j ′ ,k−1
′
′
′
is
0 < s < N and 0 ≤ j < s . The rate γs′ −j ′ ,j ′
calculated using Eq. (2) corresponding to the state [i +
(s′ − j ′ ), j + j ′ , k − 1]. During this state transition, s′ − j ′
SU1 calls and j ′ SU2 calls are terminated.
b) State Transitions under DSA-C2 Scheme: Fig. 2 also
represents the state transitions under the DSA-C2 scheme for
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the various cases of Y . According to the handoff mechanism
under DSA-C2 scheme, the number of terminated SU1 and
SU2 calls are given as l′ = l − min(r, l) and m′ = max(0, m −
max(0, r − l)), respectively. All state transitions shown in Fig. 2
occur similar to those of the DSA-C1 scheme. Apart from the
state transitions given in Fig. 2, transitions occur from states
[i+i′ , j+j ′ , k−1] (in which i+j+(k−1)N = N (M −1)) to the state
[i, j, k] when Y = M N , where 0 ≤ i′ , j ′ < N and 0 < i′ + j ′ < N .
2) Centralized DSA Schemes with Buffer: The state of
the CTMC for the centralized DSA schemes with buffer
(DSA-C3 and DSA-C4) is denoted as [i, j, k, lq , mq ], where
i ∈ {0, 1, . . . , M N }, j ∈ {0, 1, . . . , M N − ζ} and k ∈ {0, 1, . . . , M }
represent the number of ongoing SU1 , SU2 , and PU calls in
the system, respectively. The variables lq ∈ {0, 1, . . . , M N } and
mq ∈ {0, 1, . . . , M N − ζ} represent the number of SU1 and SU2
calls waiting in the buffer due to unsuccessful handoff. Here
also, Y = i+j +kN . For a valid state [i, j, k, lq , mq ], the following
conditions must hold:
Y ≤ M N, i + j + lq + mq ≤ M N
and
j + mq ≤ M N − ζ.
(3)
As in Section III-A1, the same three cases of Y are
considered to explain the state transitions. The state transitions
are also classified according to the buffer status (empty and
non-empty).
a) State Transitions under DSA-C3 Scheme: Fig. 3
shows the transitions of state [i, j, k, lq , mq ] for the DSA-C3
scheme when the buffer is empty (i.e., lq + mq = 0). For
lq + mq = 0, except for the transitions between the states
[i, j, k, 0, 0] and [i − l′ , j − m′ , k + 1, l′ , m′ ] for Y = M N , the
state transitions under DSA-C3 scheme and the DSA-C1
scheme (as shown in Fig. 2) are the same for all cases of
Y . Here, l′ = s − min(j, s) and m′ = m − min(j, s). During a
PU call arrival for Y = M N , l′ SU1 calls and m′ SU2 calls
are placed in the buffer. As a result, [i, j, k, 0, 0] changes to
i,j,k
[i−l′ , j −m′ , k+1, l′ , m′ ] with rate γli,j,k
′ ,m′ . As γl′ ,m′ is independent
of buffer status, it is calculated using Eq. (2). A PU departure
in state [i − l′ , j − m′ , k + 1, l′ , m′ ] reassigns all the SU1 and SU2
calls in the buffer and hence, state changes to [i, j, k, 0, 0].
Fig. 4 shows the state transitions under the DSA-C3 scheme
when the buffer is non-empty (i.e., lq + mq > 0) which occurs
only for the case Y = M N . A new SU1 or SU2 call arrival
cannot be accommodated when the buffer is non-empty. A PU
call arrival adds l′ + m′ = N SUs to the buffer. SU calls in the
buffer are reassigned sub-channels following a departure event
(PU/SU1 /SU2 ) according to their priority (refer Section II-A3).
For the variables l̂, m̂, l′′ and m′′ shown in Fig. 4, when a SU1
call (or SU2 ) departs l̂ = min(1, lq ) and m̂ = mq − (1 − min(1, lq )).
