Performance Analysis of a Communication Failure and Repair Mechanism with Classified Primary Users in CRNs

: Due to the deficiency of radio spectrum resources caused by the progress in technology, cognitive radio networks (CRNs) have made significant progress. CRNs have two types of users, namely, primary users (PUs) and secondary users (SUs). Considering that PUs have a higher priority and diversified data transmission requirements, this study divides PUs into two levels, namely, PU1s with a higher priority and PU2s with a lower priority. On the other hand, the occurrence of failures is inevitable in CRNs, which affects the data transmission of users. In this paper, combined with an adjustable PU packets transmission rate mechanism, a communication failure and repair mechanism with classified PUs based on the single-channel CRNs is proposed, and different pre-emption principles are set according to different system states. A queueing model is established and analyzed with a Markov chain, the performance index expressions that need targeted research are listed, numerical experiments are conducted, and the system performance change trends are obtained. The comparison experiment shows that the proposed communication failure and repair mechanism with classified PUs can improve the throughput of PU1 packets and reduce the blocking rate of PU1 packets compared with the conventional communication failure and repair mechanisms with unclassified PUs.


Introduction
Wireless communication technology has entered the stage of rapid development, becoming the fastest-developing and most widely used technology in information communication in recent years.Current networks require communication technology to expand capacity, speed up data transmission and reduce latency further [1].Cognitive radio (CR) technology has a promising future, which supplies lower delay and more agile services [2], and it is an important research technique to meet the above needs.Achieving a higher spectrum utilization and addressing the spectrum shortage are essential goals of resource allocation in cognitive radio networks (CRNs) [3][4][5].In CRNs, secondary users (SUs) possessing a lower priority can opportunistically occupy some spectrums that primary users (PUs) possessing a higher priority have not used for the time being [6,7].
Hardware failure, software failure, or inherent characteristics, such as fading or shadowing, may lead to channel failure, resulting in the degradation of CRN performance [8].A centralized channel allocation strategy is common in CRNs, but it needs to be more robust when it encounters things like spectrum server failures [9,10].In addition, network nodes usually depend on each other to transmit data in multi-hop CRNs, and connectivity is affected when nodes run out of power [11,12].The systems mentioned above may be affected in various circumstances collectively referred to as communication failure.The occurrence of communication failures has a momentous influence on CRNs, so we ought to conduct in-depth research on this area.
Communication failure has an essential influence on the CRN system performance.In [13], a continuous-time Markov chain (CTMC) model was designed, and all the performance metrics under different PUs' and SUs' arrival and channel failure rates were estimated.In [14], under multi-channel malfunction and PUs' arrival rates, a model was formulated to evaluate the network performance.In [15], the authors described the most common failure sources and offered a failure classification program for wireless networks using CRs, and again emphasized that the dominating requirement for an SU is to respect the priority of PUs.From [13][14][15], we can find that failure rate is an essential variable in the performance evaluation of CRN models, and most studies on CRNs have focused on the priority between PUs and SUs, but priorities within users of the same category are not considered.The same type of users also have different transmission needs [16], such as different requirements for real-time performance.Therefore, to reduce the impact of communication failure on users with higher priorities, it is worth considering the classification of users and arranging a reasonable preemption principle.
Moreover, spectrum sensing and spectrum allocation are hot topics in CRNs.CRNs require reliable cognitive algorithms to detect signals from licensed primary radios and find unexploited spectrum holes to avoid harmful interference [17].However, we note that the focus of this paper is not spectrum sensing, but spectrum allocation, that is, how to design a reasonable and efficient spectrum allocation strategy to effectively use spectrum resources under the background of communication failure and repair.
Considering the digital characteristic of data transmission, we use a discrete-time queueing model to analyze the proposed mechanism.The main mathematical tool of discrete-time queueing analysis is Markov chain, which refers to a random process in the state space that goes through a transition from one state to another, in which the probability of state transition at a certain moment depends only on its previous state.Markov chain is conceptually very intuitive and easy to implement.In our paper, we apply the widely used Markov chain for model analysis since we are concerned with the state transition of the system.
In summary, the purpose of this study is as follows: 1. Explore the impact of communication failure and repair on the system.2. Considering the transmission needs of different PUs, establish a reasonable channel allocation mechanism to improve the network performance of the system.3. Find a suitable model framework to model the proposed mechanism and express the obtained numerical results clearly.
These research objectives can provide a foundation for the overall study and provide a framework for evaluating the results.
In this paper, we propose a communication failure and repair mechanism with classified PUs to improve the throughput of PU packets with higher transmission requirements and reduce the influence of communication failure on CRN systems.On the basis of different requirements of real-time invisibility, PUs are divided into two levels: PU1s and PU2s.The real-time invisibility of PU1s is higher than that of PU2s.Different preemption rules are set according to whether the system is faulty.Our primary research results are as follows: 1. Communication failure is a problem that cannot be ignored in current network communication.This paper considers network communication failure and repair to explore their impact on system performance.2. To meet the diversified data transmission requirements of PUs, a communication failure and repair mechanism with classified PUs in CRNs is proposed.3. Through the analysis of the proposed mechanism, a discrete-time queueing model and a four-dimensional Markov chain (4DMC) are established to evaluate the proposed mechanism.The steady-state distribution and important performance indexes of the system are derived.4. The critical performance indexes are analyzed by numerical experiments, and some indicators of the proposed and traditional mechanisms are contrasted and analyzed.
Other sections of this article are listed hereafter.Section 2 records the preliminary preparation for the study.The proposed mechanism and the corresponding modeling process are introduced in detail in Section 3. In Section 4, the performance indicator expressions of the proposed mechanism are listed and explained accordingly.The changes in each performance index are described by numerical experiments, and the comparison curves of important performance indexes between the proposed mechanism and the traditional mechanism are described in Section 5. Section 6 presents a summary of the full text.

