![Admissible region for the normalized traffic workloads (ρ p , ρ s ), where the average cumulative delay constraint can be satisfied when t s = 0 (slot), E[X p ] = 20 (slots/arrival) and E[X s ] = 10 (slots/arrival).](https://www.researchgate.net/profile/Chung-Ju-Chang/publication/224251576/figure/fig2/AS:340768393842708@1458256924458/Admissible-region-for-the-normalized-traffic-workloads-r-p-r-s-where-the-average_Q320.jpg)
![Effects of secondary connections' service time E[X s ] on the cross-point for the trafficadaptive channel selection approach, where t s = 1 (slot), E[X p ] = 20 (slots/arrival), and λ s = 0.01 (arrivals/slot).](https://www.researchgate.net/profile/Chung-Ju-Chang/publication/224251576/figure/fig1/AS:340768393842704@1458256924405/Effects-of-secondary-connections-service-time-EX-s-on-the-cross-point-for-the_Q320.jpg)
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Modeling and Analysis for Spectrum
Handoffs in Cognitive Radio Networks
Li-Chun Wang, Fellow, IEEE , Chung-Wei Wang, Student Member, IEEE, and
Chung-Ju Chang, Fellow, IEEE
Abstract—In this paper, we present an analytical framework to evaluate the latency performance of connection-based spectrum
handoffs in cognitive radio (CR) networks. During the transmission period of a secondary connection, multiple interruptions from the
primary users result in multiple spectrum handoffs and the need of predetermining a set of target channels for spectrum handoffs. To
quantify the effects of channel obsolete issue on the target channel predetermination, we should consider the three key design
features: 1) general service time distribution of the primary and secondary connections; 2) different operating channels in multiple
handoffs; and 3) queuing delay due to channel contention from multiple secondary connections. To this end, we propose the
preemptive resume priority (PRP) M/G/1 queuing network model to characterize the spectrum usage behaviors with all the three
design features. This model aims to analyze the extended data delivery time of the secondary connections with proactively designed
target channel sequences under various traffic arrival rates and service time distributions. These analytical results are applied to
evaluate the latency performance of the connection-based spectrum handoff based on the target channel sequences mentioned in the
IEEE 802.22 wireless regional area networks standard. Then, to reduce the extended data delivery time, a traffic-adaptive spectrum
handoff is proposed, which changes the target channel sequence of spectrum handoffs based on traffic conditions. Compared to the
existing target channel selection methods, this traffic-adaptive target channel selection approach can reduce the extended data
transmission time by 35 percent, especially for the heavy traffic loads of the primary users.
Index Terms—Cognitive radio, spectrum handoff, spectrum mobility, preemptive priority, preemption, queuing theory.
Ç
1INTRODUCTION
C
OGNITIVE radio (CR) can significantly improve spectrum
efficiency by allowing the secondary users to tempora-
rily access the primary user’s under-utilized licensed
spectrum [1], [2], [3], [4]. Spectrum mobility issues arise
when the primary user appears at the channels being
occupied by the secondary users. The secondary users need
to return the occupied channel because the primary users
have the preemptive priority to access channels. Spectrum
handoff techniques can help the interrupted secondary
user vacate the occupied licensed channel and find a
suitable target channel to res ume its unfinished data
transmission [5], [6].
One fundamental issue for spectrum handoff modeling
in CR networks is the multiple interruptions from the
primary users during each secondary user’s connection [7].
The issue of multiple interruptions results in the require-
ment of designing the target channel pool for a series of
spectrum handoffs in a secondary connection. In this paper,
we define the connection-based modeling techniques for
spectrum handoff as the schemes that incorporate the
effects of multiple interruptions from the primary users in
an event-driven manner, and the slot-based modeling
techniques mean that the interruptions to the secondary user
are modeled in a time-driven manner. That is, the
connection-based method characterizes the spectrum hand-
off only when the primary user appears, while for the slot-
based methods the spectrum handoff can be performed at
each time slot.
Spectrum handoff mechanisms can be generally categor-
ized into two kinds according to the decision timing of
selecting target channels [8]. The first kind is called the
proactive-decision spectrum handoff,
1
which decides the
target channels for future spectrum handoffs based on the
long-term traffic statistics before data connection is estab-
lished [22], [23], [24]. The second kind is called the reactive-
decision spectrum handoff scheme [25]. For this scheme, the
target channel is searched in an on-demand manner [26],
[27]. After a spectrum handoff is requested, spectrum
sensing is performed to help the secondary users find idle
channels to resume their unfinished data transmission. Both
spectrum handoff schemes have their own advantages and
disadvantages. A qua ntitat ive comparison of the two
spectrum handoff schemes was provided in [8].
In this paper, we focus on the modeling technique and
performance analysis for the proactive-decision spectrum
handoff scheme, while leaving the related studies on the
reactive-decision spectrum handoff in [25]. Compared to
IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 9, SEPTEMBER 2012 1499
. L.-C. Wang and C.-J. Chang are with the Department of Electrical
Engineering, National Chiao Tung University, ED817, 1001 University
Road, Hsinchu 300, Taiwan.
E-mail: lichun@cc.nctu.edu.tw, cjchang@mail.nctu.edu.tw.
. C.-W. Wang is with MStar Semiconductor, Inc., Taipei, Taiwan.
E-mail: hyper.cm91g@nctu.edu.tw.
Manuscript received 7 July 2010; revised 2 July 2011; accepted 15 July 2011;
published online 30 July 2011.
For information on obtaining reprints of this article, please send e-mail to:
tmc@computer.org, and reference IEEECS Log Number TMC-2010-07-0327.
Digital Object Identifier no. 10.1109/TMC.2011.155.
1. In this paper, we assume that spectrum handoff request is initiated
only when the primary user appears as discussed in the IEEE 802.22
wireless regional area networks standard. In this scheme, the proactive
spectrum handoff represents the spectrum handoff scheme with the
proactively designed target channel sequences. It is different from the
proactive spectrum handoff in [9], [10], [11], [12], [13], [14], [15], [16], [17],
[18], [19], [20], [21] that assumes spectrum handoff can be performed before
the appearance of the primary users.
1536-1233/12/$31.00 ß 2012 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS
the reactive spectrum handoff scheme, the proactive
spectrum handoff is easier to achieve a consensus on the
target channels between the transmitter and its intended
receiver because both the transmitter and receiver can know
their target channel sequence for future spectrum handoffs
before data transmission. Furthermore, the channel switch-
ing delay of the proactive spectrum handoff is shorter than
that of the reactive spectrum handoff because scanning
wide spectrum to determine the target channel is unneces-
sary at the moment of link transition. Nevertheless, the
proactive spectrum handoff scheme shall resolve the
obsolescent channel issue because the predetermined target
channel may not be available any more when a spectrum
handoff is requested.
To characterize the channel obsolescence effects and the
spectrum usage behaviors with a series of interruptions in
the secondary connections, we suggest a new performance
metric—the extended data delivery time of the secondary
connections. It is defined as the duration from the instant of
starting transmitting data until the instant of finishing the
whole connection, during which multiple interruptions
from the primary users may occur. In the context of the
connection-based spectrum handoffs, how to analyze the
extended data delivery time is challenging because three
key design features must be taken into account: 1) general
service time distribution, where the probability density
functions (PDFs) of service time of the primary and
secondary connections can be any distributions; 2) different
operating channels in multiple handoff; and 3) queuing
delay due to channel contention from multiple secondary
connections. To the best of our knowledge, an analytical
model for characterizing all these three features for multiple
handoffs has rarely been seen in the literature.
In this paper, we propose a preemptive resume priority
(PRP) M/G/1 queuing network model to characterize the
spectrum usage behaviors of the connection-based multiple-
channel spectrum handoffs. Based on the proposed model,
we derive the closed-form expression for the extended data
delivery time of different proactively designed target
channel sequences under various traffic arrival rates and
service time distributions. We apply the developed analy-
tical method to analyze the latency performance of spec-
trum handoffs base d on the target channel sequences
specified in the IEEE 802.22 wireless regional area networks
(WRAN) standard. We also suggest a traffic-adaptive target
channel selection principle for spectrum handoffs under
different traffic conditions.
