Home Data transmission mechanism of vehicle networking based on fuzzy comprehensive evaluation
Article Open Access

Data transmission mechanism of vehicle networking based on fuzzy comprehensive evaluation

  • Hongtao Zhang , Liancheng Zhang EMAIL logo , Yi Guo and Zhenxing Wang
Published/Copyright: December 31, 2022
Download Article (PDF)
Open Mathematics
From the journal Open Mathematics Volume 20 Issue 1

Abstract

Because the communication link connection in the Internet of Vehicles is transient and intermittent, the established connection may be disconnected at any time, which cannot meet the requirements of the data transmission of the Internet of Vehicles. Therefore, based on the traditional data transmission mechanism, the fuzzy comprehensive evaluation method is used to achieve the optimal design of the data transmission mechanism of the Internet of Vehicles. First, according to the operation mechanism of the Internet of Vehicles build the Internet of Vehicles model. Then in this model, the fuzzy comprehensive evaluation is used to analyze the data transmission characteristics of the Internet of Vehicles, and the characteristics evaluation results of data transmission are obtained. Finally, set the data transmission protocol of the Internet of Vehicles, select the appropriate data transmission path, allocate the data transmission load, and realize the data transmission of the Internet of Vehicles. The experimental results show that compared with the traditional data transmission mechanism of the Internet of Vehicles, the speed of the designed transmission mechanism is increased by 3.58 MB/s, and the packet loss rate is reduced by 41%.

Keywords: fuzzy comprehensive evaluation method; vehicle networking; data transmission; transmission mechanism; transport protocol; transmission path switching
MSC 2010: 08-XX; 20-XX

1 Introduction

Intelligent transportation includes people, roads, vehicles, data transmission, and management service platform. Among them, vehicle networking technology is one of the key technologies in intelligent transportation system [1]. The Internet of Vehicles refers to connecting cars to form a network. Cars and cars form a car network, which is connected to the Internet. Based on a unified protocol, the three realize the data exchange among people, cars, roads and clouds, and finally realize the functions of intelligent transportation, intelligent car, and intelligent driving. Vehicle networking is a self-organized and distributed data transmission network that is constructed rapidly and dynamically in the road traffic network. Its purpose is to realize the data transmission among the nodes in the intelligent traffic system in real time, accurately and efficiently. The vehicle network is the vehicle terminal equipment, which uses a variety of wireless communication technologies to communicate with each other or with the roadside infrastructure, and then connects the data transmission to the Internet [2]. At present, many scholars have done a lot of research in this area. Ren Tiaojuan proposed a data transmission algorithm (DTA) for the Internet of Vehicles based on channel switching. The DTA considers a three-layer network composed of vehicle nodes, relay nodes, and aggregation nodes; classifies nodes according to the driving direction of the vehicle; and proposes different channels. The channel allocation and switching mechanism reduces the interference of data transmission, reduces unnecessary loss, improves the data reception rate of the sink node, reduces the average number of data packet hops, and improves the coverage rate of data transmission [3]. However, this method still lacks in ensuring the reliability and stability of data transmission. Peng Xin proposed a V2R/V2V data transmission scheduling algorithm. The algorithm first generates an initial scheduling operation according to the vehicle’s data transmission request and builds an initial scheduling conflict graph and a conflict matrix based on the conflict relationship between the initial scheduling operations. Second, it proves that the conflict matrix is on the basis of semi-definiteness, and a semi-definite planning method is used to allocate channels and improve the scheduling conflict map. Finally, according to the vehicle’s detention time in the service area and the amount of data requested for transmission, different service weights are assigned to it, based on the scheduling conflict map, and the V2R/V2V coordinated transmission method completes the scheduling in time sharing [4]. However, this method does not solve the problem of transmission efficiency. In order to ensure the transmission of multimedia data in Internet of Vehicles, DWAB proposes a device-to-device-based car networking similarity secure multimedia data transmission mechanism. By measuring static and dynamic vehicle attributes, back-propagation neural network is used to quickly and accurately calculate vehicle similarity, and an Internet of Vehicles communication group is established based on attribute similarity [5]. The use of vehicle attributes to generate communication keys to protect the privacy of the vehicle can reduce data delay to a certain extent, but there is also the problem of low reliability.

