ANALYSIS AND OPTIMIZATION OF A GATED POLLING BASED SPECTRUM ALLOCATION MECHANISM IN COGNITIVE RADIO NETWORKS

. In Cognitive Radio Networks the licensed users and the cognitive users are called Primary Users and Secondary Users, respectively. The Primary Users enjoy preemptive priority during the spectrum usage, while the Secondary Users are allowed to access the unused parts of the spectrum oppor-tunistically. In this paper we focus on the problem of improving the fairness of spectrum usage for real-time applications. We propose a novel centralized spectrum allocation mechanism with a gated polling strategy, which we model by a gated polling system with a non-zero switchover times. The approximate analysis of this polling model is performed. We derive formulas for estimating the system measures in terms of throughput of the system, average latency and delay jitter of the Secondary Users packets as well as the spectrum switching ratio and the spectrum utility. Numerical results based on the analysis and the simulation are provided to validate the analytical results and to investigate the impact of diﬀerent parameters on the system performance. Finally we discuss the optimal system design by the help of building an appropriate cost function.


1.
Introduction.With the development of wireless technology and the proliferation of wireless applications, there has been a dramatic increase in the demand for radio spectrum [12].As most spectrum has been assigned to licensed users, also called Primary Users (PUs), for exclusive use, the spectrum has become a scarce resource.However most of the already allocated radio bands are either not used, or are sporadically used [2].Existing spectrum measurement reports indicate that up to 85% of the spectrum remains unoccupied at any given time and location [8].Therefore the development of a spectrum allocation mechanism with high utilization becomes a matter of great importance.

SHUNFU JIN, WUYI YUE AND ZSOLT SAFFER
In Cognitive Radio Networks (CRNs) a dynamic spectrum allocation strategy is proposed to improve the spectrum utilization [4].Therefore cognitive users, who are also called Secondary Users (SUs), are allowed to access the spectrum opportunistically.Recently many experts entered into the related research on spectrum allocation strategies and performance analysis in the context of CRNs.
One of the necessary issues to be addressed is how to enhance the spectrum utility with appropriate constraint of other performance measures.Do et al. considered a sensitive delay network, and proposed an algorithm to distribute the SU packets to those groups of channels which satisfy an appropriate delay constraint [3].They analyzed the performance of the SUs by applying an M/G/1 queueing model.Treeumnuk et al. investigated how to adapt the duration of the spectrum sensing window to enhance the detection probability of the spectrum holes and their actual utilization [15].They could improve the spectrum hole utilization by applying a scheme with a variable sensing window length instead of the one with fixed sensing duration.Wu et al. studied the system in the context of security and offered a channel hopping defense strategy [16].They proposed two learning schemes, which are based on the interaction between the SUs and the attackers.They also derived the Nash equilibrium for the Colonel Blotto game, which is used to minimize the worst-case damage.
Another objective in the CRNs is that the PUs should not suffer from the utilization of the unused part of the spectrum by the SUs.Li et al. offered a modified hybrid opportunistic scheduling method by pre-selecting a set of the SUs based on their interference to the PUs and optimized the throughput of the SUs [9].Mihov analyzed the cross-layer performance by taking into account both the traffic capacity and the quality of service provision [11].In this work also the call dropping probabilities of the SUs were evaluated for both the saturation network and the non-saturation network cases.Htike et al. investigated the problem of maintaining the connectivity among the SUs with a small amount of channel access delay [5].They proposed a hybrid MAC protocol by combining a Common Control Channel (CCC) and a Time to Rendezvous (TTR).
However in the literatures mentioned above, the research focused either on improving the spectrum utility or retaining the transmission quality of PU packets.In contrast to the above references in this paper we deal with the problem of ensuring a fair access among SUs to the unused spectrum part in the CRNs.We improve the fairness for the unoccupied spectrum access among the SUs by a spectrum allocation mechanism based on a gated polling strategy, which we introduced in [6].Thus this work can be seen as the continuation of the above work.We model this spectrum allocation mechanism by a non-zero switchover times gated polling model with possible service interruption.We provide an approximate analysis of this model.Afterwards we estimate several system performance measures including the throughput of the system, the average latency and the delay jitter of the SU packets as well as the spectrum switching ratio and the spectrum utility.We validate our analytic model by simulation.The presented numerical results are also used to study the effect of several parameters to the system performance.We also build a proper cost function, which is used for the optimal system design.
