Abstract
The complexity of the channel condition in the Internet of vehicles (IoV) may increase the bit error rate (BER) of the intelligent vehicle terminals, resulting in data transmission failures or errors. Therefore, it is necessary to improve the performance of communication protocols under error-prone channel conditions. This article investigates the influence of the access categories’ (ACs) performance with channel errors by using four to cause service differentiation based on the enhanced distributed channel access (EDCA) mechanism of the IEEE 802.11p. To address the error-prone characteristics of the channel and unsaturated traffic conditions, a three-dimensional Markov model is developed first, followed by an analysis of the characteristics and mutual transition probabilities of the seven classes of states in the model, and then, the steady-state equations of the system are developed to derive the steady-state distribution to study system performance. The model considers the backoff phase, the freezing of the backoff counter, the retransmission limit, the probability of collisions occurring, the size of the maximum and minimum contention window, and the number of interframe intervals. These parameters are chosen to meet the requirements for the protocol to operate, while also preventing overestimation of throughput and avoiding having packets being served all the time. We derive expressions for the throughput and delay of under the conditions of error channels and unsaturated traffic. The impact of channel errors on the throughput and delay of is evaluated by numerical simulation. Numerical results show that too many stations in the system will increase the average access delay and decrease throughput. The increase in BER will seriously decrease the performance of high-priority . The throughput of the is also modeled to vary with frame length and BER, and the variation curves of the optimal frame lengths for and were obtained.
1. Introduction
As one of the main tools serving vehicle communication and an important component of intelligent transport systems, the vehicular ad hoc network (VANET) [1] has been widely applied in applications related to traffic, vehicles, and pedestrians on the roads. Vehicle-to-everything (V2X) refers to the interaction of information between vehicles and everything in the outside world, including the communication scenarios about vehicle-to-vehicle (V2V), vehicle-to-pedestrian (V2P), vehicle-to-infrastructure (V2I), and vehicle-to-network (V2N). To improve the communication capability of V2X [2], IEEE 802.11p [3] was introduced as a new paradigm into the media access control (MAC) layer and physical layer in 2010.
IEEE 802.11p inherits the enhanced distributed channel access (EDCA) mechanism of the IEEE 802.11e protocol [4], which improves the quality of service (QoS) of the system by setting different parameters in the EDCA mechanism. The EDCA mechanism introduces differentiated services by exploiting the priority of the four access categories () during channel access. The purpose of prioritizing is achieved by setting different competition parameters for each access category to improve the quality and performance of communications [5] in the Internet of vehicles (IoV). These contention parameters are also efficient tools for analytical modeling and studying system performance metrics, including the values of the maximum and minimum contention windows and the number of arbitration interframe intervals.
Under normal circumstances, a collision may occur in an IoV system if more than one vehicle starts transmitting packets within the same time slot. In turn, the probability of packet collisions increases the probability of transmission errors. At the same time, transmission errors can also become apparent due to complex conditions such as path loss in the wireless channel, thermal noise, channel fading, or interference from other radio sources in the vehicle terminal. Therefore, it is necessary to study the impact of errors in data frames on the throughput and delay of the system. However, in recent years, a lot of research works [6–8] have focused on modeling and analyzing the IEEE 802.11 standard under an ideal channel (without error), by estimating and improving its performance such as throughput and delay. On the contrary, most of the existing works do not consider channel error rates and confuse data frame collisions with bit errors. In fact, data collisions and bit errors are essentially two different concepts and both cause the transmission error of data frames.
Therefore, in order to solve the problem of confusion between data frame collisions and bit error occurring, based on the EDCA mechanism of IEEE 802.11p, we intend to improve on the model proposed in [6]. Under the condition of unsaturated and error-prone channels, the quality of service of different is analyzed by establishing a Markov model of the system operation. The reasons for considering unsaturated traffic in the model are as follows: (i) the actual network is unsaturated, (ii) to take into account the interarrival time and burstiness in the network, and (iii) saturated conditions mostly make the network unstable. In addition, in the Gaussian wireless error channel, it is assumed that the bit error rate (BER) is the same for each data frame, so the error probability of a data frame is determined only by the length of the data frame and the BER [9, 10].