Related Works
In the current research on channel allocation strategies in CRNs, the internal classification of SUs is often considered.In [18], a channel allocation strategy was proposed to classify SUs according to real-time requirements, in which the priority of SU1 packets was higher than SU2 packets, and the performance index analysis and system behavior optimization were carried out for SU2.In [19], SUs were divided into two levels according to delay sensitivity, and two different active spectrum switching strategies were derived for two types of SUs.In [20], SUs were divided into real-time traffic SU1s with high priority and non-real-time traffic SU2s with low priority to offer better performance for SU2s without influencing SU1s.From [18][19][20], we can find that it is widespread to classify SUs, but in the literature, scholars rarely classify PUs.When a CRN system is faulty, the transmission success rate of packets generated by users is significantly reduced.In this case, PUs with higher real-time requirements should be given priority.Therefore, it is necessary to consider the classification of PUs.
In conventional CRNs, channel preemption usually occurs between PUs and SUs.Similarly, the preemption principle between different levels of PUs should be considered after the hierarchical processing of PUs.There are two standard methods to deal with it: complete preemption and non-preemption [21,22].When considering the internal priority of the SUs, complete preemption means that the channel of the SU possessing a lower priority can be preempted by the SU possessing a higher priority, and the principle of non-preemption means that the data transmission of the SU possessing a lower priority cannot be interrupted by the SU possessing a higher priority [23].In [24], the authors found that complete preemption of PUs to SUs could reduce the waiting time of PUs, and full non-preemption of PUs to SUs could reduce the waiting time of SUs.In [25], to diminish the delay time of SUs, the authors put forward a hybrid preemptive/non-preemptive resume priority model.From [24,25], we conclude that a mix of complete preemption and non-preemption between users should be considered, depending on the different scenarios.Therefore, we can set different preemption rules to apply to PUs of different levels.When the system state is normal, PUs of different levels are equal and do not preempt each other's channel.When the system is affected by the failure, to ensure the data transmission of PUs with high real-time requirements, PUs who are with high real-time requirements can interrupt the data transmission of PUs who are with low real-time requirements.Moreover, we note that audio, video, or real-time services have high real-time requirements, so we can think of them as the packets with the highest priority.Due to the high priority, their real-time service transmission needs can be guaranteed.
A CRN system can break down for various reasons, and many researchers have studied the problem according to the wholly stopped service area of the server.On account of the complicacy of modern operating systems, system failure may not terminate service entirely to users [26].In [27], a partially failed and interruptible setup/shutdown strategy was proposed, and the system maintained a low service in the case of failure.In [28], the authors studied the equilibrium strategies in the almost observable and almost unobservable M/M/1 queues with partial failure, and the service rate in partial failure states was lower than the standard service rate.In [29], the equilibrium behavior of customers in Markov queues with setup times and partial failure was considered.When the system was faulty, services were provided at a low speed, and no new users were received.In [30], the authors assumed that the PU packets' transmission would be maintained at a low speed under the condition of system failure and would be resumed at a high speed after the failure was repaired.According to the experimental results in [27][28][29][30], under the condition that the system does not entirely collapse but partially fails, it is beneficial to improve the system performance for the system to maintain a low speed to provide services to users.In refining our strategy, we are able to provide this service for PU packets with a higher priority, that is, to continue receiving assistance in the event of system failure.
Moreover, queueing theory is often used to solve problems in CRNs.In [31], the authors introduced a queueing method that considered server outages to analyze the performance of the CRN system under periodic failures and outages.In [32], a simulation of a queueing model for evaluating the performance and reliability of CRNs is discussed.In [33], a hybrid PRP/NPRP M/G/1 queueing model based on interruption priority was proposed to describe the spectrum usage in the CRN with multi-level SUs and multiple switches.Queueing theory was used to analyze system performance, user grading, and failure interruption problems in CRNs.In addition, discrete-time queueing theory is in line with the development characteristics of today's digital age, so we establish and dissect a discrete-time queueing model to perform the system performance assessment in this paper.