The rest of this paper is organized as follows.We describe the proposed spectrum allocation mechanism with gated polling and build the corresponding queueing model in section 2. In section 3 we derive the approximate analysis and derive the formulas for the performance measures.In section 4 we present numerical results to validate the analysis and to get insight into the behavior of the system.Finally we draw our conclusions in section 5.

2.
CRN system with spectrum allocation mechanism and its queueing model.In this section first we explain the gated polling based spectrum allocation mechanism, then we describe the CRN system with such allocation mechanism and its corresponding queueing model.

2.1.
A gated polling based spectrum allocation mechanism.In CRNs with centralized spectrum allocation mechanisms the PUs enjoy preemptive priority at all times.The Central Scheduler (CS) allocates part of the spectrum bands to the SUs, which is temporarily unused by the PUs.Due to the existence of the CS the centralized spectrum allocation mechanism can satisfy diverse needs of different users and prevent users from mutual interference as much as possible.
For some network environments, such as "Free Public WiFi", users concern not only efficiency but also equity in spectrum allocation.In order to guarantee fairness among the SUs of CRNs when accessing to the spectrum bands we propose the centralized spectrum allocation mechanism with gated polling strategy, which it is known to be more fair comparing to the pure exhaustive strategy [14].Moreover we consider real-time traffic, such as multimedia scenario, which implies that the interrupted SU packets are dropped by the system.Thus the retransmissions of SU packets are not needed to be considered in this work.
We focus on an SU being polled, and call this SU as a "tagged SU".The tagged SU will opportunistically use one of the spectrum bands, which are licensed to PUs.According to the gated polling strategy the CS polls the SUs on cyclic manner.If the tagged SU has no waiting packets to be transmitted at polling instant then it does not send sensing result to the CS.In this case the CS invokes a switchover and polls the next SU.Otherwise the tagged SU sends the sensing result to the CS, which as a next step allocates one detected free spectrum band to the SU.Then the SU starts the transmission of its packets.According to the gated polling strategy during a transmission period only those packets of the tagged SU are transmitted, which are present at that SU already at the polling instant.Therefore the transmission of the packets arriving at the tagged SU during the actual transmission period will be delayed until the next assignment of a free spectrum band to the same SU.
2.2.CRN system with the gated polling based spectrum allocation mechanism.In this subsection we describe the CRN system with the gated polling based spectrum allocation mechanism.The CRN system consists of multiple spectrum bands and each spectrum band is licensed to one PU.Moreover there are N SUs in the CRN system, which use these spectrum bands opportunistically.The operation of the system can be described as follows: (1) The sensing process.Time is divided into a sequence of fixed length intervals, called slots.At the beginning instant of each slot, in which the tagged SU has waiting packets to transmit, the tagged SU will sense the spectrum bands for the PU activity (idle or busy) and send the sensing results to the CS.(2) The free spectrum band allocation at polling instant.If the tagged SU has no waiting packets for transmission, when it is polled by the CS, then there will be no sensing results sent to the CS.In this case the CS invokes a swithover and polls the next SU.In the other case, when the tagged SU has packets to transmit at the polling instant, the tagged SU sends sensing results to the CS, which allocates a free sensed spectrum band to the tagged SU. (3) The gated polling strategy.The SUs are polled in a fixed cyclic order according to the gated polling strategy.If the SU being polled has packets to be transmitted, then the packets present in the SU's buffer at polling instant will be transmitted continuously.The SU packets arriving at the tagged SU during the actual transmission period will wait until the next polling instant in the buffer of that SU. (4) The transmission interruption.The PU packets can arrive at any slot, and have preemptive priority on using the spectrum band.If there is no transmission interruption due to the arrival of the PU, the tagged SU will use one spectrum band throughout its transmission period.In case of transmission interruption by an arriving PU packet the tagged SU will drop the packet being transmitted at the interruption instant, which behavior is in line with the requirements of real-time application.At the same time the CS will allocate another free spectrum band to the tagged SU, and the transmission procedure of the tagged SU will be continued with its next SU packet.We suppose here that there is always at least one available spectrum band in the system.Thus if transmission interruption occurs during the transmission of a packet of the tagged SU then the expected length of the transmission period of that SU packet becomes shorter.On this way the transmission of the packets of the tagged SU will occur continuously over one or more spectrum bands according to the number of transmission interruptions during the transmission period of that tagged SU.
The operation of the CRN system with the gated polling based spectrum allocation mechanism is illustrated in Fig. 1.The corresponding queueing model of the above described CRN system with the gated polling based spectrum allocation mechanism is the gated polling model with non-zero switchover times.Therefore a correspondence can be established between the elements of the CRN system with the gated polling based spectrum allocation mechanism and the non-zero switchover times gated polling model.