As this article considers unsaturated traffic conditions, an initial state is added when modeling. In order to avoid confusing the collisions in data frames with bit errors, the two concepts are considered separately. That is, after the data frame enters the queue when transmission begins, the station first determines whether the data frame has collided, and if so, it will backoff; otherwise, it will move to the attempted transmission state. Then, in the attempted transmission state, it determines whether an error has occurred in the data frame, and if so, it will backoff; otherwise, it will move to the successful transmission state. Consequently, a three-dimensional Markov model is established based on the basic states of the idle state, backoff state, attempted transmission state, and delay state to analyze the state transition probability of the system as well as the steady-state distribution. The parameters such as transition probability, collision probability, and channel busy probability of are then obtained based on the state transition probability and the steady-state distribution to analyze the performance of in terms of throughput and delay.
The remainder of the article is organized as follows: Section 2 provides related work of literature review in this area. Section 3 describes the model of the established IEEE 802.11p EDCA mechanism. Section 4 analyzes system performance. The numerical results of the system model are compared, discussed, and analyzed in section 5. Section 6 concludes this article.
2. Related Work
In recent years, the IEEE 802.11p protocol has been widely used on the IoV system, making the relationship between road traffic, pedestrians, and vehicles harmonious and orderly. This is due to extensive work that has been conducted to study and analyze the performance of IEEE 802.11p. In [6], the throughput and delay of the EDCA mechanism were investigated using the three-dimensional Markov model, but only two access categories and were used, thus reducing the internal collision probability of the station considerably and making the performance analysis less accurate. Unlike most literature, Zheng and Wu [11] not only constructed a two-dimensional Markov model to analyze delay and throughput performance but also established a one-dimensional Markov model to simulate the competition period of queues and analyzed the performance of the protocol under saturated and unsaturated conditions. Similar to [11], two-dimensional Markov and one-dimensional Markov models were presented in [12] to calculate the transition probability and collision probability, respectively. Both of its models considered transmission opportunities not utilized by IEEE 802.11p to improve the performance of infotainment applications. In [8], the authors considered the characteristics of the EDCA mechanism under saturation conditions, such as different competition windows for each access class, internal collisions of stations, and arbitration interframe space (AIFS). In [7], Cao et al. expanded the model of [8] by adding a carrier listening process to make the analysis results more accurate. However, the abovementioned literature was carried out in the ideal channel.
In real radio channels, it is inevitable that vehicle terminals will experience error codes due to fading, noise, path loss, and congestion [13], so studying protocol performance under nonideal channels becomes essential. The authors of [9, 14–17] analyzed the throughput and delay of the system under the error-prone channel. In [15], the authors analyzed the relationship between the probability of error and the capture effect under Rayleigh fading conditions and verified that the proposed IEEE 802.11 DCF mechanism model was more suitable for the actual situation than the results of the simulation by establishing a two-dimensional Markov chain model. In [14], Harkat et al. considered all the parameter effects of IEEE 802.11p, compared the parameter changes of the four access categories, analyzed the probability of internal and external collisions between stations, and obtained that the use of small data frames in saturated traffic can effectively improve system performance. Unlike other literature that does not take into account the time it takes for a node to wait for an acknowledgment frame after transmitting packets until a timeout occurs, the authors in [16] constructed a four-dimensional Markov model based on IEEE 802.15.6 that considered the wait time after sending a packet, which also proved that this model is more accurate. However, the aforementioned literature was carried out under saturation conditions.