Communication Failure and Repair Mechanism with Classified PUs
In a single-channel CRN system, there are three types of users: one PU1, one PU2, and one SU, where PU1 has a higher priority than PU2, and SU has the lowest priority.As the source of data, each type of user generates one corresponding packet at most in each slot.In the transmission process, the central controller is responsible for spectrum scheduling.Due to the low priority of SU packets, setting a cache with limited capacity for SU packets can appropriately reduce the occurrence of SU packets leaving the system.PU packets require high real-time performance, so no cache is set for them.We define the system as being in a normal state if there is no failure.If a system failure occurs, the system enters a failure state.To balance the influence of the existence of the failure on the two types of PU packets, we set the preemption principle based on the system state.No preemption behavior will exist between PU1 and PU2 packets in the system's normal state.In the failure state of the system, PU1 packets can preempt PU2 packets' right to use the channel.In addition, both PU1 and PU2 packets can preempt SU packets' channel access right whatever the system's state is.
Once a failure happens, SU packets' transmission is interrupted.While PU1 and PU2 packets have higher real-time requirements, we set them to be transmitted at a low speed when the system is in a failure state to effectively enhance the throughput of PU1 and PU2 packets within a unit time slot.
Based on the proposed communication failure and repair mechanism, the system actions for the three types of packets are described as follows: For PU1 packets, when there are no other PU packets in the channel, the newly arrived PU1 packet can directly enter the channel.If an SU packet exists in the channel, the newly arrived PU1 packet will preempt the channel used by the SU packet and the SU packet will enter into the cache to wait.When the system state is normal, and there is a PU1 packet or a PU2 packet in the channel, the freshly arrived PU1 packets can only leave the system.If the system state is failure, when the channel contains a PU1 packet, and the freshly arrived PU1 packet leaves the system; moreover, when the channel includes a PU2 packet, the channel used by the PU2 packet is preempted by the newly arrived PU1 packet and the PU2 packet leaves the system.A PU1 packet entering the channel is transmitted at a low speed if the system is in a failure state and at a high speed if the system state is normal.
For PU2 packets, when there are no other PU packets in the channel, the newly arrived PU2 packet can directly enter the channel, and if there are other PU packets in the channel, the newly arrived PU2 packet can only leave the system.The channel used by the SU packet is snatched by the newly arrived PU2 packet if an SU packet exists in the channel, and the SU packet enters the cache for waiting.A PU2 packet entering the channel is transmitted at a low speed if the system is in a failure state and at a high speed if the system state is normal.
For SU packets, if the system state is failure, the newly arrived SU packet directly enters the cache to wait, and the SU packet being transmitted is interrupted and enters the cache.If the system state is normal, the newly arrived SU packet enters the channel for transmission if there are no other packets in the channel.If there are other packets in the channel, the newly arrived SU packet enters the cache and waits.When the cache is full, the interrupted or newly arrived SU packets cannot enter the cache.When the channel is empty and the system state is normal, the SU packet at the head of the cache queue can enter the channel for further transmission.