The CS allocating the spectrum band is the hidden entity operating the polling mechanism and the SUs correspond to the stations of the polling model.Since we focus on the problem of enhancing the fairness of spectrum usage, in this paper the sensing results are supposed to be perfect, and the sensing time is neglected.Moreover the server of polling model corresponds to the spectrum band in the CRN system actually used by the tagged SU as well as the SU packets are the customers in the polling model.Additionally the transmission of SU packet corresponds to the customer service and the SU packet transmission interruption by PU can be seen in the polling model as customer service interruption.
From now on we use the terminologies of the above described CRN system with the gated polling based spectrum allocation mechanism and of the corresponding non-zero switchover times gated polling model on mixed way.

2.3.
Queueing model.The queuing model is a discrete-time non-zero switchover times gated polling model.We apply a Late Arrival System (LAS), which assumes that the SU packets arrive at the end of a slot, the initiation and termination for the transmission of an SU packet occurs at the beginning instant of a slot.We assume symmetric settings, i.e. the arrival process, the transmission time of the SU packets, the switchover times from the SUs and the arrival probability of an PU packet are the same at every station (SU).As in more previous works (e.g., [5], [7], [17]) we assume that the SU packet arrivals follow a Bernoulli process.Let p be the probability parameter of the Bernoulli arrival process.The transmission time of the SU packets follows a geometric distribution with the probability parameter µ.Let S denote the transmission time of an SU packet.The switchover times are assumed to be constant and their time length is denoted by ω.A PU packet arrives in a slot with probability α.Recall that after the interrupted transmission of an SU packet no retransmission occurs.Furthermore we assume that for each SU its packets are transmitted according to a First-In First-Out (FIFO) strategy.Due to the symmetric settings the traffic load ρ of the whole system is given as ρ = N p/µ.
We introduce several terms.The service period is defined as the time period elapsed from the polling instant of the tagged SU to the start of the next switchover.The switchover time is defined as the time period required for the CS to switchover from the tagged SU to the next one.The vacation period, from the point of view of the tagged SU, is the time period elapsed from the start of switchover from that tagged SU to the next polling instant to the same SU.The cycle or service cycle is defined as time interval between two consecutive polling instants of the same tagged SU.A cycle is the sum of a service period and a vacation period.The length of the random variable service period, vacation and cycle is denoted by T Sp , T V and T C , respectively.
3. Performance analysis.In this section we provide the approximate analysis of the queueing model and derive estimations for several performance measures.
3.1.Probability generating functions.The probability distribution of the transmission time of an SU packet, S, can be given as follows: When the PU accesses to a spectrum band during the transmission procedure of an SU packet, the transmission of this SU packet will be interrupted, and the interrupted SU packet will be dropped from the system immediately.Therefore, the actual transmission time T of an SU packet is shorter than the transmission time S of an SU packet.The Probability Generating Function (PGF) T (z) of T is given as follows: where ᾱ = 1 − α.
Let P I be the probability that the transmission of an SU packet is interrupted by the arrival of a PU packet.Similarly let P N I be the probability that the transmission of an SU packet is completed successfully without interruption.P I and P N I can be given by Note that P I and P N I are conditional probabilities, given that there is a SU packet transmission.Let Q b be the number of SU packets which presents in the system at the end instant of a vacation V .Due to the gated service Q b is the number of SU packets arriving during the previous cycle.Let Q b (z) be the PGF of Q b .Additionally let T Sp (z) be the PGF of T Sp and T V (z) be the PGF of T V .