Data transmission in the Internet of Vehicles can be divided into parallel transmission, serial transmission, asynchronous transmission, synchronous transmission, and simplex transmission. Fj et al. [6] proposed the Internet of Vehicles intrusion detection based on logarithmic ratio oversampling, outlier detection, and metric learning. This method improves the effectiveness of intrusion detection in three main ways: first, oversampling a few classes based on a new strategy; second, a new feature based on unbalance ratio is introduced; third, by combining outlier detection and distance metric learning, we can reduce outliers and actively rescale the original samples to make the decision boundary clearer. In addition, genetic algorithm is used to extract the optimal subset of features. Kumar et al. [7] proposed green computing in social networking of vehicles defined by software. Considering the vehicle network structure defined by software, a meta heuristic solution was developed to solve the problem of green traffic data transmission in scalable input/output virtualization, namely bidirectional particle swarm optimization. Compared with the most advanced technology, a large number of simulation experiments have been carried out to evaluate the performance of bidirectional particle swarm optimization. Rathee et al. [8] proposed the block chain-based cognitive radio transmission technology for the Internet of Vehicles, which senses channels through a decision-making technology, so as to provide security for the Internet of Vehicles in the process of spectrum sensing and information transmission using the radio network. Decision-making technology is a technology that arouses the trust of cognitive users by analyzing some predefined attributes. In addition, the block chain is maintained in the network to track every activity that stores information. For the baseline solution in the Internet of Vehicles, the proposed mechanism is strictly verified according to several security metrics using various spectrum sensing and security parameters. However, the above-mentioned traditional vehicle networking data transmission mechanism has problems such as long transmission delay, high transmission interruption rate, and slow transmission speed. Therefore, the fuzzy evaluation method is introduced. The innovation of the research content is to use the fuzzy comprehensive evaluation method, in which the comprehensive evaluation refers to the process of people evaluating and recognizing the relatively complex and abstract evaluation standard system. Using the method of fuzzy comprehensive evaluation, the optimal design of vehicle network data transmission mechanism is realized, so as to improve the reliability and efficiency of vehicle network data transmission.

The main contributions of the research on the data transmission mechanism of the Internet of Vehicles based on the fuzzy comprehensive evaluation method are as follows:

  1. According to the operation mechanism of the Internet of Vehicles, this article constructs the Internet of Vehicles model.

  2. In this model, fuzzy comprehensive evaluation is used to analyze the data transmission characteristics of the Internet of Vehicles, and the evaluation results of data transmission characteristics are obtained.

  3. Set the data transmission protocol of the Internet of Vehicles, select the appropriate data transmission path, distribute the data transmission load, and realize the research on the data transmission mechanism of the Internet of Vehicles based on the fuzzy comprehensive evaluation method.

The results show that the mechanism has good data transmission performance.

2 Design of data transmission mechanism of vehicle networking

The structure diagram of the three-layer vehicle networking is shown in Figure 1.

Figure 1 Structure of the three-layer vehicle networking.
Figure 1

Structure of the three-layer vehicle networking.

It can be seen from Figure 1 that on the basis of a three-layer network structure composed of vehicle nodes, relay nodes, and sink nodes, the vehicle node is the bottom layer of the three-layer network structure, which is installed in the running vehicle to collect and send vehicle driving data. The information is sent from the vehicle node to the higher level relay node and exchanged with the neighbor vehicle node. As the link between vehicle node and convergence node, relay node is installed on the infrastructure such as streetlamps which can supply power on both sides of the road to realize data forwarding with vehicle node and other relay nodes. As the top layer of the three-layer network structure, the sink node collects the data of all relay nodes in the area and forwards it to the server. The three-layer network structure realizes the data transmission, diffusion, and convergence, which lays the foundation for the rapid data transmission. In this network structure environment, the data transmission of the vehicle networking is completed according to the flow of Figure 2.