The rest of this paper is organized as follows: Section 2
reviews the current spectrum usage models for the
proactive spectrum handoff schemes in the literature. An
illustrative example for multiple handoff issue is given in
Section 3. In Section 4, we present the PRP M/G/1 queuing
network model, which can characterize the spectrum usage
behaviors with multiple handoffs. Based on this model,
Section 5 evaluates the extended data delivery time of the
secondary connections with various target channel se-
quences. Then, Section 6 investigates the latency perfor-
mance of the spectrum handoffs resulting from the two
typical target channel sequences mentioned in the IEEE
802.22 WRAN standard. Analytical and simulation results
are given in Section 7. Finally, we give our concluding
remarks in Section 8.
2RELATED WORK
In order to characterize the multiple handoff behaviors in
CR networks, we should consider the three key design
features, consisting of 1) general service time distribution;
2) various operating channels; and 3) queuing delay due to
channel contention from multiple secondary connections.
Based on these three features, Table 1 classifies the existing
modeling techniques for the proactive spectrum handoff. In
the table, the signs “” and “” indicate that the proposed
model “does” and “does not” consider the corresponding
feature, respectively. In the literature, the modeling
techniques for spectrum handoff behaviors can be categor-
ized into the following five types:
1. the two-state Markov chain;
2. the arbitrary ON/OFF random process;
3. the Bernoulli random process;
1500 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 9, SEPTEMBER 2012
TABLE 1
Comparison of Various Channel Usage Models
4. the birth-death process with multidimensional
Markov chain; and
5. the PRP M/G/1 queuing model.
One can observe that the current modeling techniques have
not considered all the aforementioned three design features.
In the following, we briefly discuss the features of these
analytical models for spectrum handoff behaviors.
. Discrete-time two-state Markov chain. In [9], [10],
[11], [12], the evolutions of the channel usage of the
primary networks at each channel were modeled as
Gilbert-Elliot channel, i.e., a discrete-time Markov
chain which has two occupancy states: busy (ON)
and idle (OFF) states. The idle state can be regarded
as a potential spectrum opportunity for the second-
ary users. Note that the Markov chain model is
suitable for the exponentially distributed service
time, and how to extend it to the case with general
service time distribution is not clear. In this model,
the target channel selection problem in every time
slot is mode led as a Markov deci sion process.
According to the channel occupancy state at the
current time slot, a decision maker (secondary user)
can preselect the best action (target channel) to
optimize its immediate reward (such as expected
per-slot throughput [9], [10], [11], or expected wait-
ing time [12]) at the next time slot. Note that this
model belongs to the slot-based modeling technique
because the secondary user shall decide its target
channel at each time slot. Even though the primary
users do not appear at the current operating channel,
the secondary user still needs to change its operating
channel, resulting in frequent spectrum handoffs.
. Arbitrary ON/OFF random process. Unlike the
authors in [9], [10], [11], [12] who assumed that the
channel usage behaviors of the primary networks
have the Markov property, the authors in [13], [14],
[15], [16], [17], [18], [19], [20], [ 21] used the
continuous-time ON/OFF random process with
arbitrary distributed ON/OFF period to characterize
the channel usage behaviors of the primary net-
works at each channel. It was assumed that the
secondary user can estimate the distributions of the
ON period and the OFF period based on long-term
observations. In each time slot, the secondary user
must calculate the expected reward such as the
average remaining idle periods of primary users
[13], [14], [15], [16], [17], [18], [19] or the average
throughout of secondary users [20], [21]. Then, the
secondary users will immediately switch to the
channel with the largest reward. This model also
belongs to the slot-based modeling technique be-
cause the target channel is decided in each time slot.
. Bernoulli random process. The authors in [28]
examined the effects of multiple interruptions from
the primary users on the connection maintenance
probability i n a connection-based environment,
where the spectrum usage behaviors of the primary
networks on each channel were characterized by a
Bernoulli random process. Her e, the connection
maintenance probability is the probability that a
secondary connection can finish its transmission
within a predetermined number of handoff trials.
Because both the busy and idle periods of the
considered primary networks follow the geometrical
distributions, it is more difficult to extend this
modeling technique to the cases with other general
service time distribution.
. Multidimensional Markov chain.In[29],the
spectrum usage behaviors of both the primary and
secondary networks were modeled by the multi-
dimensional Markov chain. The actions of each
primary and secondary user are indicated in the
states of the Markov chain. Here, the action of each
user can be “idleness”, “wait ing at queue”, or
“communication”. It was assumed that the second-
ary user must stay on its current operating channel
after the primary user’s interruption. This analytical
model is suitable for the single channel network, and
the issue of different operating channels in multiple
handoffs has not been addressed.
. M/G/1 queuing model. Some researchers used the
preemptive resume priority M/G/1 queuing model
to characterize the spectrum usage behaviors in a
single-channel CR network. The effects of multiuser
sharing and multiple interruptions on the extended
data delivery time of the secondary users were
studied in [30], [31], [32], [33], [34], [35], [36], [37],
[38]. However, the authors in [30], [31], [32], [33],
[34], [35], [36], [37], [38] assumed that the secondary
users must stay on the current operating channel to
resume their unfinished transmissions when they
are interrupted.
To summarize, the first three analytical models, two-state
Markov chain, arbitrary ON/OFF random process, and
Bernoulli random process, did not incorporate the effects of
the traffic loads of the secondary users on the statistics of
channel occupancy. How to extend these models to consider
the queuing delay due to channel contention from multiple
secondary connections is unclear. The last two models,
multidimensional Markov chain and M/G/1 que uing
model, can characterize the effects of spectrum sharing
between multiple secondary users. However, these two
models assumed that the interrupted secondary user must
stay on the current operating channel, and have not dealt
with the handoff interaction issue among different channels.
In this paper, we propose a PRP M/G/1 queuing network
model to take into account of all the effects of the general
service time distributions of the primary and the secondary
connections, various operating channels, and the queuing
behaviors of multiple secondary connections. In the next
sections, we will dis cuss the analytical framework of
proactive-decision spectrum handoff based on the PRP
M/G/1 queuing network model.
3SYSTEM MODEL
3.1 Assumptions
In this paper, we consider a CR network with M
independent channels, where each channel has its own
high-priority and low-priority queues as discussed in [38].
WANG ET AL.: MODELING AND ANALYSIS FOR SPECTRUM HANDOFFS IN COGNITIVE RADIO NETWORKS 1501
The traffic loads of the primary and secondary users,
respectively, enter the high-priority and low-priority
queues before transmitting data. Then, according to the
time that traffic arrival at queues, the primary connections
and the secondary connections are established for the primary
and the secondary users,
2
respectively. Here, we assume
that the connections with the same priority follow the first-
come-first-served (FCFS) scheduling policy in a centralized
manner regardless of uplink or downlink.
3
Assume that the considered CR network is a time-slotted
system as [9], [24], [39], [40], [41]. In order to detect the
presence of primary connections, each secondary user must
perform spectrum sensing at the beginning of each time
slot. If the current operating channel is idle, the secondary
user can transmit or receive data in the remaining duration
of this time slot. Otherwise, the secondary user must
perform spectrum handoff procedures to resume its
unfinished transmission at the preselected target channel.
This kind of listen-before-talk channel access scheme is
implemented in many wireless techniques, such as the quiet
period of the IEEE 802.22 standard [42] and the clear
channel assessment (CCA) of the IEEE 802.11 standard [43].
3.2 Illustrative Example of Spectrum Handoffs with
Multiple Interruptions
A secondary connection may encounter multiple interrup-
tion requests during its transmission period. Because
spectrum handoff procedures must be performed whenever
an interruption occurs, a set of target channels will be
sequentially selected, called the target channel sequence in this
paper. Fig. 1 shows an example that three spectrum handoff
requests occur during the transmission period of the
secondary connection SC
A
. In this example, SC
A
’s initial
(default) channel is Ch1 and its target channel sequence for
spectrum handoffs is (Ch2, Ch2, Ch3, ...). The extended data
delivery time of SC
A
is denoted by T . Furthermore, D
i
is the
handoff delay of the ith interruption. Here, the handoff delay
is the duration from the instant when the transmission is
interrupted until the instant when the unfinished transmis-
sion is resumed. We assume that the transmitter of SC
A
plans
to establish a connection flow consisting of 28 slots to the
intende d receiver. Then, the transmission process with
multiple handoffs is described as follows:
1. In the beginning, SC
A
is established at its default
channel Ch1. When an interruption event occurs,
SC
A
decides its target channel according to the
predetermined target channel sequence.
2. At the first interruption, SC
A
changes its operating
channel to the idle channel Ch2 from Ch1 because
the first predetermined target channel is Ch2. In this
case, the handoff delay D
1
is the channel switching
time (denoted by t
s
).