Model Building
We establish an early arrival discrete-time queueing model for a single service desk according to the proposed strategy.The service desk is an abstraction of the channel, and the user packets are equivalent to the customers in queueing theory.The entire timeline is separated into time slots of the same length.The slot boundary points are t 1 , t 2 , • • • , t n , and at most one user packet can be transmitted in the channel in each time slot.In addition, the size of the cache that holds SU packets is k.
The probability that the system state changes from normal to failure due to the occurrence of failure is f ( f = 1 − f , 0 < f < 1), and f represents the communication failure rate.The probability that the system returns from the failure state to the normal state through the repair process is r (r = 1 − r, 0 < r < 1), and r represents the system repair rate.All user packets' arrival intervals and transmission time also conform to the geometric distribution.The arrival rate of PU1 packets is α 11 (ᾱ 11 = 1 − α 11 , 0 < α 11 < 1), the arrival rate of PU2 packets is α 12 (ᾱ 12 = 1 − α 12 , 0 < α 12 < 1), and the arrival rate of SU packets is α 2 (ᾱ 2 = 1 − α 2 , 0 < α 2 < 1).When the system state is normal, the transmission rates of PU1 and PU2 packets are β 11 ( β11 = 1 − β 11 , 0 < β 11 < 1) and β 12 ( β12 = 1 − β 12 , 0 < β 12 < 1), and the transmission rate of SU packets is . When the system is in a failure state, the transmission rates of PU1 and PU2 packets are At time t + , the number of all packets is U t , in which there are V t packets of PU1 and W t packets of PU2, and the system state is O t .Then, {(U t , V t , W t , O t ) : t ≥ 0} composes a four-dimensional Markov chain (4DMC).The system's state space is defined as E.
The state (l, m, n, s) in Equation ( 1) indicates a total of l user packets in the system at present, including m PU1 packets and n PU2 packets.In addition, the system state is determined by s.If s is 1, the system state is failure; if s is 0, the system state is normal.

Model Analysis
To simplify the matrices, we simplify some formulas.The concrete representation of some symbols in the below matrices is as follows: The system's total number of user packets varies from 0 to k + 1, where k (k > 1) is the cache capacity.The total state transition matrix H is shown in Equation (3), and its submatrix H a,b is shown in Equations ( 4)- (15), where H a,b represents the one-step state transition matrix of the total user packets from a to b.

Performance Metrics
The performance indicators covered in this paper are PU1 packets' blocking rate and throughput; PU2 packets' blocking rate, loss rate, and throughput; and SU packets' blocking rate, loss rate, and throughput.Blocking rate, loss rate, and throughput reflect the loss and successful transmission of packets.We note that other indicators in network analysis, such as average queue length, average delay, and interruption rate, cannot visually represent the "in and out" of the system.Therefore, we focus on blocking rate, loss rate, and throughput to show the performance of the system in this paper.

PU1 Packets' Performance Metrics
The amount of PU1 packets that is blocked and leave per time slot is defined as PU1 packets' blocking rate B P1 .
The amount of PU1 packets with completed transmission per time slot is defined as PU1 packets' throughput T P1 .

PU2 Packets' Performance Metrics
The amount of PU2 packets that is blocked and leave per time slot is defined as PU2 packets' blocking rate B P2 .
The amount of PU2 packets that leave due to interrupted transmission per time slot is defined as PU2 packets' loss rate L P2 .
The amount of PU2 packets with completed transmission per time slot is defined as PU2 packets' throughput T P2 .