When a PU call departs l′′ = min(N, lq ) and m′′ = mq − (N −
min(N, lq )). When transition occurs from state [i, j+j ′ , k−1, 0, 0],
lq = 0 and mq = j ′ where j > 0 and 0 < j ′ < N . Similarly, for
the transition occurring from state [i + (s′ − j ′ ), j + j ′ , k − 1, 0, 0],
lq = s′ − j ′ and mq = j ′ where j = 0, 0 < s′ < N and 0 ≤
j ′ < s′ . In Fig. 4, δ4 = 1(N (M −1)≤i+(j+j ′ )+(k−1)N <M N ) and
δ5 = 1(N (M −1)≤(i+(s′ −j ′ ))+(j+j ′ )+(k−1)N <M N ) .
b) State Transitions under DSA-C4 Scheme: Fig. 3 and
Fig. 4 also represent the state transitions under the DSA-C4
scheme. However, for the DSA-C4 scheme, l′ = l − min(r, l)
6
and m′ = max(0, m − max(0, r − l)). The order of reassignment
of SU calls from the buffer is the same in the DSA-C3 and
DSA-C4 schemes.
i, j , k − 1,0,0
i − 1, j , k ,0,0
λ1
kµ p
i + 1, j , k ,0,0
λp
λ1
iµ1
(i + 1) µ1
i, j , k ,0,0
δ1 ⋅ λ2
δ 2 ⋅ λ2
jµ 2
i, j − 1, k ,0,0
γ li′,,mj , k′
(k + 1) µ p
( j + 1) µ 2
i, j + 1, k ,0,0
i − l ′, j − m ′, k + 1, l ′, m ′
Fig. 3. State transitions for centralized DSA schemes with buffer, lq = 0
and mq = 0.
i + l ′′, j + m ′′, k − 1, l q − l ′′, m q − m ′′
iµ1
kµ p
)
)
i + l , j + m, k − 1,
)
)
lq − l , mq − m
i, j + j ′, k − 1,0,0
δ 4 ⋅ γ 0i ,, jj+′ j ′,k −1
i, j , k , l q , m q
δ 5 ⋅ γ si ′+−( sj ′′,−j ′j ′), j ′+ j ′, k −1
jµ 2
γ li′,,mj , k′
i + ( s ′ − j ' ), j + j ′, k − 1,0,0
i − l ′, j − m ′, k + 1, l q + l ′, m q + m ′
Fig. 4. State transitions for centralized DSA schemes with buffer, lq +mq >
0.
B. Analytical Models for Distributed CRN
In this section, we develop the analytical models for the
distributed DSA schemes (DSA-D1 and DSA-D2) using two
different CTMCs.
1) DSA-D1 Scheme: Similar to the DSA-C1 and DSA-C2,
the state of the CTMC under the DSA-D1 scheme (i.e., without
buffer case) is denoted as [i, j, k] where i, j and k have the same
meanings as those defined in Section III-A1.
The state transitions for the state [i, j, k] under the DSAD1 scheme are shown in Fig. 5, where l′ ∈ {0, . . . , N }, m′ ∈
{0, . . . , N } and l′ + m′ ∈ {s, . . . , N } (s is determined by Eq. (1)).
Similar to Section III-A1, the state transitions can be explained
on the basis of Y (some transitions are ignored depending on
Y ). For the cases Y ≤ N (M − 1) and N (M − 1) < Y < M N ,
all the state transitions shown in Fig. 5 occur. For the case
Y = M N , the transitions between the states [i, j, k] and [i+1, j, k]
do not occur, and the transitions between the states [i, j, k] and
[i, j + 1, k] also do not occur.
′
The transition rate ξli,j,k
′ ,m′ from state [i, j, k] to state [i − l , j −
m′ , k + 1] in Fig. 5 is calculated as Pd (l′ , m′ |i, j, k) · λp , where
Pd (l′ , m′ |i, j, k) denotes the probability that l′ SU1 and m′ SU2
calls are dropped following a PU call arrival. Pd (l′ , m′ |i, j, k) is
expressed as follows:
Pd (l′ , m′ |i, j, k) =
∑
Pd (l′ , m′ |l, m, i, j, k) · P (l, m|i, j, k) .
(4)
∀l,m
In the above equation,
P (l, m|i, j, k) is calculated
( N ) ((M −k−1)N )
· i−l,j−m
l,m
P (l, m|i, j, k) =
((M −k)N )
i,j
as
(5)
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7
where l, m, r and s are determined by Eq. (1) for state z. The
(c)
notation a,b
denotes the number of ways of arranging a SU1
calls, b SU2 calls in c (≥ a + b) sub-channels without repetition.
As l′ + m′ = s depends only on l, m and r corresponding to state [i, j, k], Pd (l′ , m′ |l, m, i, j, k) can be rewritten as
Pd (l′ , m′ |l, m, r). Accordingly, Eq. (4) is modified as
Pd (l′ , m′ |i, j, k) =
∑
Pd (l′ , m′ |l, m, r) · P (l, m|i, j, k) .