3. At the second interruption, SC
A
stays on its current
operating channel Ch2 because the second target
channel is Ch2. SC
A
cannot be resumed until all the
high-priority primary connections finish their trans-
missions at Ch2. In this case, the handoff delay D
2
is
the duration from the time instant that Ch2 is used
by the primary connections until the time instant
that the high-priority queue becomes empty. This
duration (denoted by Y
ð2Þ
p
) is called the busy period
resulting from the transmissions of multiple primary
connections at Ch2.
4. At the third interruption, SC
A
changes its operating
channel to Ch3 because the third target channel is
Ch3. In this example, because Ch3 is busy, SC
A
must
wait in the low-priority queue until all the data in
the present high-priority and low-priority queues of
Ch3 are served.
4
Hence, the handoff delay D
3
is the
sum of this waiting time and the channel switching
time t
s
.
5. Finally, SC
A
is completed on Ch3.
When a secondary connection changes its operating channel
from channel k to k
0
where k
0
6¼ k, the expected handoff
delay is the sum of the channel switching time t
s
and the
average waiting time of channel k
0
(denoted by E½W
ðk
0
Þ
s
) for
the secondary connections. Note that this waiting time W
ðk
0
Þ
s
is the duration from the time instant that a secondary
connection enters the low-priority queue of channel k
0
until
it gets a chance to transmit at channel k
0
. After the secondary
connection’s operating channel is changed to channel k
0
, one
of two situations will occur. If channel k
0
is idle as the first
interruption in Fig. 1, the expected handoff delay is t
s
since
E½W
ðk
0
Þ
s
j channel k
0
is idle¼0. On the other hand, the ex-
pected handoff delay is t
s
þ E½W
ðk
0
Þ
s
j channel k
0
is busy if
channel k
0
is busy as the third interruption in Fig. 1.
4ANALYTICAL FRAMEWORK
4.1 The PRP M/G/1 Queuing Network Model
In this section, a PRP M/G/1 queuing network model is
proposed to characterize the spectrum usage behaviors
between the primary and the secondary connections with
multiple spectrum handoffs in different channels. Key
features of the proposed PRP M/G/1 queuing network
model are listed below:
. Each server (channel) can accept two types of
customers (connections): the high-priority connec-
tions from the primary users and the low-priority
connections from the secondary users.
. The primary users have the preemptive priority to
use channels and can interrupt the transmission of
the secondary users. The interrupted secondary user
can resume the unfinished transmission instead of
retransmitting the whole connection [22]. Note that
the target channel of a n interrupted secondary
1502 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 9, SEPTEMBER 2012
2. We assume the primary and secondary users always hav e packets to
send during the connections, and the considered two queues have an
infinite length for simplification.
3. This model can be also applied to the decentralized CR network
architectures. In this case, the channel contention time and retransmission
in the medium access control (MAC) layer should be taken into account
when calculating the latency performance of the secondary connections [8].
4. Here, the 1-persistent waiting policy is adopted. That is, the
interrupted secondary user must stay on the selected target channel even
though the selected channel is busy and then transmit unfinished data
when channel becomes idle. Another possible approach is to reselect a new
channel at the next time slot when a busy channel is selected in the current
time slot. However, this approach is more impractical because it will lead to
many channel-switching behaviors during a secondary connection.
connection can be different from its current operat-
ing channel. This concept is different from the
spectrum usage models of [30], [31], [32], [33], [34],
[35], [36], [37], [38], which is also based on the PRP
M/G/1 queuing theory.
. During the transmission period, a secondary con-
nection may encounter multiple interruptions from
the primary users.
To ease analysis, we further make the following
assumptions:
. A default channel is preassigned to each secondary
user through spectrum decision algorithms in order
to balance the overall traffic loads of the secondary
users to all the channels [44]. When a secondary
transmitter has data, it can transmit handshaking
signal at the default channel of the intended receiver
to establish a secondary connection [45], [46]. If the
intended receiver’s default channel is busy, the
secondary transmitter must wait at this channel
until it becomes available [9].
. Each primary connection is assigned with a default
or licensed channel.
. Each secondary user can detect the presence of the
primary user. In fact, this model can be also
extended to consider the effects of false alarm and
missed detection [47].
. Any time only one user can transmit data at one
channel.
4.2 Example
Fig. 2 shows an example of the PRP M/G/1 queuing network
model with three channels, in which the traffic flows of the
primary connections and the secondary connections are
directly connected to the high-priority queue and the low-
priority queue, respectively. When a primary connection
appears at the channel being occupied by the secondary
connection, the interruption event occurs. The interrupted
secondary connection decides its target channel for spectrum
handoff according to the target channel predetermination
algorithm which is implemented in the channel selection
point
S. In our queuing network model, the interrupted
secondary connection can either stay on its current channel
or change to another channel through different feedback
paths. If a secondary connection chooses to stay on its current
operating channel, its remaining data will be connected to
WANG ET AL.: MODELING AND ANALYSIS FOR SPECTRUM HANDOFFS IN COGNITIVE RADIO NETWORKS 1503
Fig. 1. An example of transmission process for the secondary connection SC
A
, where t
s
is the channel switching time, T is the extended data delivery
time of SC
A
, and D
i
is the handoff delay of the ith interruption. The gray areas indicate that the channels are occupied by the existing primary
connections (PCs) or the other secondary users’ connections (SCs). Because SC
A
is interrupted three times in total, the overall data connection is
divided into four segments.
Fig. 2. The PRP M/G/1 queuing network model with three channels where
ðkÞ
p
,
ðkÞ
s
, and !
ðkÞ
n
are the arrival rates of the primary connections, the
secondary connections, and the type-ðnÞ secondary connections (n 1) at channel k. Furthermore, f
ðkÞ
p
ðxÞ and f
ðkÞ
i
ðÞ are the PDFs of X
ðkÞ
p
and
ðkÞ
i
,
respectively. Note that represents that the traffic workloads of the interrupted secondary connections are merged.
the head of the low-priority queue of its current operating
channel. On the other hand, if the decision is to change its
operating channel, the remaining data of the interrupted
secondary connection will be connected to the tail of the low-
priority queue of the selected channel after channel switch-
ing time t
s
. In order to characterize the handoff delay from
channel switching time t
s
, S must be regarded as a server
with constant service time t
s
. Note that in the figure
represents that the traffic workloads of the interrupted
secondary connections are merged. Furthermore, when the
interrupted secondary connection transmits the remaining
data on the target channel, it may be interrupted again.
Hence, this model can incorporate the effects of multiple
interruptions in multichannel spectrum handoffs.
4.3 Traffic Parameters
The proposed PRP M/G/1 queuing network model
requires the following traffic parameters. Assume that the
arrival p rocesses of the primary and the secondary
connections on the queues of each channel are Poisson.
Let
ðÞ
p
(arrivals/slot) be the traffic arrival rate of the
primary connections at channel , and
ðÞ
s
(arrivals/slot) be
the secondary connection’s initial arrival rate at channel .
Furthermore, let X
ðÞ
p
(slots/arrival) and X
ðÞ
s
(slots/arrival)
be the corresponding service time of the primary and the
secondary connections, respectively, as well as f
ðÞ
p
ðxÞ and
f
ðÞ
s
ðxÞ be the PDFs of X
ðÞ
p
and X
ðÞ
s
, respectively. If the four
traffic parameters
ðÞ
p
,
ðÞ
s
, f
ðÞ
p
ðxÞ, and f
ðÞ
s
ðxÞ can be
obtained by certain traffic pattern prediction methods [48],
many performance measures for the multichannel spectrum
handoffs with multiple interruptions can be derived.
Now, we define the type-ðiÞ secondary connection as the
secondary connection that has experienced i interruptions,
where i 0. For the type-ðiÞ secondary connections, two
important system parameters !
ðkÞ
i
and
ðkÞ
i
are defined as
follows:
. !
ðkÞ
i
is the arrival rate of the type-ðiÞ secondary
connections at channel k.
5
How to derive !
ðkÞ
i
from
the four traffic parameters is discussed in App-
endix A, which can be found on the Computer
Society Digital Library at http://doi.ieeecomputer
society.org/10.1109/TMC.2011.155.
.
ðkÞ
i
istheeffectiveservicetimeofthetype-ðiÞ
secondary connections at channel k. That is,
ðkÞ
i
is
the transmission duration of a secondary connection
between the ith and the ði þ 1Þth interruptions at
channel k. Furthermore, let f
ðkÞ
i
ðÞ be the PDF of
ðkÞ
i
.