At the same time, some related work was conducted under unsaturated conditions and error-prone channels. The authors in [14] encrypted service application data of vehicular ad hoc networks based on the data steganography method of nonorthogonal multiaccess bit padding on the physical layer of the IEEE 802.11p protocol, to achieve data confidentiality. However, the authors only considered an active station in the EDCA mechanism. In [17], the authors established a three-dimensional Markov model based on the IEEE 802.15.6 protocol under unsaturated and error-prone conditions, showing that the element that improves network performance is the selection of different access lengths for users of different priorities. However, eight different priorities increase the complexity of the calculation.
In addition, the IEEE 802.11p protocol supports multichannel input. In [10, 18], the authors both modeled and analyzed protocol performance under the nonideal channel and unsaturated conditions using the parameter requirements of the EDCA mechanism. The authors in [10] analyzed the performance of service and security applications under multichannel switching. However, only two types of active are considered and no other are applied. In [18], the authors proposed an adaptive multichannel allocation coordination scheme that addresses the IEEE 1609.4 protocol [19] for differentiating and autonomously switching security and service channels. However, only security data and service data are modeled in the literature, and security data have a higher priority. In [20], Peng et al. studied the performance effects of multirow communication based on the distributed coordination function of IEEE 802.11p, but their Markov model was based on the models of [21, 22], without taking into account short retries, packet retransmission limits, the backoff counterfreezing, and the problem of having only one active station. However, expanding the access category to four is relatively difficult.
In this article, we model and analyze the performance of the IEEE 802.11p protocol EDCA mechanism under unsaturated conditions with the nonideal channel. We consider some parameters that affect the performance of the IEEE 802.11p protocol, such as limiting the number of retransmissions, freezing of the backoff counter when the channel is busy, the value of the maximum and the minimum contention window, interframe interval of arbitration frames, the backoff period, the external collision between frames, the virtual internal collision, and channel transmission errors. We develop a three-dimensional Markov chain model for the four of the EDCA mechanism to obtain the steady distribution of the , the transition probability, and the probability of collisions and errors occurring. This allows us to analyze the impact of channel error rates and unsaturated conditions on system performance. In this case, an initial state is added to accommodate unsaturated traffic environments. When a new packet arrives in the queue, the channel is first detected for idleness and if the channel is idle and no collisions have occurred, the packet will attempt transmission. If the channel is busy or if a packet collision occurs, the packet will move to a backoff state of a randomly selected contention window from the backoff phase. We also extend the packet transmission state in the event of an error in the channel so that when the packet reaches the next state after the attempted transmission, the station detects whether the packet has bit errors. If no error occurs, the transmission will be successful. Otherwise, the packet enters a backoff state. The main contributions are summarized as follows:(1)We discuss the collision in a data frame separately from bit errors, after the data frame has access to the channel, the station first detects whether a collision has occurred in the channel and then detects whether bit errors have occurred in order to avoid confusing data frame collisions with bit errors and to make the system model more accurate.(2)According to the parameters of the IEEE 802.11p protocol, we set the status of the idle state, backoff state, attempted transmission state, and delay of data transmission. A three-dimensional Markov model of the system operation is designed based on these states, and the steady distribution of the system, as well as the transition probabilities are obtained by discussing the state transition probabilities of the system.(3)We derive expressions for the throughput and delay of under the conditions of error channels and unsaturated traffic by analyzing the steady distribution, transition probability, and transmission time. The impact of channel errors on the throughput and delay of is evaluated by numerical simulation and comparison.(4)We demonstrate through numerical results that BER has a serious impact on the throughput and delay of . Therefore, it is necessary to consider channel errors in real life. The numerical results demonstrate that the optimal length of data frame transmission varies with the channel error bit rate. Finally, the peak throughput corresponding to the optimal frame length for any BER, i.e., the curve of the maximum throughput versus the optimal frame length and BER is obtained for high-priority on the space-curved surface of a 3D coordinate system.