Figure 2 Data transmission flow chart of vehicle networking.
Figure 2

Data transmission flow chart of vehicle networking.

In order to ensure the smooth operation of the data transmission mechanism of the vehicle networking, relevant transmission equipment is installed under the network structure, including high-precision Beidou module, STM32 processor module, OBD data acquisition module, wireless module, voice playing module, touch screen, and power module. In the process of vehicle node operation, the OBD data acquisition module is used to obtain vehicle data; the Beidou module is used to obtain the location data of vehicle node; the touch screen is used to interact with the user; the voice broadcast module is used for path guidance and intelligent alarm; and the wireless module is used to send its own data to other vehicle nodes or relay nodes. The relay node is mainly composed of STM32 processor module, touch screen, wireless module, and power module. During the operation of the relay node, the wireless module is used to obtain the data of other relay nodes or vehicle nodes and report the road status; the touch screen is used to display the road condition data of the current road section; and the STM32 processor is used to analyze the current road congestion, whether there are accident vehicles, etc.

2.1 Building the vehicle networking model

Supposing that the whole vehicle network is divided into several sections, each section has a local controller. The communication range of the local controller can cover the whole section, and the areas responsible by different local controllers do not overlap each other. There are multiple vehicles on each road section, and each vehicle has a certain communication range. The vehicle can only distribute data with other vehicles in the communication range, while the vehicles not in the communication range can only realize data routing through multi-hop forwarding [9]. Each vehicle knows its neighbor’s vehicle ID and location. When the vehicle enters the communication range of the local controller, it can find the local controller in its area. The vehicle communicates with the local controller. The vehicle and the local controller can only communicate control information, and the local controller cannot help the vehicle to forward data. G R ( V , E ) is defined as the topological structure of the road, where V is the set of road intersections and E is the set of road edges [10]. Choose the optimal path to deliver the data packet. If the fuzzy comprehensive evaluation method fails to receive the data packet successfully after the acceptable time threshold, it will choose the suboptimal path, and so on. For paths belonging to different evaluation grades, the higher the grade, the higher the priority; for paths belonging to the same grade, the higher the evaluation value, the higher the priority, so as to determine the parameter values in the method used. It is assumed that the distance between vehicles follows an exponential distribution, namely:

(1) f ( x ) = 1 ρ i j e − 1 ρ i j x , x > 0 0 , x ≤ 0 ,

where ρ i j represents the average density of vehicles on path r i j , then the average delay of packet transmission on path r i j is as follows:

(2) t i j = e − R ρ i j d i j ρ i j − 1 d i j R + e − R ρ i j d i j ρ i j − 1 d i j 2 v i j ,

where e − R ρ i j d i j ρ i j − 1 indicates that the vehicle density on the path r i j is large, and when the spacing is less than the vehicle communication radius R, the probability of data packet transmission by multi-hop is shown; e − R ρ i j d i j ρ i j − 1 indicates the probability that the spacing between at least one vehicle on the path r i j and the adjacent vehicle is greater than R, d i j represents the distance coefficient between vehicles, and v i j represents the data value transmitted by nodes between vehicles. At this time, due to the inability to communicate with the adjacent vehicle, the data packet can only be transmitted by carrying [11]. The final results of the vehicle networking model are shown in Figure 3.

Figure 3 Schematic diagram of vehicle networking model.
Figure 3

Schematic diagram of vehicle networking model.

2.2 Fuzzy comprehensive evaluation and analysis of data transmission characteristics

Supposing there are n evaluation units in the evaluation system, (a + b) evaluation indexes in total, including a quantitative index (m inputs, s outputs) and b non-quantitative indexes [12]. Data envelopment analysis is used to calculate the relative efficiency of quantitative index. Then the characteristics of the data to be transmitted are analyzed according to the comprehensive evaluation process shown in Figure 4.

Figure 4 Flow chart of comprehensive evaluation.
Figure 4

Flow chart of comprehensive evaluation.