(6)
transitions except those corresponding to SU call arrivals are
valid.
i,j,k,lq ,mq
In Fig. 6, the rate Pl,m
is equal to P (l, m|i, j, k) ·
λp , where P (l, m|i, j, k) is calculated using Eq. (5). The
q ,mq
is given by P (ls , ms |lq , mq , r′ ) · λp , where
rate ξli,j,k,l
s ,ms
′
P (ls , ms |lq , mq , r ) is also calculated using Eq. (7), by replacing
l, m and r in Ps (ls , ms |l, m, r) with lq , mq and r′ = M N − Y .
i, j , k − 1
∀l,m
where ls = l − l′ and ms = m − m′ denote the number SU1 and SU2 calls experiencing successful
handoff. The probability Ps (ls = e, ms = f |l, m, r) (where
0 < e + f ≤ (l + m) − s) is calculated recursively as in Eq. (7),
( )
where Pr (l, g) = gl (1/r)g (1 − 1/r)l−g denotes the probability
that g out of l SU1 calls contend for the same sub-channel.
( )
Similarly, Pr (m, h) = m
(1/r)h (1 − 1/r)m−h in Eq. (7) denotes
h
the probability that h out of m SU2 calls contend for the same
sub-channel. The meaning of Eq. (7) is explained as follows.
Consider one of the r available sub-channels to be tagged.
The left-hand side of Eq. (7) denotes the probability that e
out of l SU1 calls and f out of m SU2 calls achieve successful
handoff, given that l SU1 calls and m SU2 calls contend for r
sub-channels. The right-hand side of Eq. (7) denotes the total
probability that at least one successful handoff (i.e., either one
SU1 call or one SU2 call or none) occurs in the tagged subchannel in which exactly g out of l SU1 calls and h out of
m SU2 calls contend, while the remaining successful handoffs
(i.e., excluding the successful handoff happening in the tagged
sub-channel) occur in the remaining r − 1 sub-channels which
are contended by the remaining l − g SU1 calls and m − h SU2
calls.
In the Eq. (7), Ps (ls = 1, ms = 0|g, h, 1) is calculated as in Eq.
(8) where △= AIF S2 − AIF S1 . Also in Eq. (7), Ps (ls = 0, ms =
1|g, h, 1) is calculated as in Eq. (9) Note that Ps (ls , ms |l, m, r) =
0 for r ≤ 0, ls > l and ms > m. The Eqs. (8) and (9) can be
explained in a similar fashion. For example, Eq. (8) gives the
probability that one displaced SU1 call gets successful handoff
while g SU1 calls and h SU2 calls contend for the same subchannel. In Eq. (8), the summations give total probability that
the tagged SU1 call gets successful handoff for choosing its
backoff value w1 ∈ [1, W1 ] while the other g − 1 SU1 calls and h
SU2 calls (contending for the same sub-channel) choose their
backoff values larger than w1 .
Ps (ls , ms |l, m, r),
C. DSA-D2 Scheme
Similar to DSA-C3 and DSA-C4 schemes, the state of the
CTMC for the DSA-D2 scheme is denoted as [i, j, k, lq , mq ]
where i, j , k, lq and mq have the same meanings as those
defined in Section III-A2. The state transitions are shown in
Fig. 6. The state transitions are explained based on the buffer
status (empty and non-empty).
When the buffer is empty (i.e., lq + mq = 0), all state
transitions except that to the state [i+ls , j +ms , k, lq −ls , mq −ms ]
are valid. The admission of an SU (SU1 or SU2 ) call is done
based on Y (= i + j + kN ), similar to other DSA schemes.
When the buffer is non-empty (i.e., lq + mq > 0), all the state
λ1
i − 1, j , k
Pd (l′ , m′ |l, m, r) in Eq. (6) is equivalent to the probability P (ls , ms handoff successfully|l, m, r) or simply denoted as
i + 1, j , k
kµ p
λ1
iµ1
δ1 ⋅ λ2
i, j − 1, k
(i + 1) µ1
i, j , k
δ 2 ⋅ λ2
jµ 2
( j + 1) µ 2
ξ li′,,mj ,k′
(k + 1) µ p
i, j , k + 1
i − l ′, j − m ′, k + 1
Fig. 5.
i, j + 1, k
State transitions for the DSA-D1 scheme.
i + l s , j + ms , k , l q − l s , mq − ms
i − 1, j , k , l q , m q
λ1
i , j , k ,l q , m q
s , ms
(1 / Tc) ⋅ ξ l
iµ1
kµ p
i, j , k , l q , m q
δ 1 ⋅ λ2
jµ 2
i, j − 1, k , l q , m q
i , j , k ,l q , m q
Pl ,m
i, j , k − 1, l q , m q
i − l , j − m, k + 1, l q + l , m q + m
Fig. 6.