3. Modeling and Analysis
As shown in Figure 1, the IoV is a complex network system, in which V2X represents the communication between the vehicle and everything, and RSU represents the roadside unit. The static and dynamic detection and data collection can be realized by installing terminal equipment to the instrument of the vehicle. The terminal device can also provide services, such as locking up, answering calls, locating and navigating, listening to music, and web searching. Information is often transmitted incorrectly or with errors due to mass vehicle access and terminal complications such as path loss, thermal noise, channel fading, or interference from other radio sources. Therefore, in the presence of channel errors and unsaturated traffic, we establish a model based on the IEEE 802.11p vehicular communication protocol to analyze and investigate the impact of channel errors on system performance. In this model, we take into account factors such as limiting the number of retransmissions, freezing of the backoff counter when the channel is busy, the value of the maximum and minimum contention windows, interframe interval of arbitration frames, external and virtual internal collisions between frames, and channel transmission errors.
Specifically, we use the four of the EDCA mechanism to achieve differentiated services, with higher priority (e.g., answering calls) getting served first and lower priority (e.g., web search) waiting for service opportunities. The priority levels of the four and their parameter settings are shown in Table 1. indicates voice, which has the highest priority; presents video, which has the next highest priority over other data services; suggests best effort, which is less sensitive to delay but vulnerable to the impact of time-extended services, such as Internet surfing; means background, which is a priority service with unlimited delay and low throughput requirements, such as file downloading and file printing. For example, when voice and file downloads are requested for transmission at the same time, the higher-priority voice is served first and the lower-priority file downloads wait to be served. In addition, the channel access mechanism used in this analytical model is the RTC/CTS method, and both are within the transmission range of the terminal, without hidden terminals.
3.1. Establishment of the Model
In a real-world IoV system, the network traffic is unsaturated. To avoid overestimating the throughput, the model is designed under unsaturated conditions. Therefore, we added an initial state to the model to ensure that the data can be served directly as soon as it arrives when the channel is empty. In order to avoid the system burden caused by multiple retransmissions, we set the retransmission limit. Additional EDCA mechanism parameters are the values of the maximum and minimum contention window and the arbitration interframe space number (AIFSN). The smaller the parameter value for each of the four access categories, the higher its priority. The AIFSN is used to calculate the arbitration interframe spacing (AIFS), , where is a time slot and SIFS is the short interframe spacing. The four access categories of the EDCA mechanism can be considered as four different stations. When there is a data frame to be transmitted, it first listens and judges whether the channel is idle during the AIFS period. If so, the data frame is then transmitted. However, when two stations listen for the channel in the same time slot and both listen for the channel to be idle at the end of AIFS, they transmit at the same time, and this results in a collision. To reduce the probability of collisions, the data frames are backed off for a period of time before being transmitted after AIFS. The value of the backoff is randomly selected from within the range of the contention window to a time slot. The size of the contention window of an is initialized to a minimum value . After each transmission failure, another backoff is executed with a doubled size until it reaches . When the maximum window value is reached, the maximum window value is held constant until the number of retransmissions is exhausted, and then, the currently transmitted packet is discarded. The value of the window remains unchanged after the maximum size of the contention window is reached. Until the number of retransmissions is exhausted, the current transmitted data packet will be discarded without retransmission. The size of the contention window depends on the phase of backoff and satisfies the following equation:where is the size of the initial contention window, , m denotes the maximum number of times to increase the contention window, i.e., , and represents the maximum backoff phase.
The notation in the model is summarized in Table 2. According to the backoff stage of the packet, ; the value of the backoff counter, , and the remaining time of the transmission process at a time t, ; a 3D Markov model is established to describe the operation mechanism of the system (as shown in Figure 2). In the figure, the pair is used to represent the state of each , and the relationship between different states and the corresponding state transition probability are marked. The remaining time of the transmission process in the modeling is divided into three categories: the remaining time of collisions, , the remaining time of errors, , and the remaining time of successful transmissions, . Figure 3 depicts the detailed process of a data frame being in the backoff state and delayed state. When a data frame is in any of the backoff states, , if the detects the channel is idle, the value of the backoff counter is decremented by one and enters the next state, ; if the detects the channel is busy, the backoff counter is frozen, and the data frame will wait for time slots, and it enters the state, . in the state, , for each time slot experienced, the remaining frozen time is decremented by one. Until the remaining frozen time is reduced to , if the channel is detected to be idle, the remaining frozen time is decremented by one. However, if at the end of the second last slot of the channel is still idle, the counter decreases by one and the data frame enters the next state ; if the channel is detected to be busy, the backoff counter is frozen, and the remaining frozen time is set to and enters the delay state again, that is, .