In Appendix B, available in the online supplemental
material, we w ill discuss how to derive f
ðkÞ
i
ðÞ
from the four traffic parameters.
Finally, we denote
ðkÞ
p
and
ðkÞ
i
as the channel busy
probabilities resulting from the transmissions of the
primary connections and the type-ðiÞ secondary connec-
tions whose current operating channels are channel k,
respectively. Moreover, the busy probability of channel k is
denoted by
ðkÞ
. Let n
max
be the maximum allowable
number of interruptions for the secondary connections.
That is, a secondary connection will be dropped when it
encounters the ðn
max
þ 1Þth interruption.
6
Then, in an
M-channel network, the following constraint shall be
satisfied for 1 k M:
ðkÞ
¼
ðkÞ
p
þ
X
n
max
i¼0
ðkÞ
i
< 1; ð1Þ
Note that
ðkÞ
p
¼
ðkÞ
p
E½X
ðkÞ
p
< 1 and
ðkÞ
i
¼ !
ðkÞ
i
E½
ðkÞ
i
< 1 as
well as
ðkÞ
can be also interpreted as the utilization factor of
channel k for each k.
Fig. 3 illustrates the physical meaning of random variable
ðkÞ
i
. Consider a two-channel network with the service time
of the secondary connections X
ð1Þ
s
and X
ð2Þ
s
at channels 1 and
2, respectively. In channel 1, random variable X
ð1Þ
s
are
generated three times in Fig. 3a. Similarly, Fig. 3b shows the
three realizations of X
ð2Þ
s
for channel 2. Each secondary
connection is divided into many segments due to multiple
primary users’ interruptions. For example, the first second-
ary connection in Fig. 3a is divided into four segments
because it encounters three interruptions in total. The first,
second, third, and fourth segments are transmitted at
channels 1, 2, 1, and 1, respectively. Thus, this secondary
connection’s default channel is Ch1 and its target channel
sequence is (Ch2, Ch1, Ch1). In Fig. 3, random variable
ð1Þ
2
,
one of the gray regions, represents the transmission
duration of a secondary connection between the second
and the third interruptions at channel 1. That is,
ð1Þ
2
is the
third segment of the first secondary connections or the third
segment of the third secondary connections in Fig. 3a, or the
third segment of the second secondary connection in Fig. 3b.
In this paper, each secondary connection is divided into
many segments due to multiple interruptions as shown in
Fig. 3. Note that the operating channel of each segment can
be any channel. Because the effective service time (
ðkÞ
i
)of
each segment is dependent on the traffic statistics of the
primary and other secondary users of the selected target
channels, it is quite complex to find the probability density
function of the effective service time of each segment.
Fortunately, based on the proposed analytical framework,
we provide a systematic approach to study the effects of
various system parameters on the effective service time and
then can derive the closed-form expression for the average
effective service time of each segment.
5ANALYSIS OF EXTENDED DATA DELIVERY TIME
Based on the proposed PRP M/G/1 queuing network
model, we can evaluate many performance metrics of the
secondary connections with various target channel se-
quences. In this paper, we focus on analysis of the extended
data delivery time, which is an important performance
measure for the latency-sensitive traffic of the secondary
1504 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 9, SEPTEMBER 2012
5. Note that when a new secondary connection arrives at channel k,it
will become the type-(0) secondary connection at channel k because this
secondary connection has experiences 0 interruptions. Hence, we have
!
ðÞ
0
¼
ðÞ
s
.
6. Intuitively, a larger value of n
max
results in the higher complexity to
determine the optimal target channel. However, a smaller value of n
max
will
reduce the quality-of-service (QoS) performance of the secondary users
because a secondary user will be dropped more frequently. Hence,
determining the optimal n
max
is a system-dependent issue.
connections. Some important notations used in this paper
are summarized in Table 2.
A secondary connection may encounter many interrup-
tions during its transmission period. Without loss of
generality, we consider a secondary connection whose
default channel is channel in the following discussions.
Let N be the total number of interruptions of this secondary
connection. Then, the average extended data delivery time
of this secondary connection can be expressed as
E½T¼
X
n
max
n¼1
E½TjN ¼ nPrðN ¼ nÞ: ð2Þ
Note that we can evaluate the extended data delivery time
resulting from various target channel sequences from (2).
Then, by comparing the extended data delivery time
resulting from all possible target channel sequences, the
optimal target channel sequence can be determined to
minimize the extended data delivery time.
First, we show how to derive the value of E½T jN ¼ n of
(2). The considered secondary connection can be divided into
many segments due to multiple interruptions as discussed in
Fig. 1. Hence, the extended data delivery time of this
secondary connection consists of the original service time
and the cumulative delay resulting from multiple handoffs.
Let D
i
be the handoff delay of the considered secondary
connection for the ith interruption. When N ¼ n, we have
D
i
¼ 0 if i n þ 1. Then, the conditional expectation of the
extended data delivery time of the considered secondary
connection given the event N ¼ n can be derived as
E½T jN ¼ n¼E½X
ðÞ
s
þ
X
n
i¼1
E½D
i
: ð3Þ
Next, we investigate how to derive the value of PrðN ¼
nÞ of (2). For the considered secondary connection, denote
s
0;
and s
i;
as its default channel and its target channel at
the ith interruption, respectively. Thus, we have s
0;
¼
and this secondary connection’s target channel sequence
can be expressed as ðs
1;
;s
2;
;s
3;
; ...Þ. Let p
ðs
i;
Þ
i
be the
probability that the considered secondary connection is
interrupted again at channel s
i;
when it has experienced i
interruption. Then, the probability that the considered
secondary connection is interrupted exactly n times can be
expressed as
WANG ET AL.: MODELING AND ANALYSIS FOR SPECTRUM HANDOFFS IN COGNITIVE RADIO NETWORKS 1505
Fig. 3. Illustration of the physical meaning of random variable
ðkÞ
i
. For example,
ð1Þ
2
is one of the third segments (gray areas) of the first and the third
secondary connections in (a) as well as the second secondary connection in (b). Note that the third secondary connection in (b) does not have the
third segment because it is interrupted only once.
TABLE 2
Definitions of Notations
PrðN ¼ nÞ¼
1 p
ðs
n;
Þ
n
Y
n1
i¼0
p
ðs
i;
Þ
i
: ð4Þ
Finally, substituting (3) and (4) into (2) yields
E½T¼E
X
ðÞ
s
þ
X
n
max
n¼1
X
n
i¼1
E½D
i
!
1 p
ðs
n;
Þ
n
Y
n1
i¼0
p
ðs
i;
Þ
i
"#
; ð5Þ
where the values of E½D
i
and p
ðkÞ
i
can be obtained from
Propositions 1 and 2, respectively.
Proposition 1.
E½D
i
¼
E
Y
ðs
i;
Þ
p
;s
i1;
¼ s
i;
E
W
ðs
i;
Þ
s
þ t
s
;s
i1;
6¼ s
i;
;
(
ð6Þ
where
E
Y
ðkÞ
p
¼
E
X
ðkÞ
p
1
ðkÞ
p
¼
E
X
ðkÞ
p
1
ðkÞ
p
E
X
ðkÞ
p
; ð7Þ
and
E
W
ðkÞ
s
¼
ðkÞ
p
E½ðX
ðkÞ
p
Þ
2
þ
P
n
max
i¼0
!
ðkÞ
i
E½ð
ðkÞ
i
Þ
2
þ
ð
ðkÞ
p
Þ
2
E½ðX
ðkÞ
p
Þ
2
1
ðkÞ
p
E½X
ðkÞ
p
E½X
ðkÞ
p
2ð1
ðkÞ
p
E½X
ðkÞ
p
P
n
max
i¼0
!
ðkÞ
i
E½
ðkÞ
i
Þ
:
ð8Þ
Proof. The handoff delay E½D
i
depends on which channel
is selected for the target channel at the ith interruption.
For the type-ði 1Þ secondary connection, its current
operating channel is s
i1;
. When it is interrupted again,
its new operating channel is s
i;
. When s
i1;
¼ s
i;
,it
means that the considered secondary connection will
stay on the current channel. When s
i1;
6¼ s
i;
,it
represents that the considered secondary connection will
change its operating channel to another channel. Both
cases are discussed as follows:
1. Staying case. When the considered secondary
connection stays on its current operating channel
s
i;
¼ k, it cannot be resumed until all the high-priority
primary connections of channel k finish their transmis-
sions. Hence, the handoff delay is the busy period
resulting from multiple primary connections of channel
k (denoted by Y
ðkÞ
p
) as discussed in Section 3.2. That is,
we can have E½ D
i
¼E½Y
ðkÞ
p
.