State transitions for the DSA-D2 scheme.
D. Performance Measures
The performance measures for each DSA scheme are
expressed using the steady state probability distribution of
its corresponding CTMC. We derive performance measures
(for both SU1 and SU2 calls) such as blocking probability,
probability of forced termination, successful call completion
rate and mean handoff delay.
Let Πz denote the steady state distribution of a CTMC
whose state is denoted as z. For the DSA-C1, DSA-C2 and
DSA-D1 schemes, z = [i, j, k] whereas for the DSA-C3, DSAC4 and DSA-D2 schemes z = [i, j, k, lq , mq ]. To simplify
the presentation, we use the same notations under all DSA
schemes. For any DSA scheme, the corresponding steady
state probability distribution Πz is obtained by finding the
corresponding transition rate matrix Q and applying the GaussSeidel algorithm [31]. Each row of Q represents the transitions
with respect to a specific state z, as a balance equation. For
example, referring to Fig. 3, one balance equation with respect
to the state [i, j, k, 0, 0] under the DSA-C3 scheme is expressed
as in Eq. (10), where Π[i,j,k,0,0] represents the steady state
probability for state [i, j, k, 0, 0] under the DSA-C3 scheme.
1) Blocking Probability: The blocking probability represents the probability with which an incoming SU call (SU1
or SU2 ) is not permitted to enter the system due to the lack
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Ps (ls = e, ms = f |l, m, r) =
m
l ∑
∑
8
(
Pr (l, g)Pr (m, h) · Ps (ls = 1, ms = 0|g, h, 1) · Ps (ls = e − 1,
g=0 h=0
ms = f |l − g, m − h, r − 1) + Ps (ls = 0, ms = 1|g, h, 1) · Ps (ls = e, ms = f − 1|l − g, m − h, r − 1)
)
+ Ps (ls = 0, ms = 0|g, h, 1) · Ps (ls = e, ms = f |l − g, m − h, r − 1)


0
if g = 0, h ≥ 0

 ∑
(g) 1 ( W1 −w1 )g−1
△
+
Ps (ls = 1, ms = 0|g, h, 1) =
w1 =1 1 W1
W

(g) 1 ( W11 −w1 )g−1 ( W2 −(w1 −△) )h

 ∑W1
if g > 0, g + h > 0
w1 =△+1 1 W1
W1
W2


0
if g ≥ 0, h = 0

 ∑
(h) 1 ( W2 −w2 )h−1
W2
if g = 0, h ≥ 1
Ps (ls = 0, ms = 1|g, h, 1) =
w2 =1 1 W2
W2


 ∑W1 −(△+1) (h)( W1 −(w2 +△) )g 1 ( W2 −w2 )h−1 if g > 0, h > 0.
w2 =1
W1
1
W2
(7)
(8)
(9)
W2
[kµp + δ2 λ2 + λ1 + γli,j,k
′ ,m′ + iµ1 + jµ2 ] · Π[i,j,k,0,0] = λp Π[i,j,k−1,0,0] + δ1 λ2 Π[i,j−1,k,0,0]
+ (j + 1)µ2 Π[i,j+1,k,0,0] + (i + 1)µ1 Π[i+1,j,k,0,0] + (k + 1)µp Π[i,j,k+1,0,0] + λ1 Π[i−1,j,k,0,0]
of sub-channels or due to SU calls on hold. The blocking
probability of SU1 calls denoted as PB1 is expressed as
∑
PB1 =
(11)
Πz .
∀z, Y =M N
The blocking probability of
expressed as
SU2
calls denoted as
∑
PB2 =
PB2
is
4) Mean Handoff Delay: The mean handoff delay for SU1
(SU2 ) calls is defined as the mean time taken by the SU1 (SU2 )
calls to perform successful handoff. Let HD1 and HD2 denote
the handoff delays for SU1 and SU2 calls, respectively. For
the DSA-C3, DSA-C4 and DSA-D2 schemes (i.e., with buffer
cases), the mean handoff delays corresponding to SU1 and SU2
calls is given as follows:
∀z, Y ≥M N −ζ
2) Probability of Forced Termination: The probability of
forced termination represents the probability with which an
ongoing SU call (SU1 or SU2 ) is terminated by an incoming
PU call. Note that forced termination occurs only with DSAC1, DSA-C2 and DSA-D1 schemes (i.e., without buffer cases).