In order to get explicit form results we simplify the analysis by an independence assumption.Moreover we assume that there is always at least one available spectrum band to be allocated to the SU in case of transmission interruption.This leads to an approximate analysis, which we validate by simulation (see section 4).The independence assumption means that we assume that the number of SU packets arriving during the service period S p and the number of SU packets arriving during the vacation period V are stochastically independent of each other.It implies that the service periods of every pair of SUs are also stochastically independent of each other.The PGF of the number of SU packets arriving within a single slot is given as Then the PGF of Q b can be expressed as Furthermore T Sp (z) can be given as Due to the symmetric settings of the model the stochastic behavior of each SU can be considered to be identical.Therefore T V (z) can be expressed as Substituting Eqs. ( 6) and ( 7) into Eq.( 5), it follows that 3.2.Performance measures.Differentiating Eq. ( 1) with respect to z at z = 1 yields the expression of the average value of the actual transmission time T , E[T ] as follows: We can also obtain the second factorial moment of the actual transmission time T from Eq. ( 1), which gives Differentiating Eq. ( 8) with respect to z at z = 1 results in the average value of the number of SU packets, which present in the buffer of a tagged SU at the polling instant (=end of vacation), Differentiating Eq. ( 6) with respect to z at z = 1, combining with Eq. ( 11), the average value of the time length of a service period, E[T Sp ], is given as Differentiating Eq. ( 7) with respect to z at z = 1 and combining with Eq. ( 12) leads to the average value of the time length of vacation period, E[T V ] as The average value of the time length of the cycle, E[T C ], is given by Let Φ be the number of SU packets transmitted at the tagged SU during a cycle.In the gated polling model Φ is identical to the number of SU packets which presents in the system at the end of a vacation (Q b ).So the average value E[Φ] is given by Let L n be the number of SU packets in the buffer of the tagged SU immediately after the completion of the transmission of the nth SU packet (transmitted successfully or interrupted due to the arrival of a PU packet).Moreover let A i (i = 1, 2, ..., n) be the number of SU packets arriving during the transmission time of the ith SU packet.Then L n can be given as: Let L be the steady state number of SU packets in the buffer of the tagged SU immediately after the transmission completion epochs.Furthermore let L(z) be the PGF of L. By applying the regeneration cycle framework to our gated polling model (see e.g. in [13]) L(z) can be expressed as fraction of sums over one cycle as Differentiating Eq. ( 15) with respect to z at z = 1 gives the average value of L, E[L] as Let W and W (z) be the waiting time of an SU packet and its PGF, respectively.Due to the FIFO service strategy the number of SU packets immediately after the transmission completion epochs of a tagged SU packet at the tagged SU equals to the number of SU packets arriving at this tagged SU during the sum of the waiting and transmission time of that tagged SU packet.Using the independency of the above mentioned waiting and transmission periods this leads on PGF level to Setting z = Λ −1 (z) in Eq. ( 17) and expressing W (z) from it yields Applying Eq. ( 15) in Eq. (18), using Λ −1 (z) = 1 − 1 − z p (see Eq. ( 4)) and simplifying results in the expression of W (z) as Expressing the first derivative of Eq. ( 19) with respect to z at z = 1 gives the expected value of W , E[W ] as which together with Eq. ( 16) justifies the Little's law for this model: We define the latency of an SU packet as the time period in slots that has elapsed from the arrival instant of an SU packet to the transmission completion epoch of that SU packet.Hence the latency of an SU packet is the sum of the waiting time W and the actual transmission time T .Using Eq. (20) the average latency of the SU packets, σ can be given as The second factorial moments E[T (T − 1)] and E[T V (T V − 1)] can be computed from the Eqs.( 1), ( 6), (7) and (8).
The delay jitter τ of the SU packets is introduced in order to measure the fluctuation of the latency of the SU packets.We define the delay jitter τ as the standard variation of the latency of the SU packets.The delay jitter τ is given as follows: where D[W ] and E W 2 is the the variation and the second moment of the waiting time of an SU packet, respectively.The second moment of the waiting time of an SU packet, (E[W ]) 2 can be computed from the Eq. ( 19).The throughput η for the SUs is defined as the average number of SU packets transmitted successfully per slot.The throughput can be computed as and the expected value on the r.h.s. of Eq. ( 23) can be given by E[number of arriving SU packets during a slot] = N p.
Applying Eqs. ( 23) and ( 24) in Eq. ( 22) and taking into account that the probability in Eq. ( 22) equals to P N I as well as applying Eq. ( 3) the throughput η can be given as The spectrum switching ratio β is defined as the number of switches among spectrum bands per slot.The spectrum switching ratio can be computed as β = E[number of SU packet transmissions during a slot] × P {interruption during a SU packet transmission | there is a SU packet transmission}. (26) Applying Eqs. ( 23) and (24) in Eq. ( 26) and taking into account that the probability in Eq. ( 26) equals to P I as well as applying Eq. ( 2) the spectrum switching ratio β can be given as We define the spectrum utility γ as the fraction of the time spent on transmitting the SU packets successfully without interruption in a slot.The spectrum utility γ is given as follows: (28) 3.3.Future research direction.One future research direction is to relax the independence assumption described in subsection 3.1.In that case the system performance can be evaluated by the help of the joint PGFs of the number of SU packets in the buffers of every SU at polling instants.This leads to computational procedure for the major results instead of closed-form formulas.