The value of E½Y
ðkÞ
p
can be derived as follows: Denote
I
p
astheidleperiodresultingfromtheprimary
connections. This idle period is the duration from the
termination of the busy period to the arrival of the next
primary connection. Because of the memoryless prop-
erty, the idle period follows the exponential distribution
with rate
ðkÞ
p
[49]. Hence, we have
E
I
ðkÞ
p
¼
1
ðkÞ
p
: ð9Þ
Next, according to the definition of the utilization factor
at channel k, we have
ðkÞ
p
¼
ðkÞ
p
E
X
ðkÞ
p
: ð10Þ
Because
ðkÞ
p
is also the busy probability resulting from
the primary connections of channel k, we have
ðkÞ
p
¼
E½Y
ðkÞ
p
E½Y
ðkÞ
p
þE½I
ðkÞ
p
: ð11Þ
Then, substituting (9) and (10) into (11), we can obtain (7).
2. Changing case. In this case, the considered second-
ary connection will change to channel s
i;
¼ k
0
from
s
i1;
¼ k. After switching channels, it must wait in the
low-priority queue of channel k
0
until all the traffic in the
high priority and the present low-priority queues of
channel k
0
are served as discussed in Section 3.2. Denote
W
ðk
0
Þ
s
as the waiting time for the secondary connections at
channel k
0
.
7
Hence, we have E½D
i
¼E½W
ðk
0
Þ
s
þt
s
.
The value of E½W
ðk
0
Þ
s
can be derived as follows: Let
E½Q
ðk
0
Þ
p
be the average number of the primary connec-
tions which are waiting in the high-priority queue of
channel k
0
and E½Q
ðk
0
Þ
i
be the average number of the
type-ðiÞ secondary connections which are waiting in the
low-priority queue of channel k
0
. Note that the type-ðiÞ
and type-ðjÞ secondary connections ha ve the same
priority to access channel for any i and j. Because the
newly arriving secondary connections cannot be estab-
lished until all the secondary connections in the low-
priority queue and the primary connections in the high-
priority queue have been served, the average waiting
time of channel k
0
is expressed as
E
W
ðk
0
Þ
s
¼ E
R
ðk
0
Þ
s
þE
Q
ðk
0
Þ
p
E
X
ðk
0
Þ
p
þ
X
n
max
i¼0
E
Q
ðk
0
Þ
i
E
ðk
0
Þ
i
þ
ðk
0
Þ
p
E
W
ðk
0
Þ
s
E
X
ðk
0
Þ
p
;
ð12Þ
where E½R
ðk
0
Þ
s
is the average residual effective service
time of channel k
0
. That is, E½R
ðk
0
Þ
s
is the remaining time
to complete the service of the connection being served at
channel k
0
. This connection being served can be the
primary connection or the type-ðiÞ secondary connection.
Furthermore, E ½Q
ðk
0
Þ
p
E ½X
ðk
0
Þ
p
and
P
n
max
i¼0
E ½Q
ðk
0
Þ
i
E ½
ðk
0
Þ
i
in (12) are the cumulative workload resulting from the
primary connections and the secondary connections in
the present queues of channel k
0
, respectively. Moreover,
the fourth term (
ðk
0
Þ
p
E½W
ðk
0
Þ
s
E½X
ðk
0
Þ
p
) in (12) is the
cumulative workload resulting from the arrivals of the
primary connections during W
ðk
0
Þ
s
.
In (12), the closed-form expression for E½
ðk
0
Þ
i
is
derived in Appendix B, available in the online supple-
mental material. Next, we will derive E½R
ðk
0
Þ
s
, E½Q
ðk
0
Þ
p
,
and E½Q
ðk
0
Þ
i
. First, according to the definition of residual
time in [51], we have
E
R
ðk
0
Þ
s
¼
1
2
ðk
0
Þ
p
E
X
ðk
0
Þ
p
2
þ
1
2
X
n
max
i¼0
!
ðk
0
Þ
i
E
ðk
0
Þ
i
2
; ð13Þ
1506 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 9, SEPTEMBER 2012
7. A secondary connection needs to change its operating channel only
when a primary connection appears. Because the arrivals of the primary
connections follow Poisson distribution, the arrivals of the interrupted
secondary connections at channel k
0
also follow Poisson distribution.
Applying the property of Poisson arrivals see time average (PASTA) to the
arrivals of the interrupted secondary connections at channel k
0
[50], all of
them must spend time duration E½W
ðk
0
Þ
s
on average to wait for an idle
channel k
0
. This waiting time is uncorrelated to the number of interruptions.
where !
ðk
0
Þ
i
is derived in Appendix A, available in the
online supplemental material. Second, according to
Little’s formula, it follows that:
E
Q
ðk
0
Þ
p
¼
ðk
0
Þ
p
E
W
ðk
0
Þ
p
; ð14Þ
where E½W
ðk
0
Þ
p
is the average waiting time of the primary
connections at channel k
0
. It is the duration from the time
instant that a primary connection enters the high-priority
queue of channel k
0
until it gets a chance to transmit at
channel k
0
. Hence, it follows that
E
W
ðk
0
Þ
p
¼ E
R
ðk
0
Þ
p
þ E
Q
ðk
0
Þ
p
E
X
ðk
0
Þ
p
; ð15Þ
where E½R
ðk
0
Þ
p
is the average residual service time resulting
from only the primary connections of channel k
0
and
E½Q
ðk
0
Þ
p
E½X
ðk
0
Þ
p
is the t otal workload of the primary
connections in the present high-priority queue of channel
k
0
. According to [51], we have E½R
ðk
0
Þ
p
¼
1
2
ðk
0
Þ
p
E½ðX
ðk
0
Þ
p
Þ
2
.
Then, solving (14) and (15) simultaneously yields
E
W
ðk
0
Þ
p
¼
E½R
ðk
0
Þ
p
1
ðk
0
Þ
p
¼
ðk
0
Þ
p
E½ðX
ðk
0
Þ
p
Þ
2
2ð1
ðk
0
Þ
p
E½X
ðk
0
Þ
p
Þ
; ð16Þ
and
E
Q
ðk
0
Þ
p
¼
ðk
0
Þ
p
E½R
ðk
0
Þ
p
1
ðk
0
Þ
p
¼
ð
ðk
0
Þ
p
Þ
2
E½ðX
ðk
0
Þ
p
Þ
2
2ð1
ðk
0
Þ
p
E½X
ðk
0
Þ
p
Þ
: ð17Þ
Next, according to Little’s formula, we can obtain
E
Q
ðk
0
Þ
i
¼ !
ðk
0
Þ
i
E
W
ðk
0
Þ
s
: ð18Þ
Finally, substituting (13), (17), and (18) into (12), we can
obtain (8). tu
Proposition 2.
p
ðkÞ
i
¼
ðkÞ
p
E
ðkÞ
i
;k¼ s
i;
0;k6¼ s
i;
:
ð19Þ
Proof. The value of p
ðkÞ
i
can be evaluated as follows: Because
the considered secondary connection will operate at
channel s
i;
after the ith interruption, we have p
ðkÞ
i
¼ 0
when k 6¼ s
i;
. Furthermore, for the case that k ¼ s
i;
,we
considerthetimeinterval½0;t at channel k.Total
ðkÞ
p
t primary connections and !
ðkÞ
i
t type-ðiÞ secondary
connections arrive at channel k during this interval.
Hence, there are total !
ðkÞ
i
tp
ðkÞ
i
type-ðiÞ secondary connec-
tions will be interrupted on average during this interval.
Furthermore, applying the property of Poisson arrivals
see time average (PASTA) to the arrivals of the primary
connections [50], we can obtain the probability that a
primary connection finds channel k being occupied by
the type-ðiÞ secondary connections is
ðkÞ
i
. Thus, during
this interval, total
ðkÞ
p
t
ðkÞ
i
primary connections can see a
busy channel being occupied by the type-ðiÞ secondary
connections. For each primary connection, it can interrupt
only one secondary connection when it arrives at a busy
channel being occupied by the secondary connection
because only one secondary user can transmit at any
instant of time. Thus, the total number of the interrupted
secondary connections at channel k is also
ðkÞ
p
t
ðkÞ
i
.
Hence, we have !
ðkÞ
i
tp
ðkÞ
i
¼
ðkÞ
p
t
ðkÞ
i
. That is,
ðkÞ
i
¼
!