The probability of forced termination for the SU1 calls denoted
as PF 1 , is expressed as
PF 1 =
∑
l′ · Qz,z′ · Πz
∀z, i≥l′ , j≥m′
(13)
λ1 (1 − PB1 )
where Qz,z′ denotes the transition rate from state z = [i, j, k]
to state z′ = [i − l′ , j − m′ , k + 1]. In Eq. (13), the numerator
denotes the probability that l′ SU1 calls are terminated in state z
whereas the denominator denotes the effective rate with which
a new SU1 call is assigned a sub-channel.
Similarly, the probability of forced termination for the SU2
calls denoted as PF 2 , is expressed as
PF 2 =
∑
∀z, i≥l′ , j≥m′
m′ · Qz,z′ · Πz
λ2 (1 − PB2 )
.
(14)
In Eqs. (13) and (14), l′ and m′ depend on the DSA scheme.
For the schemes DSA-C3, DSA-C4 and DSA-D2 (i.e., with
buffer cases), PF 1 = 0 and PF 2 = 0.
3) Call Completion Rate: The call completion rate under
a given SU priority class represents the mean number of calls
having that priority, and successfully completing their service.
Let η1 and η2 denote the call completion rate for SU1 and
SU2 calls, respectively. The call completion rate η1 is given
by η1 = λ1 (1 − PB1 )(1 − PF 1 ). The call completion rate η2 is
given by η2 = λ2 (1 − PB2 )(1 − PF 2 ).
l′
∑
z lq Πz
l′ · Qz,z′ · Πz
∑
m′
z mq Πz
·∑
HD2 =
′·Q
m
m
′
′
z,z′ · Πz
l ,m ,z
HD1 =
(12)
Πz .
(10)
where
l
·∑
l′ ,m′ ,z
(15)
(16)
represents the transition rate from state z =
to state z′ = [i − l′ , j − m′ , k + 1, lq + l′ , mq + m′ ].
In the above equations, l and m denote the mean number
of SU1 and SU2 calls displaced during a PU call arrival,
∑
respectively. They are calculated as l = l,m,z l · P (l, m|z)Πz
∑
and m = l,m,z m · P (l, m|z)Πz . l′ and m′ denote the mean
number of SU1 and SU2 calls experiencing unsuccessful handoff during a PU call arrival. They are calculated as l′ =
∑
∑
′
′
′
′
′
l′ ,m′ ,l,m,z m ·
l′ ,m′ ,l,m,z l · P (l , m |l, m)P (l, m|z) and m =
′
′
′
′
P (l , m |l, m)P (l, m|z), where P (l , m |l, m) is equal to 1 if l′
and m′ are valid for the given l and m corresponding to
the state z, otherwise P (l′ , m′ |l, m) = 0. Here, P (l, m|z) (or
P (l, m|i, j, k, lq , mq )) is equivalent to P (l, m|i, j, k) as l and m
are independent of lq and mq . Therefore, P (l, m|i, j, k, lq , mq ) is
also calculated using Eq. (5).
For the DSA-C1, DSA-C2 and DSA-D1 schemes (i.e.,
without buffer cases) as the unsuccessful handoff calls are
dropped immediately, HD1 = 0 and HD2 = 0.
Qz,z′
[i, j, k, lq , mq ]
IV. R ESULTS AND D ISCUSSION
In this section, we evaluate the performance of the CRN
under each proposed DSA scheme using the performance
measures derived in the Section III. The accuracy of the
analysis is verified through simulations. In our experiments,
we use the following parameter settings, M = 3, N = 4, λ1 = 1,
λ2 = 1, λp ∈ {0.4, . . . , 1}, µ1 = 0.5, µ2 = 0.5, µp = 1.8, ζ = 1,
Ts = .1s and Tc = 0.02s (Table II gives the description for
the parameter settings). For convenience, the arrival rates and
service rates are expressed in calls/second. For the DSA-D1
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9
Symbols
Description
M
N
λ1 , λ2 and λp
µ1 , µ2 and µp
Number of channels in the system
Number of sub-channels per channel
Mean arrival rate of SU1 , SU2 and PU calls
Mean service rate of SU1 , SU2 and PU
calls
Number of sub-channels reserved for SU1
call arrival
Slot duration
Maximum contention duration
Arbitrary inter-frame space for SU1 and
SU2 calls
Contention window size for SU1 and SU2
calls
ζ
Ts
Tc
AIF S1 and AIF S2
W1 and W2
A. Call Completion Rate
Fig. 7(a) and Fig. 7(b) show the effect of PU call arrival rate
(λp ) on call completion rate of the SU1 and SU2 calls under
the different proposed DSA schemes, respectively. The call
completion rate corresponding to the DSA-C4 scheme is the
same as that corresponding to the DSA-C3 scheme and hence,
it is not shown. It can be seen from Fig. 7(a) and Fig. 7(b) that
as λp increases, the call completion rate of the SU calls (η1
and η2 ) decreases under all the DSA schemes. This is because
the number of busy sub-channels increases with an increase
in λp , causing higher blocking probabilities for the SU calls
and subsequently lower call completion rate.