3.2. One-Step Transition Probability and Steady Distributions of Systems
In the Markov chain shown in Figure 2, the following seven types of state transfer relations exist.(1)State represents the initial state of a data frame. When a data frame is ready for transmission, detects if the channel is idle. The backoff stage is activated when the channel is detected to be busy or when the channel has a collision, and a value from the contention window of backoff stage 0 is randomly selected for backoff. Its transition probability is expressed as(2)In the state , detects the channel is idle and no other tries to transmit at the same time; then, a data frame moves to the next state , that is, In the state , detects whether an error has occurred in the data. If no transmission error occurs, the frame will move the state , to Otherwise, it will enter the error state , that is, For state , during the transmission, time r is decremented by one for each time slot, that is, After a successful transmission, a new packet is scheduled for transmission, that is, The aforementioned state transition probabilities can be expressed as(3)For state , the data frame encounters a collision when attempting to transmit the state and then enters the state , which is expressed as During the collision period, the collision residual time r is decremented by one at each time slot, and thus, we have When the collision residual time decrements to 1, doubles the size except when it reaches , and the data frame selects a random one from the contention window in the phase and enters the next backoff stage , that is, The aforementioned state transition probabilities can be expressed as(4)When a data frame does not collide in the attempted transmission state and , it will enter the state . That is, In state , detects whether an error has occurred in the data frame, and if there is no error in the transmission, the data frame will enter the state , which means that the transmission is successful, that is, Otherwise, it will enter the state , which is expressed as The aforementioned state transition probabilities can be expressed as(5)For state , an error occurred during the transmission of the data frame. During the error period, the error residual time is decremented by one at each time slot, that is, When the error residual time decrements to 1, doubles the size except when it reaches ; then, the data frame enters the next backoff stage , by selecting a random one from the contention window in the phase, that is, The aforementioned state transition probabilities can be expressed as(6)When the data frame transmission reaches the retransmission limit , if the data frame collides, it will be discarded without backoff, and then a new data frame will enter the initial state , that is, If the data frames do not collide and no transmission error occurs, then it will be successfully transferred, that is, However, once it has a transmission error, then it will also be discarded and a new data frame will enter the initial state , that is, The aforementioned state transition probabilities can be expressed as(7)When the data frame stays in the backoff state , the backoff is frozen as soon as detects that the channel is busy, and the data frame has to wait for time slots; then, it enters the delayed state , that is,
In the delayed state , the delay time is decremented by one for each time slot experienced until it reaches the state , which is expressed as
In states , the AC will detect again the channel during the arbitration interframe interval . If the channel remains idle during , its delay time is decremented by one after each time slot; However, if at the end of the second last slot of the the channel is still idle, the counter decreases by one and the data frame enters the next state , that is,
If detects the channel is busy during the arbitration interframe interval , the data frame will enter the delayed state again , that is,
However, if the channel is detected to be idle in the backoff state , the value of the backoff counter is subtracted by one, that is,
The aforementioned state transition probabilities can be expressed as
We denote the probability of state as , where and . By iterating and simplifying the state transition probabilities of equation (29), we obtain the following expression:
From the relationship between the states, it follows that
Therefore, the following steady-state distribution can be obtained
The derivation of equation (32) is shown in Appendix A.
According to the relationship between states , and other states, the relationship formula between them is obtained, which can be simplified aswhere .