SU Packets' Performance Metrics
The amount of SU packets that is blocked and leave per time slot is defined as SU packets' blocking rate B S .
The amount of SU packets that leaves because they are interrupted and cannot enter into the cache per time slot is defined as SU packets' loss rate L S .L S = ψ k+1,0,0,0 ( f ᾱ11 ᾱ12 + ᾱ11 α 12 β2 + α 11 β2 ) The amount of SU packets with completed transmission per time slot is defined as SU packets' throughput T S .

Numerical Results and Discussion
To better describe the changes in various performance indicators along with some parameters, we design numerical experiments through MATLAB to describe the changing trend in the form of broken lines, and we elaborate on the problems reflected in the curves.

Performance Analysis
We describe the performance of PU1, PU2, and SU packets in different network environments.Table 1 shows the parameters with fixed values.As shown in Figure 1, when the communication failure rate f increases, PU1 packets' blocking rate B P1 increases while throughput T P1 decreases.When the repair rate r increases, B P1 decreases while T P1 increases.When f increases, the possibility of the system state being failure increases, so the time PU1 packets are present in the channel increases due to the low-speed transmission of PU1 packets in the failure state.Therefore, the probability of newly arrived PU1 packets being blocked increases, and the number of transmitted PU1 packets decreases in unit time correspondingly.When r increases, the possibility of the system maintaining a normal state increases, the probability of PU1 packets being transmitted at a high speed increases, which reduces the transmission time, and the chance of the channel being idle to meet those newly arrived PU1 packets increases; therefore, less blocking occurs and the number of transmitted PU1 packets increases.
From Figure 1, we can find that as PU1 packets' arrival rate α 11 increases, PU1 packets' blocking rate B P1 and throughput T P1 increases simultaneously.As PU2 packets' arrival rate α 12 increases, B P1 increases, and T P1 decreases.Considering the priority of PU1 packets is higher, as α 11 increases, the probability that PU1 packets are present in the channel increases.Therefore, the amount of PU1 packets with completed transmission rises.Meanwhile, there can only be at most one packet in the channel, so the probability of PU1 packets being blocked also increases.When α 12 increases, the probability of PU2 packets entering the channel increases.However, in the system's normal state, when PU2 packets are being transmitted in the channel, PU1 packets cannot t preempt the channel, so the probability that PU1 packets are blocked increases, and the number of PU1 packets with completed transmissions decreases accordingly.