(b)
1
0.95
0.95
Call completion rate of SU2 calls, η2 (calls/sec)
Call completion rate of SU1 calls, η1 (calls/sec)
(a)
1
0.9
0.85
0.8
DSA−C1 <a>
DSA−C1 <s>
DSA−C2 <a>
DSA−C2 <s>
DSA−D1 <a>
DSA−D1 <s>
DSA−C3 <a>
DSA−C3 <s>
DSA−D2 <a>
DSA−D2 <s>
0.75
0.7
0.65
0.4
0.6
0.8
1
PU arrival rate, λp (calls/sec)
0.9
0.85
0.8
DSA−C1 <a>
DSA−C1 <s>
DSA−C2 <a>
DSA−C2 <s>
DSA−D1 <a>
DSA−D1 <s>
DSA−C3 <a>
DSA−C3 <s>
DSA−D2 <a>
DSA−D2 <s>
0.75
0.7
0.65
0.4
0.6
0.8
1
PU arrival rate, λp (calls/sec)
Fig. 7. Effect of PU call arrival rate on call completion rate for (a) SU1
calls and (b) SU2 calls, under all DSA schemes.
It can also be seen that the DSA schemes using handoff
buffer give higher call completion rate (η1 and η2 ) compared
to those without buffer. This is because the forced termination
of SU calls is prevented in the DSA schemes with buffer (i.e.,
DSA-C3, DSA-C4 and DSA-D2). The call completion rate
of the DSA-D2 scheme is less than those of the centralized
DSA schemes which use buffer, because the handoff calls wait
longer time in the buffer due to contention process, resulting in
a longer service time for SU calls. It is observed that the DSAD1 scheme gives the lowest values of η1 and η2 among all the
(a)
(b)
DSA−C1 <a>
DSA−C1 <s>
DSA−C2 <a>
DSA−C2 <s>
DSA−D1 <a>
DSA−D1 <s>
0.25
Forced termination probability of SU2 calls, PF 2
TABLE II
D ESCRIPTION FOR PARAMETER SETTINGS .
DSA schemes. This is because some SU1 and SU2 calls are
terminated due to collision during handoff. It is also observed
that the DSA-C1 scheme gives higher value of η1 than the
DSA-C2 scheme. Further, the DSA-C2 scheme has higher
value of η2 than the DSA-C1 scheme. The reason for both
these behaviors is the same, i.e., some SU2 calls are terminated
by the displaced SU1 calls during handoff under the DSA-C1
scheme but no such termination occurs under the DSA-C2
scheme. This fact is confirmed by the Fig. 8(a) and Fig. 8(b)
which show the effect of PU call arrival rate on the probability
of forced termination for the SU1 and SU2 calls, respectively.
Forced termination probability of SU1 calls, PF 1
and DSA-D2 schemes, AIF S1 = 1, AIF S2 = 2, W1 = 2 and
W2 = 3. The symbols < a > and < s > in the figures indicate
analytical and simulation results, respectively.
0.2
0.15
0.1
0.05
0
0.4
0.6
0.8
1
PU arrival rate, λp (calls/sec)
DSA−C1 <a>
DSA−C1 <s>
DSA−C2 <a>
DSA−C2 <s>
DSA−D1 <a>
DSA−D1 <s>
0.25
0.2
0.15
0.1
0.05
0
0.4
0.6
0.8
1
PU arrival rate, λp (calls/sec)
Fig. 8. Effect of PU call arrival rate on forced termination probability of (a)
SU1 calls and (b) SU2 calls, under DSA schemes without buffer.
It can be seen that the PF 1 for the DSA-C1 scheme is lower
than that of the DSA-C2 scheme, and PF 2 for DSA-C2 scheme
is lower than that of the DSA-C1 scheme. Fig. 8(a) shows
that the distributed case (DSA-D1) has the highest value of
PF 1 . Similarly, Fig. 8(a) shows the distributed case having
the highest PF 2 . Further, it is intuitive that an increase in
λp causes an increase in both PF 1 and PF 2 , as shown in
Fig. 8(a) and Fig. 8(b). The analysis and simulation results
match well for the successful call completion rates (η1 and η2 )
and probability of forced termination (PF 1 and PF 2 ), under all
the DSA schemes.