3.3. Calculation of and Transition Probability
By applying the stationary distribution normalization condition, the sum of all probabilities of the system in the Markov chain model is equal to 1. Thus, we have
After some algebraic manipulation, we can obtain
The derivation of equation (35) is shown in Appendix B.
Once the values of , , , , , , m, h,, and are known, all steady-state probabilities can be obtained from equations (30)–(35). In fact, , , , m, h, , and can be known for a given , so the key to the problem is to calculate the probabilities of , , and . Because the Markov model is for the case of one active and each station has multiple active s at the same time, so and depend on the other stations of the model as well as on the other s within the same station.
Donate is the transmission probability of in a randomly chosen time slot, where . In the Markov model, attempts transmission as long as the value of the backoff counter equals 0, regardless of the backoff phase. Therefore, can be expressed as the sum of the steady-state probabilities of state , where . Thus, we have
From the station’s perspective, the probability of a station attempting to access the channel is equal to the probability of accessing it via one of its four . Therefore, the probability that a station will attempt to enter the channel can be calculated as
For one , the channel is in the occupied state when it is in collision, error, or successful transmission mode. So, the probability that the channel is occupied by is given by
Similarly, the probability of a station occupying the channel can be expressed as
When the channel is not occupied, it is considered to be idle. The probability of a channel being busy can, therefore, be defined aswhere M is the total number of stations. does not collide, which means that no with a higher priority than it transmits and the other M − 1 stations do not transmit. Therefore, the collision probabilities of iswhere means that has a higher priority than , . Without loss of generality, we assume that the Gaussian wireless error channel is introduced in our system and a constant channel bit error rate is predetermined; that is, each bit has the same bit error rate. The error in the data frame is thus mainly influenced by the channel BER and the packet length. Therefore, the error probability of a data frame can be expressed as a function of the BER and the length of the data frame iswhere L is the length of the packet and BER is the bit error rate of the channel.
4. Performance Analysis
4.1. Throughput Analysis
The throughput of a given is equal to the ratio of the time occupied by the successful transmission to the interval between two consecutive transmission times. According to this definition, the throughput of can be expressed aswhere is the conditional probability of successful transmission of , is the average length of a data frame, is the average idle time before the frame is transmitted, and , , and denote the collision time, the successful transmission time, and the error time, respectively, which are given by [12]where H is the physical and MAC layer header and L is the length of the packet.
The conditional successful transition probability, , is given bywhere is the probability of successful transmission of , and it can be expressed as
Finally, the average idle time can be obtained as
4.2. Delay Analysis
The average access delay can be defined as the average time between the first attempt to transmit a data frame and it is being successfully transmitted. The access delay can be derived by using the recursive theory.
We denote the average delay from the current state to a successful transmission as . Assuming that is known, the relationship between states and can be obtained as
For state , either a collision occurs or the attempted transmission succeeds and moves to the next state, so the delay can be expressed aswhere can be obtained from the following equation. Hence, for state , , we have
For state , either the transmission is successful or an error occurs, so the delay is given bywhere can be obtained from the following equation. Hence, for state , we have
For the initial state , the delay can be obtained as
For the whole Markov chain, once is obtained, the access delay of all states can be calculated recursively. In fact, for the state , if the packet collides and cannot be sent out at this time, it will be discarded, so the delay is a time slot and, . For state , if an error occurs in the packet in the channel, it is also discarded, so the delay is also a time slot and, thus, .
Therefore, from the above analysis, the average access delay of this system can be calculated as
5. Numerical Results
This section focuses on the analysis of the numerical results of the system using MATLAB. The simulations are completed with Monte Carlo simulators, and Monte Carlo simulation is over 103 times. The simulation results are compared with the theoretical results to verify the validity of the theoretical derivation. In the analysis of throughput and delay versus the number of stations, the length of a frame is 512 bytes, and the other parameters used for the numerical simulations are shown in Table 3.