4. Numerical results and optimization.In this section we first provide numerical results based on both analysis and simulation.The purpose of these results is to verify the model assumptions and to validate the accuracy of the presented approximate analytic model as well as to investigate the influence of the traffic load of the SUs on the system performance.Furthermore we build an optimization framework to obtain the optimal value of the arrival probability of the PU packets.
4.1.Numerical results.We use the same settings for the system parameters as in [17].According to this the number N of the SUs in the system is set to N = 8, the time length ω of the switchover times from one SU to the next SU is set to ω = 4.
The simulation follows the operation of the real system without any assumption.The simulation results are obtained by averaging over 8 independent runs, and each run is conducted for 2 × 10 7 slots.We conclude from Figs. 2-6 that the analysis and simulation results match well.Moreover these matching verify also the model assumptions including the independence assumption.
Figure 2 depicts the average latency of the SU packets (σ) as a function of the traffic load of the SUs (ρ) with different arrival probabilities of the PU packets (α) and different transmission parameters of SU packets (µ).One can observe in the figure that for the same traffic load of the SUs (ρ) and the same transmission parameter of SU packets (µ), the higher the arrival probability of the PU packets (α) is, the less the average latency of the SU packets (σ) will be.The reason is that the higher the arrival probability of the PU packets is, the more the SU packets will be interrupted by a PU packet.Therefore the actual transmission time of the interrupted SU packets is shorter and thus the average latency of the SU packets will decrease.For the same arrival probability of the PU packets (α) and the same transmission parameter of SU packets (µ), the higher the traffic load of the SUs (ρ) is, the greater the average latency of the SU packets (σ) will be.This is because the higher traffic load of the SUs is, the greater number of the SU packets will be waiting at the polling instant, so the average latency of the SU packets will increase.For the same arrival probability of the PU packets (α) and the same traffic load of the SUs (ρ), the higher the transmission parameter of SU packets (µ) is, the greater the average latency of the SU packets (σ) will be.It is because the higher transmission parameter of SU packets (µ) implies higher probability parameter (p) to have the same traffic load of the SUs (ρ).
The change trend for the delay jitter of the SU packets (τ ) versus the traffic load of the SUs (ρ) with different arrival probabilities of the PU packets (α) and different transmission parameters of SU packets (µ) is plotted in Fig. 3.In general the delay jitter of the SU packets (τ ) changes with the traffic load of the SUs (ρ).For the same arrival probability of the PU packets (α) and the same transmission parameter of SU packets (µ), the delay jitter of the SU packets (τ ) will increase as the traffic load of the SUs (ρ) increases.The reason is that the larger the traffic load of the SUs is, the greater number of the SU packets will be waiting in the buffer, so the greater the deviation from the mean value of the waiting time of the SU packets will be.For the same traffic load of the SUs (ρ) and the same transmission parameter of SU packets (µ), the delay jitter of the SU packets (τ ) will decrease as the arrival probability of the PU packets (α) increases.This is because the greater the arrival probability of the PU packets is, the more often the SU packets will be interrupted, and the waiting time of the remaining SU packets in the buffer will be reduced, so their waiting time will be closer toward the mean waiting time.For the same arrival probability of the PU packets (α) and the same traffic load of the SUs (ρ), the delay jitter of the SU packets (τ ) will increase as the transmission parameter of SU packets (µ) increases.This is because the greater transmission parameter of SU packets implies higher probability parameter (p) to have the same traffic load of the SUs (ρ).
In Fig. 4 we show the throughput of the SUs (η) versus the traffic load of the SUs (ρ) for different arrival probabilities of the PU packets (α) and different transmission parameters of SU packets (µ).
We can conclude from Fig. 4 that when the traffic load of the SUs (ρ) and the transmission parameters of SU packets (µ) are given, the throughput of the SUs  (η) will decrease along with an increase in the arrival probability of the PU packets (α).The reason is that the interrupted SU packets will be dropped from the system in the proposed spectrum allocation mechanism.The higher the arrival probability of the PU packets is, the more the SU packets will be interrupted and dropped, and therefore the less the throughput will be.For the same arrival probability of the PU packets (α) and the same transmission parameters of SU packets (µ), the throughput of the SUs (η) will increase as the traffic load of the SUs increases (ρ).The intuitive reason is that the greater the traffic load of the SUs is, the more SU packets will be transmitted successfully, thus the throughput will increase.For the same arrival probability of the PU packets (α) and the same traffic load of the SUs (ρ), the throughput of the SUs (η) will increase as transmission parameters of SU packets (µ) increases.The larger transmission parameters of SU packets is, the quickly the SU packets will be transmitted, as a result the throughput will increase.