B. Mean Handoff Delay
Fig. 9(a) shows the effect of the PU call arrival rate (λp )
on the mean handoff delay of SU1 calls (HD1 ) under the
centralized and distributed schemes using handoff buffer. It can
be seen that as λp increases D1 also increases. This is because
the channels mostly carry PU traffic as λp increases. Fig. 9(a)
shows that the DSA-C3 scheme has the lowest value of HD1 .
This is because under this scheme, the SU1 calls get immediate
handoff as long as some ongoing SU2 calls are present (i.e.,
in such scenario, handoff delay is zero). As a result, the mean
handoff delay (HD1 ) is smaller. Fig. 9(a) shows the DSA-D2
scheme having higher value of HD1 than that of the centralized
DSA schemes. This is because the contention and collision
during handoff lead to longer handoff times.
Fig. 9(b) shows the effect of the PU call arrival rate (λp )
on the mean handoff delay of SU2 calls (HD2 ) under the
centralized and distributed schemes which use handoff buffer.
It can be seen that as λp increases HD2 also increases. The
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY (ACCEPTED)
10
(b)
DSA−C3 <a>
DSA−C3 <s>
DSA−C4 <a>
DSA−C4 <s>
DSA−D2 <a>
DSA−D2 <s>
0.1
Mean handoff delay of SU2 calls, HD2 (sec)
Mean handoff delay of SU1 calls, HD1 (sec)
0.12
0.08
0.06
0.04
0.02
0
0.4
0.6
0.8
1
PU arrival rate, λp (calls/sec)
DSA−C3 <a>
DSA−C3 <s>
DSA−C4 <a>
DSA−C4 <s>
DSA−D2 <a>
DSA−D2 <s>
0.1
0.9
0.8
0.7
0.6
SU1 : Pm = 0, Pf = 0
SU1 : Pm = 0.1, Pf = 0.1
0.5
SU2 : Pm = 0, Pf = 0
SU2 : Pm = 0.1, Pf = 0.1
0.4
0.4
0.6
0.8
0.9
0.8
0.7
0.6
SU1 : Pm = 0, Pf = 0
1
SU1 : Pm = 0.1, Pf = 0.1
0.5
SU2 : Pm = 0, Pf = 0
SU2 : Pm = 0.1, Pf = 0.1
0.4
PU arrival rate, λp (calls/sec)
0.4
0.6
0.8
1
PU arrival rate, λp (calls/sec)
Fig. 10. Call completion rate for different sensing errors for SU1 and SU2
calls under (a) DSA-C2 scheme and (b) DSA-C4 scheme.
0.08
0.06
0.04
0.02
0
1
Call completion rate of SU1 and SU2 calls (calls/sec)
(a)
0.12
Call completion rate of SU1 and SU2 calls (calls/sec)
1
reason is the same as that given for HD1 . Fig. 9(b) shows
the DSA-C3 scheme having higher value of HD2 than that of
the DSA-C4 scheme. This is because under DSA-C3 scheme,
the number of displaced SU2 calls is more than that in the
DSA-C4 scheme (as some SU2 calls are also displaced due to
SU1 handoff). Fig. 9(b) also shows that the DSA-D2 scheme
gives the highest value for HD2 . This reason is the same as that
explained for HD1 . Again, the simulation results and analytical
results match well for both HD1 and HD2 under all the DSA
schemes with buffer.
0.4
0.6
0.8
1
scheme. From the analysis, we found that the optimal value
of ζ is 4 for DSA-C1 scheme. The analysis results can be
verified from simulation. Fig. 11 shows the simulation results
for the above parameter settings under different values of ζ
with DSA-C1 scheme. Fig. 11 shows that the desired blocking
probability of 5% for the SU1 calls is satisfied when ζ = 4 subchannels. Similarly, the optimal ζ can be found for the other
DSA schemes.
PU arrival rate, λp (calls/sec)
0.13
Fig. 9. Effect of PU call arrival rate on the mean handoff delay of (a) SU1
calls and (b) SU2 calls, under DSA schemes with buffer.