Let the input and output vectors corresponding to the jth decision-making unit be X j , respectively, and its expression is as follows:

(3) X j = ( x 1 j , x 2 j , ⋯ , x m j ) T > 0 Y j = ( y 1 j , y 2 j , ⋯ , y s j ) T > 0 .

That is to say, each decision-making unit has m types of “input” and s types of “output.” Where x m j is the input of the jth decision unit to the ith input and y s j is the output of the jth decision unit to the rth output [13]. Let the weight vectors of input and output be v and u, respectively. Efficiency index refers to the ratio of output to input when input is v T X j 0 and output is u T Y j 0 under the weight coefficients v and u. The higher the efficiency index is, the more output the data can get with less input. When optimizing the efficiency index of a single decision-making unit, the efficiency evaluation index of the decision-making unit is used:

(4) h j 0 = u T Y j 0 v T X j 0 .

The maximum is the optimization objective, with the efficiency index of all decision-making units as the constraint, to form the following linear evaluation expression:

(5) ( P ) = max _ Y j 0 s . t . ( v u ) T X j − Y j ≥ 0 ( v u ) T X j 0 = 1 v u = 0 ,

where s . t . ( v u ) T represents the number of conditions of the decision-making unit, X j represents the weight coefficient, and Y j represents the constraint coefficient. The input and output data of n decision-making units to be evaluated are substituted into the above-mentioned linear programming P to solve their optimal solutions, respectively, and then the efficiency evaluation indexes of each evaluation unit are obtained [14,15]. Then, the isosceles triangle membership function of Figure 5 is used for fuzzy processing.

Figure 5 Membership function under fuzzy comprehensive evaluation.
Figure 5

Membership function under fuzzy comprehensive evaluation.

The final comprehensive evaluation can be carried out with the fuzzy unified and non-quantitative FCA results of data envelopment analysis. By calculating the fuzzy index weight, the characteristic evaluation results of data transmission are obtained.

2.3 Setting the data transmission protocol of the vehicle networking

The behavior of data transmission protocol in the vehicle networking is embodied in four core mechanisms: encoding and decoding, Media access control, Frame and signature processing, and Clock synchronization. In addition, the controller host interface can be used as the core mechanism of the host, so that it can cooperate with each other in a systematic way and can also be used to provide feedback to the host for the core mechanism. There are eight basic protocol operation control states in the nodes on the bus, and the nodes complete different functions in each protocol operation state. All nodes in the communication system follow the protocol given in the figure for state transition, and then complete the normal communication of nodes [16]. The specific eight states include default configuration state, parameter configuration state, ready state, wake-up state, start state, normal active state, normal passive state, and stop state. Code is to process the source data frame to be sent, such as adding signature and check bit. The decoding process is the reverse process of encoding, which is used to analyze the received data frame and extract the effective data according to the specification. Protocol coding can be divided into data frame coding and signature coding. The basic format of the protocol frame is shown in Figure 6.

Figure 6 Format of transmission protocol frame.
Figure 6

Format of transmission protocol frame.

The main function of the transmission protocol frame format shown in Figure 6 is to provide a reference for analyzing the transmission mode of the received and extracted data frames, the frame header consists of 5 bytes (40 bits), the first bit is reserved bit, and the next 4 bits are index bits, indicating payload, empty frame, synchronous frame, and start frame in turn, followed by 11 bit frame ID, 7-bit payload length, 11 bit frame header CRC, and 6-bit cycle counting digit [17]. Frame ID is used to prompt the time slot during transmission. In each communication cycle, a frame ID can only be used once, with an effective range of 1–2,047. In the static segment, the data segment length of all frames is fixed and equal, while in the dynamic segment, the load length of different frames can be different. The head cycle check CRC is calculated by logical polynomials according to the agreed indication bits and is available in the system. The data can only be received when the CRC of the frame header sent by the transmitting node and calculated by the receiving node is equal. The period count records the number of cycles of the data frame when the data are sent, and the range is 0–63.