5.1. Analysis of Transition Probabilities
In this section, we focus on the impact of the BER and the number of vehicles on the probability of transmission per , the channel busy probability, and the collision probability, as shown in Figures 4–6. From these plots, we can see that the simulated results and numerical results fit well, illustrating the validity of the theoretical results. We can see from Figures 4–6 that the higher the priority of , the higher the transmission probability and the lower the collision probability; thus, differentiated service of the channel can be achieved with the four . In Figures 4 and 6, the packet sizes and BER are set to bytes and , respectively. It can be seen that the higher the priority of , the lower the collision probability. When the number of stations is large, the collision probabilities of with low priority are essentially the same. This is because when the number of stations increases, with the highest priority transmits first, resulting in other lower priority always sensing that the channel is busy and entering the backoff or waiting state. Figure 5 shows the number of stations versus the transmission probability for and . From the figure, we can obtain that the transmission probability of the station is smaller under an error-prone channel than under an error-free channel, which is in line with the actual transmission. Also, with high priority are more affected by changes in BER, mainly because it will be served first once a higher priority arrives, so that its state is less stable.
5.2. Throughput and Delay Performance Analysis
5.2.1. The Impact of the Number of Stations
Figures 7 and 8 show the relationship between the number of stations and the throughput and delay, respectively, when the length of the data frame is 512 bytes, and . As the number of stations increases, the throughput of decreases while the delay increases. This is due to the fact that when the number of stations increases, the channels are constantly being contented by , so the channels are always occupied. As a result, the performance of will be degraded. It can also be clearly seen that has the best performance compared to the other when the number of stations increases. Also, has a lower delay. This indicates that the EDCA mechanism of the IEEE 802.11p protocol enables service differentiation. From these figures, it can also be seen that the simulation results fit well with the analysis results, which confirms the correctness of the theoretical analysis.
5.2.2. The Impact of BER
Figure 9 shows the impact of BER on the system throughput for the number of stations is and , where the length of the data frame is 512 bytes. It can be seen from Figure 9 that, as the BER increases, the system throughput gradually decreases and even tends to zero. This is due to the fact that the larger the BER the higher the error probability, resulting in the channel being occupied all the time, the less efficient the are in using the channel, and the lower the system throughput. When the number of stations increases from 5 to 15, the throughput of the system decreases rapidly, which shows that the number of stations has a significant impact on the system throughput.
Figure 10 illustrates the obtained results and focuses on the impact of BER on the average access delay per . Indeed, it can be clearly seen that, as the BER of the channel increases, the access delay of with high priority also increases, while the delay of with low priority first increases and then decreases. This can be explained by the fact that the probability of errors occurring in increases when the BER increases. When an error occurs, the high-priority will remain channel occupied so that its delay increases. On the contrary, as with higher priority are occupying the channel, the low-priority will either not transmit or backoff, and thus, its delay will decrease. It is also related to the number of stations. As the number of stations increases, the collision probability of increases and the transmission probability of decreases. Thereby, the high-priority will keep the channel occupied, causing the low-priority to be unable to transmit so that its delay is reduced.
5.2.3. The Impact of the Frame Length
This section gives the impact of the length of the frame on the system throughput and delay. The optimal frame length for is 512 bytes for a given bit error rate, . The choice of small frames is necessary for applications with more sensitive delay. Figure 11 gives the impact of frame length on the throughput of when the number of stations is 7 and 15, from which it can be seen that an increase in the number of stations not only reduces the throughput of but also affects the optimal frame length of . The throughput of reaches its maximum when the frame length increases, with an optimum frame length of 512 bytes. As the frame length increases again, the throughput starts to drop. Because the frame is too long, the use efficiency of the system is reduced, resulting in a decrease in the performance of the system.