ðkÞ
i
ðkÞ
p
p
ðkÞ
i
: ð20Þ
Next, we consider a type-ðiÞ secondary connection at
channel k. Before the ði þ 1Þth interruption event occurs,
its effective service time is E½
ðkÞ
i
. Thus, from queuing
theory, we can have
ðkÞ
i
¼ !
ðkÞ
i
E
ðkÞ
i
: ð21Þ
Comparing (20) and (21), we can obtain (19). tu
6APPLICATIONS TO PERFORMANCE ANALYSIS
BASED ON TWO TYPICAL TARGET CHANNEL
SEQUENCES
To demonstrate the usefulness of the developed analytical
method, we apply these analytical results in Section 5 to the
two typical target channel sequences used in the IEEE
802.22 WRAN standard. Specifically, we consider the
always-staying and always-changing spectrum handoff se-
quences, which are, respectively, introduced in the non-
hopping mode and the phase-shifting hopping mode of the
IEEE 802.22 standard [52]. From the analytical results, an
adaptive target channel selection approach can be provided.
6.1 Derivation of Extended Data Delivery Time
For the always-staying sequence, a secondary connection
always stays on its default channel when it is interrupted.
That is, its target channel sequence can be expressed as
(Ch;Ch;Ch;...) and thus s
i;
¼ for any i n
max
.
Hence, we can have E½D
i
¼E½Y
ðÞ
p
for any i n
max
in
(5). Then, the average extended data delivery time of
the secondary connections for the always-staying sequence
can be expressed as follows:
E½T
stay
¼E
X
ðÞ
s
þ
X
n
max
n¼1
X
n
i¼1
E
Y
ðÞ
p
!
1 p
ðÞ
n
Y
n1
i¼0
p
ðÞ
i
: ð22Þ
Next, we consider the always-changing sequence. In this
case, the secondary connection sequentially changes its
operating channel to the next neighboring channel. With-
out loss of generality, its corresponding target channel
sequence can be expressed as (Chð þ 1Þ;Chð þ 2Þ; ...;
ChM; Ch1; Ch2; ...;Ch;Chð þ 1Þ; ...), where channel is
the default channel of the secondary connection. That is, at
the ith interruption, the target channel of the interrupted
secondary connection is channel s
i;
MODði þ ; M Þ
where MODða; bÞ is the Modulus function and it returns
the remainder when a is divided by b. Hence, we have
E½D
i
¼E½W
ðs
i;
Þ
s
þt
s
for any i n
max
in (5). Thus, the
average extended data delivery time of the secondary
conne ctions for the always-changing sequence can be
expressed as follows:
WANG ET AL.: MODELING AND ANALYSIS FOR SPECTRUM HANDOFFS IN COGNITIVE RADIO NETWORKS 1507
E½T
change
¼E½X
ðÞ
s
þ
X
n
max
n¼1
X
n
i¼1
E
W
ðs
i;
Þ
s
þ t
s
!
1 p
ðs
n;
Þ
n
Y
n1
i¼0
p
ðs
i;
Þ
i
"#
:
ð23Þ
Based on the analytical results, the secondary connec-
tion can adaptively adopt the better target channel
sequence to reduce its extended data delivery time. Thus,
the average extended data delivery time with this adaptive
channel selection principle (denoted by E½T
) can be
expressed as follows:
E½T
¼min E½T
stay
; E½T
change
: ð24Þ
6.2 An Example for Homogeneous Traffic Loads
Now, we give an example to explain how to apply our
analytical results to find the better target channel sequence
when traffic parameters are given. We consider a special
case that the primary and the secondary connections have
the same traffic parameters in a three-channel system (i.e.,
ð1Þ
p
¼
ð2Þ
p
¼
ð3Þ
p
p
,
ð1Þ
s
¼
ð2Þ
s
s
, and E½X
ð1Þ
p
¼E½X
ð2Þ
p
¼
E½X
ð3Þ
p
E½X
p
). Because the three channels are identical,
three channels have the same performance metrics. Thus,
the superscript (k) can be dropped to ease the notations.
Furthermore, we assume that the servi ce time of the
secondary connections follows the same exponential
distribution, i.e., f
ð1Þ
s
ðxÞ¼f
ð2Þ
s
ðxÞ¼f
ð3Þ
s
ðxÞf
s
ðxÞ¼
s
e
s
x
.
Hence, we have E½X
ð1Þ
s
¼E½X
ð2Þ
s
¼E½X
ð3Þ
s
E½X
s
¼
1
s
.
6.2.1 Derivation of p
ðÞ
i
and E½Y
ðÞ
p
in (22)
First, according to Appendix B, available in the online
supplemental material, we can derive E½
ðÞ
i
as follows:
E
ðÞ
i
¼ E½
i
¼
1
p
þ
s
: ð25Þ
Then, the value of p
ðÞ
i
can be derived from (19) as follows:
p
ðÞ
i
¼
ðÞ
p
E
ðÞ
i
¼
p
p
þ
s
p
i
: ð26Þ
Next, referring to (7), it follows that:
E
Y
ðÞ
p
¼ E½Y
p
¼
E½X
p
1
p
E½X
p
: ð27Þ
Finally, substituting (26) and (27) into (22), we can obtain
the closed-form expression for the extended data delivery
time with the always-staying target channel sequence.
6.2.2 Derivation of E½W
ðs
i;
Þ
s
and p
ðs
i;
Þ
i
in (23)
Referring to Appendices A and B, available in the online
supplemental material, we can have
!
ðs
i;
Þ
i
¼ !
i
¼
s
p
p
þ
s
i
; ð28Þ
and
E
ðs
i;
Þ
i
2
¼ E
ð
i
Þ
2
¼
2
ð
p
þ
s
Þ
2
: ð29Þ
Next, substituting (25), (28), and (29) into (8), we can have
E
W
ðs
i;
Þ
s
¼ E½W
s
¼
p
E½ðX
p
Þ
2
þ
2
s
E½X
s
ð
p
þ
s
Þ
þ
ð
p
Þ
2
E½ðX
p
Þ
2
1
p
E½X
p
E½X
p
2ð1
p
E½X
p
s
E½X
s
Þ
:
ð30Þ
Then, referring to (19), it follows that:
p
ðs
i;
Þ
i
¼ p
i
¼
p
p
þ
s
: ð31Þ
Finally, substituting (30) and (31) into (23), we can obtain
the closed-form expression for the extended data delivery
time with the always-changing target channel sequence.
Note that this closed-form expression for p
i
in this special
case was discussed in [7]. However, [7] cannot extend to the
case with the general service time distribution.
In summary, the average extended data delivery time
with our adaptive target channel selection approach can be
expressed as follows:
E½T
¼
E½T
stay
; E½Y
p
E½W
s
þt
s
E½T
change
; E½Y
p
E½W
s
þt
s
:
ð32Þ
Note that the always-staying and the always-changing
sequences have the same extended data delivery time when
E½Y
p
¼E½W
s
þt
s
.
7NUMERICAL RESULTS
We show numerical results to reveal the importance of the
three key design features of modeling spectrum handoffs as
discussed in Section 2, which consist of 1) general service time
distribution; 2) various operating channels; and 3) queuing
behaviors of multiple secondary connections. Here, we only
show the effects of these key design features on E½T . The
effects on other performance metrics (such as E½T =E½X
s
)
can be derived based on similar manners.
7.1 Simulation Setup
In order to validate the proposed analytical model, we
perform simulations in the continuous-time cognitive radio
systems, where the interarrival time and service time can be
the duration of noninteger time slots. We consider a three-
channel CR system with Poisson arrival processes of rates
p
and
s
for the high-priority primary connections and the
low-priority secondary connections, respectively. The high-
priority connections can interrupt the transmissions of the
low-priority connections, and the connections with the
same priority follow the first-come-first-served (FCFS)
scheduling discipline.
8
Referring to the IEEE 802.22 stan-
dard, we adopt time slot duration of 10 msec in our
simulations [54].
7.2 Effects of Various Service Time Distributions for
Primary Connections
First, we investigate the effects of various service time
distributions for primary connections on the extended data
delivery time of the secondary connections. The truncated
Pareto distribution and the exponential distribution are
1508 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 9, SEPTEMBER 2012
8. In fact, the analytical results of mean values obtained in this paper can
be applied to other scheduling discipline which is independent of the
service time of the primary and secondary connections because the averages
of system performance metrics will be invariant to the order of service in
this case (see [53, p. 113]).
considered in our simulations. Referring to [49], these two
distributions match the actual data and voice traffi c
measurements very well, respectively. The truncated Pareto
distribution is expressed as follows:
f
X
ðxÞ¼
K
x
þ1
;K x m
K
m
;x¼ m
:
ð33Þ
According to [55], the traffic shaping parameter ¼ 1:1 and
the scale parameter K ¼ 81:5, and the truncated upper bound
m ¼ 66;666 bytes in (33). Based on this setup, the average
connection length is 480 bytes for the primary connections.