We examine the impact of the traffic load of the SUs (ρ) on the spectrum switching ratio (β) besides different arrival probabilities of the PU packets (α) and different transmission parameters of SU packets (µ) in Fig. 5.
It can be observed in the figure that besides the same traffic load (ρ) and the same transmission parameter of SU packets (µ), the spectrum switching ratio β will increase as the arrival probability of the PU packets (α) increases.The reason is that the greater the arrival probability of the PU packets is, the higher the possibility is that the transmission of the SU packets will be interrupted, the more frequently the spectrum band will be switched, so the spectrum switching ratio will increase.For the same arrival probability of the PU packets (α) and the same transmission parameter of SU packets (µ), the spectrum switching ratio β will increase as the traffic load of the SUs (ρ) increases.This is because the greater the traffic load of the SUs is, the busier the spectrum band is, so the spectrum switching ratio will increase.When the arrival probability of the PU packets (α) and the traffic load (ρ) are given, the spectrum switching ratio β will decrease as the transmission parameters of SU packets (µ) increase.It is because the greater the transmission parameter of SU packets is, the less busier the spectrum band is, so the spectrum switching ratio will decrease.In Fig. 6 we plot the function of the spectrum utility (γ) versus the traffic load of the SUs (ρ) with respect to different arrival probabilities of the PU packets (α) and different transmission parameters of SU packets (µ).We can see in the figure that for a certain traffic load the SUs (ρ) and certain transmission parameters of SU packets (µ), the spectrum utility (γ) will decrease as the arrival probability of the PU packets (α) increases.The reason is that the greater the arrival probability of the PU packets is, the more often the SU packets will be interrupted.Any interrupted packets will be forced to leave the system, so the spectrum utility will decrease.For the same arrival probability of the PU packets (α) and the same transmission parameters of SU packets (µ), the spectrum utility (γ) will increase as the traffic load of the SUs (ρ) increases.This is because the greater the traffic load of the SUs is, the more SU packets will be transmitted successfully, so the spectrum utility will increase.For the same arrival probability of the PU packets (α) and the same traffic load of the SUs (ρ), the spectrum utility (γ) will increases as the transmission parameter of SU packets (µ) increases.This is because the greater transmission parameters of SU packets implies higher probability parameter (p) to have the same traffic load of the SUs (ρ).4.2.Optimization.We can observe from the above numerical results that the larger the arrival probability of the PU packets is, the lower the average latency of the SU packets is.However the throughput of the SUs will also be lower.On the other hand, the lower the arrival probability of the PU packets is, the greater the throughput of the SUs is, while the average latency of the SU packets will be longer.Therefore we conclude that depending on the arrival probability of the PU packets there is a trade-off between these two performance measures.In order to find an optimum value of arrival probability of the PU packets we build a cost function F (α) as follows: where C 1 and C 2 are the impact factors for the average latency of the SU packets and the throughput of the SUs to the system cost, respectively.
In practice we will set the values of C 1 and C 2 according to the requirements of the application in order to obtain the optimal value of the arrival probability of the PU packets and the corresponding minimum cost.

5.
Conclusions.The way of improving the spectrum utilization in cognitive radio networks is currently one of the most important issues in wireless communication systems.In this paper we addressed the question of ensuring the fair access to the spectrum bands among the SUs.This is achieved by proposing a gated polling based spectrum allocation mechanism for the SUs in CRNs.The appropriate queueing model of this system is the non-zero switchover times gated polling model.We presented a simplified approximate analysis of the system and we derived closedform estimation formulas for several performance measures such as the throughput of the SUs, the average latency and the delay jitter of the SU packets, the spectrum switching ratio and the spectrum utility.We also provided numerical results to validate the analysis and to study the impact of the traffic load of the SUs on the system performance besides different arrival probabilities of the PU packets and different service rates of SU packets.Finally we built up a cost function in order to facilitate an optimal design in terms of the arrival probability of the PU packets.

Figure 1 .
Figure 1.Operation of the CRN system with the gated polling based spectrum allocation mechanism.

η
= E[number of SU packet transmissions during a slot] ×P {successful transmission of SU packet | there is an SU packet transmission}.(22) In stable system E[number of SU packet transmissions during a slot] = E[number of arriving SU packets during a slot],(23)