C. Optimal Sub-channel Reservation
As mentioned in Section II, some sub-channels (ζ ) are
reserved for the SU1 call arrivals. Using the sub-channel
reservation, some low priority SU calls are blocked to improve
the performance of the high priority SU calls. Based on the
given parameter settings and blocking probability requirement
of the SU1 calls, an optimal number of sub-channels (ζ ) to be
reserved under the DSA schemes can be determined from our
analysis. Here, optimal number means the minimum number
of sub-channels to be reserved to guarantee that the blocking
probability requirement of the SU1 calls is satisfied. For
instance, consider the following parameter setting: λ1 = 1.8,
λ2 = 1.8, λp = 0.06, µ1 = 0.8, µ2 = 0.3, µp = 0.09 and a desired
blocking probability of 5% for the SU1 calls under the DSA-C1
B1
0.11
0.1
1
Blocking probability of SU calls, P
The results can be summarized as follows.
The distributed DSA schemes are relatively complex compared to the centralized DSA schemes. However, the centralized DSA schemes incur infrastructure cost. While the DSA
schemes with handoff buffer improve the SU call completion
rate, they introduce handoff delay which consequently increases the blocking of incoming SU calls. In our future work,
we will analyze the effect of sensing errors on the performance
of our DSA schemes. For instance, it can be observed from
Figs. 10(a) and 10(b) corresponding to DSA-C2 and DSA-C4
schemes (simulation results) show that the sensing error causes
degradation in the call completion rate of the SU1 and SU2
calls. In the Figs. 10(a) and 10(b), Pf denotes the probability
of false alarm (i.e., probability of wrongly sensing an idle
channel) and Pm denotes the probability of miss detection (i.e.,
probability of wrongly sensing an active PU call).
DSA−C1 <s>
0.12
0.09
0.08
0.07
0.06
0.05
0.04
0
1
2
3
4
Number of sub−channels reserved for SU1 calls, ζ
5
6
Fig. 11. Simulation: Optimal sub-channel reservation under DSA-C1 scheme.
V. C ONCLUSION
We have investigated the spectrum handoff prioritization
using various novel DSA schemes under different CRN architectures (i.e., centralized and distributed). For simplicity, we
have considered two levels of prioritization in the SU traffic.
The analytical models for the CRN under all the proposed
DSA schemes have been presented. For performance evaluation, we have derived the blocking probability, the forced
termination probability, the call completion rate and the mean
handoff delay for the two priority classes in the SU traffic. We
have also investigated the case of sub-channel reservation for
the high priority SUs and obtained the optimal sub-channel
reservation. The analytical results have been verified through
simulations. In the future, we will analyze the optimal number
of channels and sub-channels required for the design. We will
also study the effects of sensing errors on the performance of
our DSA schemes.
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY (ACCEPTED)
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Vamsi Krishna Tumuluru received his B.E. degree
in Electronics and Communication Engineering from
University of Madras, Chennai, India in 2003. He
received his M.Tech degree in Electrical Engineering
from National Institute of Technology, Rourkela,
India in 2007. He is currently pursuing his Ph.D. in
Nanyang Technological University, Singapore. His
research interests include Cognitive Radio Network
and its Application, Resource Allocation in Wireless
Networks and Queuing Systems.
Ping Wang (M’08) received the B.E. in 1994 and
M.E. degrees in 1997, from Huazhong University
of Science and Technology, China, and the Ph.D.
degree in 2008 from the University of Waterloo,
Canada, all in electrical engineering. She is currently
an assistant professor at School of Computer Engineering, Nanyang Technological University, Singapore. Her current research interests include QoS
provisioning and resource allocation in multimedia wireless communications. She is an Editor of
EURASIP Journal on Wireless Communications and
Networking, International Journal of Communication System, and International Journal of Ultra Wideband Communications and Systems.
Dusit Niyato (M’09) is currently an assistant professor in the School of Computer Engineering, at
the Nanyang Technological University, Singapore.
He received B.E. from King Mongkut’s Institute
of Technology Ladkrabang (KMITL) in 1999. He
obtained his Ph.D. in Electrical and Computer Engineering from the University of Manitoba, Canada in
2008. His research interests are in the area of radio
resource management in cognitive radio networks
and broadband wireless access networks.
Wei Song (M’09) received her Ph.D. degree in electrical and computer engineering from the University
of Waterloo, Canada, in 2007. In 2008, she worked
as a postdoctoral research fellow at the Department
of Electrical Engineering and Computer Sciences,
University of California, Berkeley. In July 2009, she
joined the Faculty of Computer Science, University
of New Brunswick, as an assistant professor. Her
current research interests include the interworking of
cellular networks and wireless local area networks
(WLANs), resource allocation for heterogeneous
wireless networks, vehicular ad hoc networks, and cross-layer optimization
for multimedia quality-of-service (QoS) provisioning.