For fair comparison, we also assume that the averag e
connection length is 480 bytes when the exponentially
distributed primary connections are considered. Moreover,
we assume that E½X
ð1Þ
s
¼E½X
ð2Þ
s
¼E½X
ð3Þ
s
E½X
s
¼10
(slots/arrival), and E½X
ð1Þ
p
¼E½X
ð2Þ
p
¼E½X
ð3Þ
p
E½X
p
.
When the data rate of the primary connections is 19.2 Kbps,
we have E½X
p
¼
4808bits
19:2Kbps
10msec
slot
¼ 20 (slots/arrival) for the
Pareto and the exponential distributions. Furthermore, we
consider that
s
¼ 0:01 (arrivals/slot). Recall that
p
is the
channel busy probability resulting from the transmissions of
the primary connections. We only consider the case that 0
p
¼
p
E½X
p
< 1
s
E½X
s
¼0:9 in the following numerical
results. When
p
þ
s
E½X
s
1 (or equivalently
p
s
E½X
s
E½X
p
¼ 0:045 (arrivals/slot)), the secondary connections will
encounter the infinite extended data delivery time on
average.
Fig. 4 compares the effects of Pareto and exponential
service time distributions for primary connections when the
always-changing spectrum handoff sequence is adopted.
First, we find that the simulation result s match the
analytical results quite well, which can validate the slot-
based assumption used in our analysis. Next, compared to
the exponentially distributed service time for primary
connections, the Pareto distributed service time results in
longer average extended data delivery time in the secondary
connections. This phenomenon can be interpreted as follows:
Because of the heavy tail property of Pareto distribution,
the second moment E½ðX
p
Þ
2
of service time with Pareto
distribution is larger than that with exponential distribution.
According to (30) and (23), an interrupted secondary
connection will encounter longer waiting time and extended
data delivery time when the primary connections’ service
time distribution is Pareto. For example, when
p
¼ 0:44 or
equivalently
p
¼
p
E½X
p
¼ 0:022 (arrivals/slot), the average
extended data delivery time with the Pareto-typed primary
connection service time is four times longer than that with
the exponential-typed primary connection service time.
Because the developed analytical framework can character-
ize the effects of general service time distribution, it is
quite useful.
When the always-staying spectrum handoff sequence is
adopted, Fig. 5 shows the average extended data delivery
time of the secondary connections. According to (22), the
extended data delivery time in this case is related to the
average busy period E½Y
p
resulting from the primary
connections. Because the considered Pareto and exponential
distributions have the same average service time, these two
distributions result in the same average busy period E½Y
p
for the primary connections according to (27), resulting in
the same average extended data delivery time as well.
7.3 Traffic-Adaptive Target Channel Selection
Principle
Fig. 6 compares the extended data delivery time of the
always-staying and the always-changing spectrum handoff
sequences when the service time of the primary connections
is exponentially distributed. Based on (32), the traffic-
adaptive channel selection approach can appropriat ely
change to better target channel sequence according to traffic
conditions. This figure shows that a cross point occurs
when
p
¼0:44 or equivalently
p
¼
p
E½X
p
¼ 0:022 (arrivals/
slot), where the always-staying and the always-changing
sequences result in the same extended data delivery time.
When
p
> 0:44, the interrupted user prefers the always-
staying sequence. This phenomenon can be interpreted as
follows: A larger value of
p
(or equivalently a larger value
of
p
) will increase the probability that an interrupted
secondary user experiences long waiting time when it
WANG ET AL.: MODELING AND ANALYSIS FOR SPECTRUM HANDOFFS IN COGNITIVE RADIO NETWORKS 1509
Fig. 4. Effects of Pareto and exponential service time distributions for
primary connections on the extended data delivery time (E½T
change
)of
the secondary connections when the always-changing spectru m
handoff sequence is adopted, where t
s
¼ 1 (slot),
s
¼ 0:01 (arrivals/
slot), E½X
s
¼10 (slots/arrival), and E½X
p
¼20 (slots/arrival).
Fig. 5. Effects of Pareto and exponential service time distributions for
primary connections on the extended data delivery time (E½T
stay
) of the
secondary connections when the always-staying spectrum handoff
sequence is adopted, where t
s
¼ 1 (slot),
s
¼ 0:01 (arri vals/slot),
E½X
s
¼10 (slots/arrival), and E½X
p
¼20 (slots/arrival).
changes its operating channel. As a result, the average
handoff delay for changing operating channel (i.e.,
E½W
s
þt
s
) will be extended. Then, the average extended
data delivery time will be also prolonged. In our case, the
secondary user prefers staying on the current operating
channel when
p
> 0:44. By contrast, when
p
< 0:44, the
traffic-adaptive channel selection approach can improve
latency performance by changing to the always-changing
sequence. For example, when
p
¼ 0:2, the traffic-adaptive
approach can improve the extended data delivery time by
15 percent compared to the always-staying sequence.
Compared to the single-channel spectrum handoff model
[30], [31], [32], [33], [34], [35], [36], [37], [38], the developed
analytical framework for multichannel spectrum handoff is
more general because it can incorporate the effects of
changing operating channels.
Fig. 7 shows the effect of secondary connections’ service
time E½X
s
on the cross point for traffic-adaptive channel
selection approach. According to (32), for a lager value of
E½X
s
, the interrupted secondary connection prefers stay-
ing on the current channel because the average handoff
delay for changing its operating channel is longer than
that for staying on the current channel. Thus, the cross
point of “al ways-staying” and “always-changing” se-
quences moves toward left-hand side as E½X
s
increases
as seen in the figure.
The analytical results developed in this paper can be
used to design the admission control rule for the arriving
secondary users subject to their latency requirement.
9
Fig. 8
shows the admissible region for the normalized traffic
workloads (or channel utilities) (
p
;
s
).
10
The maximum
allowable average cumulative delay resulting from multi-
ple handoffs is 20 ms for the Voice over IP service [56].
Assume E½X
p
¼20 (slots/arrival) and E½X
s
¼10 (slots/
arrival). The admission control policy can be designed
according to this figure. When
p
< 0:166, a CR network
can accept all arrival requests from the secondary users
until the CR network is saturated, i.e.,
p
þ
s
’ 1.
Furthermore, when 0:166 <
p
< 0:312, a part of traffic
workloads of the secondary users must be rejected in order
to satisfy the delay constraint for the secondary users. In
this case, 0:31 <
p
þ
s
< 0:645. For example, whe n
p
¼ 0:25, a CR network can support at most 0.214 work-
load for the secondary users. That is, a CR network can
accept at most
s
¼ 0:0214 (arrivals/slot) based on the
results shown in the figure when
p
¼ 0:0125 (arrivals/
slot). In order to design the most allowable
s
to achieve
this arrival rate upper bound for the secondary connec-
tions, many arrival-rate control methods can be considered,
such as the p-persistent carrier sense multiple access
(CSMA) protocol in [57] and the call admission control
mechanisms in [29], [58], [59]. Finally, when
p
> 0:312,no
secondary user can be accepted.
7.4 Performance Comparison between Different
Channel Selection Methods
Now, we compare the extended data delivery time of the
following three schemes: 1) the slot-based target channel
selection s cheme; 2) the ra ndom-based target channel
selection scheme; and 3) the traffic-adaptive target channel
selection scheme. We consider a three-channel network with
1510 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 11, NO. 9, SEPTEMBER 2012
Fig. 6. Comparison of the extended data delivery time for the always-
staying and always-changing spectrum handoff sequences as well as
the traffic-adaptive channel selection approach, where t
s
¼ 1 (slot),
s
¼
0:01 (arrivals/slot), E½X
p
¼20 (slots/arrival), and E½X
s
¼10 (slots/
arrival).
Fig. 7. Effects of secondary connections’ service time E½X
s
on the cross
point for the traffic-adaptive channel selection approach, where t
s
¼ 1
(slot), E½X
p
¼20 (slots/arrival), and
s
¼ 0:01 (arrivals/slot).