Performance Analysis of PU2 Packets
Figure 2 depicts the variation trends of PU2 packets' blocking rate B P2 , loss rate L P2 , and throughput T P2 under the proposed communication failure and repair mechanism.As shown in Figure 2, if the communication failure rate f rises, PU2 packets' blocking rate B P2 and loss rate L P2 increase while throughput T P2 decreases.When the repair rate r increases, B P2 and L P2 decrease while T P2 increases.When f increases, the probability of the system state being failure rises, and the low-speed transmission of PU packets reduces the channel's idle time, so the probability of the newly arrived PU2 packets being blocked increases.If the system state fails, the channel preemption behavior of PU1 packets to PU2 packets becomes frequent, and the probability of PU2 packets being lost increases accordingly.Due to the increased blocking and loss rates, the amount of PU2 packets that is transmitted completely decreases.When r increases, the possibility of the system maintaining a normal state increases, and the high-speed transmission of PU1 and PU2 packets makes the channel more free to meet the newly arrived PU2 packets, so the blocking rate reduces.If the system state is normal and PU1 packets will not preempt the channel of PU2 packets, the probability of PU2 packets being preempted decreases.Therefore, the probability of PU2 packets being lost decreases, and more PU2 packets are transmitted successfully.
From Figure 2, we can find that as PU1 packets' arrival rate α 11 increases, PU2 packets' blocking rate B P2 and loss rate L P2 increase while throughput T P2 decreases.As PU2 packets' arrival rate α 12 increases, B P2 , L P2 , and T P2 all increase.When α 11 increases, the probability that the channels are occupied by PU1 packets increases, so the probability that those newly arrived PU2 packets are unable to enter into the channel increases.Meanwhile, when the system is in the failure state, the preemption behavior of PU1 packets to PU2 packets increases, resulting in more lost PU2 packets, and the amount of PU2 packets transmitted completely decreases.Because at most one packet can exist in the channel at a time, when α 12 increases, the number of PU2 packets blocked grows, and more PU2 packets entering the channel encounter PU1 packets and lose channel access right; therefore, B P2 increases.According to our parameter setting, α 12 has a larger increase compared with B P2 and L P2 , so after performance calculation, T P2 also shows an increasing trend.As shown in Figure 3, SU packets' blocking rate B S and loss rate L S increase while throughput T S decreases if the communication failure rate f is enhanced.When the repair rate r increases, B S and L S decrease while T S increases.As f increases, more SU packets enter the cache after their transmission is suspended by the communication failure.As a result, the cache space decreases.In that case, the newly arrived SU packets have less chance to enter the cache and the blocking rate increases.When there is no free space in the cache, SU packets can only leave the system if they are interrupted.Therefore, the loss rate also rises, and the amount of SU packets with completed transmission per unit time decreases accordingly.When r increases, the probability of the system state being normal increases, the probability of SU packets being transmitted grows, and the probability of SU packets being blocked and leaving decreases.The probability of SU packets being interrupted due to communication failure decreases, and the probability of being forced to leave the system because of interruption also decreases correspondingly; thus, the amount of SU packets with finished transmission increases.
From Figure 3, we can observe that as PU1 packets' arrival rate α 11 grows or PU2 packets' arrival rate α 12 grows, SU packets' blocking rate B S and loss rate L S increase while throughput T S decreases.With the increase in α 11 or α 12 , the probability that PU packets are present in the channel rises, and so does the probability of SU packets' transmission being interrupted.Therefore, the probability of SU packets being blocked and lost rises, so the number of SU packets transmitted completely reduces.

System Performance Comparison
Regarding the two performance indexes of PU1 packets' throughput T P1 and blocking rate B P1 , we designed numerical experiments to make curve comparisons between the proposed failure and repair mechanism with classified PUs and the traditional failure and repair mechanism with unclassified PUs.In the traditional mechanism, unclassified PUs mean that PU packets generated by PUs with different demands are transmitted equally.
There is no mutual preemption in different system states, and they have the same rights.The parameters of each numerical experiment are displayed in Table 2.By observing Figure 4, we can find that under both of the two mechanisms, for PU1 packets, the throughput decreases and the blocking rate increases while the communication failure rate increases, but our proposed mechanism can enhance the throughput of PU1 packets and reduce the blocking rate of PU1 packets compared to the mechanism with unclassified PUs.So, prioritized PU packets and different preemption principles make PU1 packets enjoy certain privileges and meet higher transmission requirements.
According to Figure 4, when the normal transmission rate of PU1 packets β 11 increases, PU1 packets' throughput T P1 increases and blocking rate B P1 decreases.With the increase in β 11 , the transmission time of newly arrived PU1 packets decreases, the number of PU1 packets with completed transmission increases, and the number of blocked PU1 packets decreases.When the normal transmission rate of PU2 packets β 12 increases, T P1 also increases and B P1 decreases.When β 12 increases, PU2 packets take less time to occupy the channel and PU1 packets have more chances to enter the channel.Therefore, the number of PU1 packets with completed transmission increases and the number of blocked PU1 packets decreases.