2.4 Selecting and switching transmission path

2.4.1 Path selection

There are many wireless connections in the environment of the vehicle networking, but the situation of each line is various and the difference is huge, so it should choose the link with good quality for transmission [18,19,20]. Therefore, a path selection method is designed: First, the bandwidth, delay, and packet loss rate of the link are estimated, and the better link is selected for data transmission considering these path parameters. Packet loss rate and delay are very important, so it is necessary to select the appropriate data transmission path. The specific selection process is shown in Figure 7.

Figure 7 Flow chart of path selection.
Figure 7

Flow chart of path selection.

At the beginning of connecting to the network, all paths are selected for data transmission. However, the nature of multiple paths is different at this time, and the transmission capacity of the network is different. Therefore, the link is evaluated to calculate the packet loss rate, delay, and other parameters of each path. Then, considering the packet loss rate of the path, all paths are traversed, and the path with the packet loss rate below the average value is selected. Paths above the average are not discarded and need to be evaluated at all times, unless they are disconnected before they are removed from the path list [21,22]. If there is more than one path at this time, then all the selected paths are traversed, to select the path with the delay below the average value, if any, these paths are used to transmit data; if not, the path with the minimum delay is selected. At this time, the whole association becomes a single path transmission, and the selected path is the link for data transmission.

2.4.2 Switching transmission channel

In order to further improve the low throughput and fairness of the system caused by vehicle competition and resource shortage, the channel scheduling scheme of the system is designed. At present, there are three kinds of road conditions: two-way road, intersection, and T-junction. Therefore, the channel switching methods of the above three road conditions are mainly analyzed [23], as shown in Figure 8.

Figure 8 Traffic connection diagram of different intersections.
Figure 8

Traffic connection diagram of different intersections.

In the two-way road, the vehicle only need to consider the driving information of the front vehicle, so the vehicle node only need to obtain the front vehicle node information from the relay node or the front vehicle node. The simulation of two-way traffic condition communication is shown in Figure 8(a). The relay nodes B1, B2, and B3 and vehicle nodes V3 and V4 adopt channel B communication. Relay nodes A1, A2, and A3 and vehicle nodes V1 and V2 use channel A communication. Vehicle node V4 broadcasts data in channel B, relay node B2 receives data and sends data packets to relay node B3, and vehicle node V3 receives data packets from vehicle node V4 and front relay node B2 for path planning and anti-collision analysis; Vehicle node V1 and vehicle node V2 communicate in channel A without interference with channel B. According to the traffic simulation diagram of T-junction shown in Figure 8(b), the traffic situation of T-road is analyzed. Vehicle V1 travels along Road B, only need to broadcast data in channel B in the process of driving; Vehicle V2 turns left from Road D to enter Road B, broadcasts vehicle data in channels B, C, and D in the process of turning left; Vehicle V3 travels on Road D, only broadcasts on channel D; Vehicle V4 passes through T-junction along road C, broadcasts channel C; and Vehicle V5 turns right from Road D into Road C and broadcasts in channels C and D. From the above analysis, it can be concluded that: at the T-junction, vehicles turning left broadcast all channels; at the junction, vehicles going straight broadcast channels on both sides and current channels; and at the junction, vehicles turning right broadcast current channels and channels to be entered, and other vehicles broadcast only in current channels. The intersection traffic simulation is shown in Figure 8(c). Vehicle V1 drives on Road D and only communicates data with vehicle nodes and relay nodes on the channel; Vehicle V2 turns left from Road D and enters road A, and then turns to pass other roads, so during the turning process, data are broadcast in the whole channel; Vehicle V3 enters road A and only communicates data on channel A; Vehicle V4 passes the intersection on road A and broadcasts data in channel C; Vehicle V5 turns right from Road D to enter Road C, which only affects channels C and D, so only broadcast data in channels C and D. From the above analysis, if the vehicle arriving at the intersection turns left, it will broadcast all channels at the intersection; if it goes straight, it will broadcast data only in the channel; and if it turns right, it will broadcast data in the current channel and the channel to be entered.