Fig. 8. Admissible region for the normalized traffic workloads (
p
;
s
),
where the average cumulative delay constraint can be satisfied when
t
s
¼ 0 (slot), E½X
p
¼20 (slots/arrival) and E½X
s
¼10 (slots/arrival).
9. The admissible region can be determined by comparing the derived
extended data delivery time and the m aximum allowable average
cumulative delay.
10.
p
¼
p
E½X
p
and
s
¼
s
E½X
s
.
various traffic loads, where
ð1Þ
p
¼
ð2Þ
p
¼
ð3Þ
p
p
,
ð1Þ
s
¼
ð2Þ
s
¼
ð3Þ
s
s
¼0:01 (arrivals/slot), ðE½X
ð1Þ
p
; E½X
ð2Þ
p
; E½X
ð3Þ
p
Þ ¼
ð5; 15; 25Þ (slots/arrival), and ðE½X
ð1Þ
s
; E½X
ð2Þ
s
; E½X
ð3Þ
s
Þ ¼
ð15; 15; 15Þ (slots/arrival). For the slot-based scheme, the
secondary connections prefer selecting the channel which
has the lowest busy probability resulting from the primary
connections in each time slot. That is, w hen handoff
procedures are initiated in the beginning of each time slot,
all the secondary connections will select channel 1 to be their
target channels. Furthermore, the random-based scheme
selects one channel out of all the three channels for the target
channel. Hence, each channel is selected with probability
1=3. Moreover, based on the considered traffic parameters,
the traffic-adaptive scheme will adopt the always-changing
sequence and the always-staying sequence when
p
0:018
(arrivals/slot) and
p
0:018 (arrivals/slot), respectively.
The three target channel selection schemes result in various
target channel sequences. Based on the proposed analytical
model, we can evaluate the average extended data delivery
time resulting from these target channel sequences.
Fig. 9 compares the extended data delivery time of the
three target channel selection methods. We ha ve the
following three important observations. First, we consider
p
< 0:018 (arrivals/slot). Because the probability of chan-
ging operating channel is higher than that of staying on the
current operating channel for the interrupted secondary
user in the random-based scheme, we can find that the
average extended data delivery time for the random-based
target channel selection scheme is similar to that for the
traffic-adaptive target channel selection scheme, which
adopts the always-changing sequence. Second, when
p
>
0:018 (arrivals/slot), the traffic-adaptive scheme can short-
en the average extended data delivery time because it
adopts the always-staying sequence. For a larger value of
p
, the traffic-adaptive scheme can improve the extended
data delivery time more significantly. Third, it is shown
that the random-based and traffic-adaptive schemes can
result in shorter extended data delivery time compared to
the slot-based scheme. For example, when
p
¼ 0:018, the
random-based and traffic-adaptive schemes can improve
the extended data delivery time by 35 percent compared to
the slot-based scheme. This is because the slot-based
scheme does not consider the queuing delay due to channel
contention from multiple secondary connections.
8CONCLUSIONS
In this paper, we have proposed a PRP M/G/1 queuing
network model to characterize the spectrum usage beha-
viors with multiple handoffs. We studied the latency
performance of the secondary connections by considering
the effects of 1) general service time distribution; 2) various
operating channels; and 3) queuing delay due to channel
contention from multiple secondary connections. T he
proposed model can accurately estimate the extended data
delivery time of different proactively designed target
channel sequences. On top of this model, we showed the
extended data delivery time of the secondary connections
with the always-staying and the always-changing sequences. If
the secondary users can adaptively adopt the better target
channel sequence according to traffic conditions, the
extended data delivery time can be improved significantly
compared to the existing target channel selection methods,
especially for the heavy traffic loads of the primary users.
Some important research issues can be extended from
this paper. For example, we can consider other reestablish-
ment policies rather than the resumption policy as in this
paper. In this paper, we assumed that the interrupted
secondary user can resume its unfinished transmission on
the suitable channel. However, in other scenarios, the
interrupted secondary user may need to retransmit the
whole connection rather than resuming the unfinished
transmission. In this situation, a CR network should be
modeled by the preemptive repeat priority queuing net-
work, and is worthwhile to investigate the latency
performance resulting from this policy. Furthermore, how
to apply the concept of priority queuing to other applica-
tions, such as electronic health (e-Health) applications [60],
is also an interesting issue.
ACKNOWLEDGMENTS
This work was presented in part at the IEEE International
Conference on Communications (ICC), 2009. This work was
supported in part by the MoE ATU Plan and by National
Science Council (NSC) grants 96-2628-E-009-004-MY3, 97-
2221-E-009-099-MY3, and 97-2917-I-009-109.
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Li-Chun Wang received the BS degree from
National Chiao Tung University, Taiwan, ROC, in
1986, the MS degree from the National Taiwan
University in 1988, and the MSc and PhD
degrees from the Georgia Institute of Technol-
ogy, Atlanta, in 1995 and 1996, respectively, all
in electrical engineering. From 1996 to 2000, he
was with AT&T Laboratories, where he was a
senior technical staff member in the Wireless
Communications Research Department. Since
August 2000, he has been an associate professor in the Department of
Communication Engineering of National Chiao Tung University in
Taiwan. He was a corecipient (with Gordon L. Stu
¨
ber and Chin-Tau
Lea) of the 1997 IEEE Jack Neubauer Best Paper Award. He has
published more than 150 journal and international conference papers
and is holding three US patents. He was elected an IEEE fellow in 2011
for his contribut ion s in cellular arch it ec tur es and radio resour ce
management in wireless networks. He served as an associate editor
for the IEEE Transactions on Wireless Communications from 2001 to
2005 and as a guest editor for the Special Issue on Mobile Computing
and Networking of the IEEE Journal on Selected Areas in Communica-
tions in 2005 and for the Special Issue on Radio Resource Management
and Protocol Engineering in Future IEEE Broadband Networks of IEEE
Wireless Communications Magazine in 2006. He holds eight US patents.
Chung-Wei Wang received the BS degree in
electrical engineering from Tamkang University,
Taipei, Taiwan, in 2003, and the minor MS and
PhD degrees in applied mathematics and com-
munication engineering from the National Chiao
Tung University, Hsinchu, Taiwan, in 2007 and
2010, respectively. From 2009 to 2010, he was a
visiting scholar at Tohoku University, Sendai,
Japan. He was awarded student travel grants
from IEEE ICC 2009 and GLOBECOM 2010. He
is currently working as a principal engineer at MStar Semiconductor,
Inc., Taipei, Taiwan, and is responsible for the development of 3GPP
technologies. His current research interests include cross-layer optimi-
zation, MAC protocol design, and radio resource management in cellular
systems, wireless sensor networks, ad hoc networks, and cognitive
radio networks. He is a student member of the IEEE.
Chung-Ju Chang received the BE and ME
degrees in electronics engineering from Na-
tional Chiao Tung University, Hsinchu, Taiwan,
in 1972 and 1976, respectively, and the PhD
degree in electrical engineering from National
Taiwan University in 1985. From 1976 to
1988, he was with Telecommunication Labora-
tories, Directorate General of Telecommunica-
tions, Ministry of Communications, Taiwan, as
a design engineer, supervisor, project man-
ager, and then division director. He also acted as a science and
technical advisor for the Minister of the Ministry of Communications
from 1987 to 1989. In 1988, he joined the Faculty of the Department
of Communication Engineering, College of Electrical Engineering and
Computer Science, National Chiao Tung University, as an associate
professor. He has been a professor since 1993 and a chair professor
since 2009. He was the director of the Institute of Communication
Engineering from August 1993 to July 1995, chairman of the
Department of Communication Engineering from August 1999 to July
2001, and dean of the Research and Development Office from
August 2002 to July 2004. Also, he was an advisor for the Ministry of
Education to promote the education of communication science and
technologies for colleges and universities in Taiwan during 1995-
1999. He acts as a committee member of the Telecommunication
Deliberate Body, Taiwan. Moreover, he served as an editor for IEEE
Communications Magazine and associate editor for IEEE Transac-
tions on Vehicular Technology. His research interests include
performance evaluation, radio resources management for wireless
communication networks, and traffic control for broadband networks.
He is a member of the Chinese Institute of Engineers and the
Chinese Institute of Electrical Engineers. He is a fellow of the IEEE.
. For more information on this or any other computing topic,
please visit our Digital Library at www.computer.org/publications/dlib.
WANG ET AL.: MODELING AND ANALYSIS FOR SPECTRUM HANDOFFS IN COGNITIVE RADIO NETWORKS 1513