Figure 12 shows the impact of frame size on the delay of when the number of stations M is 5 and 15. From the figure, it can be observed that the larger the length of the frame, the larger the delay. This increasing trend is more pronounced when the number of stations is increased from 5 to 15. This can be explained by the fact that an increase in the number of stations and frame length increases the probability of errors and collisions, resulting in increased delay. Therefore, choosing small frames for applications with stringent delay requirements will improve the timeliness of the system.
5.2.4. The Impact of Optimal Frame Length and BER
In this section, we provide a three-dimensional plot of the throughput of as the function of BER and the length of data frames when the number of stations is 10. As shown in Figure 13, in the 3D plots of and , the throughput increases as the length of the data frame increases and the BER decreases. For a given BER, the throughput increases and then decreases as the length of the data frame increases, so there is a maximum throughput that can be observed in the figure, at which point the frame length of the data is the optimum length for transmission. The red line in the subfigures of AC3 and AC2 represents the peak throughput corresponding to the optimal frame length for any BER. For , on the contrary, a local peak occurs when the value of BER is around ; and for low priority , its local peak becomes the global peak. This is due to an increase in BER, resulting in an increased probability of errors in backoff or delayed states in and with high priority. So, and with low priority must start listening to the channel to increase their throughput until they reach their peaks.
6. Conclusion
In this article, we focus on the influence of the access categories’ (ACs) performance with channel errors by using four to cause service differentiation based on the enhanced distributed channel access (EDCA) mechanism of the IEEE 802.11p in the Internet of vehicles (IoV), and we successfully derived the expressions for the throughput and delay of under the conditions of error channels and unsaturated traffic by establishing and analyzing the Markov chain accurately. First, we consider unsaturated traffic conditions and a Gaussian wireless error channel with a constant BER to obtain the error probability of a data frame. Subsequently, we designed a three-dimensional Markov model based on the aforementioned environment and IEEE 802.11p protocol compliant metrics and obtained the probability of a channel being busy, the probability of transmission per , as well as the probability of a collision occurring based on the steady distribution of the model. We then derived and analyzed the aforementioned performance metrics to obtain analytical expressions of system throughput and delay. Finally, numerical results were provided to evaluate the impact of the number of stations, the length of the data frames, and the BER on the throughput and delay, as well as the transition probability. In addition, Monte Carlo simulations over 103 have been completed to verify the correctness of the analysis results obtained in this article. By comparing the simulation results with the numerical analysis results based on the Markov chain’s close expressions, it can be found that the numerical results are consistent with the simulation results. We concluded that the increase in the number of stations, length of data frames, and BER reduces the system performance, reduces throughput, and increases delay. Especially, for and with lower priorities, when BER increases, their throughput is very low and the delay is reduced significantly. This is due to the fact that, as the BER increases, the probability of errors occurring in high-priority and also increases. So, the high-priority are in a constant state of occupied channels, leaving the lower-priority in a waiting state without transmission opportunities. Subsequently, the average access delay was reduced. Likewise, for a certain number of stations, when the length of the data frame changes, the throughput of increases and then decreases so that the throughput of has a maximum value and the optimal length of the data frame can be obtained. For example, when , the optimal data frame length for is 512 bytes.
Appendix
A. Derivation of Equation (32)
According to the Markov chain, the steady probabilities can be expressed bywhere . Thus, we have
Then, mathematical induction can be used in equation (A.2). After some mathematical simplifications, we obtain
According to the Markov chain, it can be observed thatwhere . Hence, we have
Using mathematical induction again, we can obtain
Therefore, equation (32) can be obtained as
B. Derivation of Equation (35)
Substituting equations (30)–(33) into equation (34), we obtain
After simplification, we have
Data Availability
The data used to support the findings of this study are available within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This research was funded in part by the National Natural Science Foundation of China under Grant no. 61663024, the Hongliu First Class Discipline Development Project of the Lanzhou University of Technology under Grant no. 225305, and the Erasmus + Programme of European Commission under Grant no. 573879-EPP-1-2016-1-FR-EPPKA2-CBHE-JP.