Discussion
Communication failure is a matter that cannot be ignored in data transmission.It has an important impact on the performance of the network.In order to minimize the negative impact of communication faults on network performance, a reasonable channel allocation mechanism is necessary.
In this section, we describe the performance trends of PU1 packets, PU2 packets, and SU packets in different network environments under the background of communication failure and repair based on the proposed channel allocation mechanism.Figures 1-3 could be summarized as follows.As the communication failure rate increased, the blocking rate of PU1 packets grew and the throughput decreased, and the blocking rates and loss rates of PU2 and SU packets increased while the throughput dropped.With the increase in repair rate, the above performance variation trends were opposite to those caused by the rise in the communication failure rate.At the same time, with the increase in PU1 or PU2 packets' arrival rate, the blocking rates and loss rates involved in the three types of packets (the loss rate not involving PU1 packets) increased.When the arrival rate of one type of packet increased, the throughput of the corresponding type of packet increased, while the throughput of the other types of packet decreased.The performances of these three types of packets were analyzed in detail and the possible reasons were explained, which helped us to better explore the impact of communication failure and repair on the system, as well as the difference in system performance in different network environments.
In addition, we compared the communication failure and repair mechanism with classified PUs proposed in this paper with that with unclassified PUs. Figure 4 demonstrates that the proposed mechanism improved the throughput and reduced the blocking rate of PU1 packets, which proved the effectiveness of the proposed mechanism for real-time services.

Conclusions
In CRNs, considering communication failure and repair, to maximize system performance and meet the different transmission requirements of PUs, we propose a communication failure and repair mechanism with classified PUs to minimize the impact of communication failure on the transmission of PU packets with a higher priority.We divided PUs into two levels and set different preemption principles according to the system state.In addition, PU1 and PU2 packets can be transmitted at a low speed under the failure state of the system.We built an early-arrival discrete-time queueing model and solved the performance expressions of the system through the system's steady-state analysis.The curve characterization and performance analysis of some performance indexes were carried out by designing numerical experiments.When the communication failure rate increased, the blocking rates of the three types of packets increased, the throughput fell, and the loss rates of PU2 and SU packets increased.As the repair rate grew, the performance change trends were opposite to those caused by the rise in the communication failure rate.When PU1 packets or PU2 packets' arrival rate increased, the blocking rates of the three types of packets rose, and the loss rates of PU2 and SU packets grew.Meanwhile, the throughput of the corresponding type of packets increased, while the throughput of the other two types of packets decreased.By comparing the proposed mechanism with the traditional mechanism, we discovered that the proposed mechanism could more effectively meet the different transmission requirements of PUs and improve the performance of PU1 packets.In summary, the experimental results reflected the performance variation trends of the proposed communication failure and repair mechanism with classified PUs in different network environments and demonstrated its effectiveness.
The limitations of this study and future work are summarized as follows: 1.After the communication failure and repair mechanism with classified PUs is presented, a discrete-time queueing model is established and analyzed.However, due to the space limitation and the possible cumbersome statements, we only list the matrix and submatrices of the one-step state transition probability of the system and do not analyze the model in detail.2. In the comparison experiments, we only compare the performance between the proposed communication failure and repair mechanism with classified PUs and that with unclassified PUs.It can be seen from the performance comparison diagrams that the proposed mechanism can effectively improve the performance of PU1 packets.However, we do not compare the proposed mechanism with existing methods, such as

Figure 1 .
Figure 1.The performance change trends of PU1 packets: (a) the change trend in B P1 ; (b) the change trend in T P1 .

Figure 2 .
Figure 2. The performance change trends of PU2 packets: (a) the change trend in B P2 ; (b) the change trend in L P2 ; (c) the change trend in T P2 .

5. 1 . 3 .
Figure 3 depicts the variation trends of SU packets' blocking rate B S , loss rate L S , and throughput T S under the proposed communication failure and repair mechanism. 0

Figure 3 .
Figure 3.The performance change trends of SU packets: (a) the change trend in B S ; (b) the change trend in L S ; (c) the change trend in T S .

Figure 4 .
Figure 4. Comparison of performance change trends of PU1 packets under the two mechanisms: (a) performance comparison in T P1 ; (b) performance comparison in B P1 .

Table 1 .
The parameters with fixed values in the performance analysis experiments.The size k of the cache that holds SU packets 10 5.1.1.Performance Analysis of PU1 Packets Figure 1 depicts the trends of PU1 packets' blocking rate B P1 and throughput T P1 under the proposed communication failure and repair mechanism.

Table 2 .
The parameters with fixed values in the comparison experiment.The size k of the cache that holds SU packets 10 Figure 4 reflects the comparison results of the changes in PU1 packets' throughput and blocking rate with the communication failure rate under the two mechanisms.