2.5 Distributing data transmission loads

In order to verify the effect of selecting and switching transmission paths, it is necessary to allocate data transmission load. Because high voltage (HV) relay transmission works in time division duplex mode, sample value (SV) has the same transmission time as SV transmission and HVs transmission. In case I, the source SV must select HV to transmit information to the destination SV. The density of active SVs or HVs is 1 2 λ 1 P h . The transmission capacity is defined as the product of user density and transmission success probability. The transmission success probability of SV and HV, HV and SV communication is respectively:

(6) P s ( S INR ≥ γ 2 ) = e 1 2 λ 1 T γ R 2 P s ( S INR ≥ γ ) = e 1 2 λ 1 T γ R 2 P 1 P 2 2 + 1 ,

where S INR represents the error penalty item of the Internet of Vehicles data transmission, γ represents the amount of forwarding control data, P 1 represents the node balanced configuration value, and P 2 represents the node balanced transmission value. The transmission capacity of communication between SV and SV working in orthogonal mode is marked as C H , 1 , which can be expressed as follows:

(7) C H , 1 = 1 2 λ 1 P h P s ( S INR ≥ γ 2 ) × P s ( S INR ≥ γ ) ,

where λ 1 represents the input value of the multimode channel and P h represents the output value of the multimode channel. The data transmission capacity is shown in Figure 9.

Figure 9 Statistics of channel load.
Figure 9

Statistics of channel load.

Before each data transmission, the capacity between the data to be transmitted and the selected transmission channel shall be compared. If the data to be transmitted are greater than 80% of the channel capacity, the data shall be allocated into multiple parts for transmission, otherwise, a single channel can be used for direct transmission.

2.6 Realizing the multi-path transmission of the vehicle networking

In the normal driving process, the data transmitted in the channel include the information of vehicle nodes, the communication information between vehicle nodes and relay nodes, and the information between relay nodes. In order to reduce the delay of communication, the single hop communication mode is adopted between vehicle nodes and between vehicle nodes and relay nodes. According to the information of the vehicle node and other relay nodes, the relay node judges the congestion, accident, and other states of the road section, and needs to transmit the road condition state information to the rear relay node and the vehicle node, so it needs to consider the fast communication between the relay nodes. In order to quickly transmit the road condition information in front to the rear and let the vehicle node quickly acquire and update the road condition information in front, it is considered that all the relay nodes on the same side should be built into the aggregation tree with the aggregation node as the root node. The vehicle node, as the leaf node of the aggregation tree, should access the aggregation tree at any time and send its vehicle driving information to the relay node of the corresponding access point. After the relay node is started, the relay node needs to establish its own routing table. The specific methods are as follows: broadcast routing packets to other relay nodes within the scope of communication and receive routing packets from other relay nodes to determine whether the relay node address is greater than its own node address. If it is greater, return information including its own address. After receiving the return messages from other relay nodes, the relay node establishes a routing table. In the routing table, by using the numbering rules of relay nodes, it can judge the current relay node and the relay node with the farthest physical location in the routing table, and select the relay node as its next hop forwarding node. To sum up, through the collaborative work of the aforementioned steps, under the vehicle networking model, the communication transmission of multiple vehicle data is realized, and the problems existing in the traditional communication mechanism are solved.

3 Performance test and analysis

3.1 Building data transmission test platform

Generally, the verification methods of theoretical research results under the environment of vehicle networking are divided into two categories: field test in the real traffic environment and simulation experiment in the network simulation environment. Due to the large cost of field test, the difficulty of deploying communication equipment in a large range, the difficulty of experiment execution, and certain risks, etc., the main verification method in the academic research in the field of vehicle networking is to build a simulation verification platform through some simulation simulators to verify and analyze the proposed design scheme. Therefore, the network simulation software NS3 is used to simulate and verify the proposed data delivery scheme. The performance evaluation indexes such as data transmission rate, transmission delay, and data packet loss are analyzed and compared to verify whether the proposed method can ensure the accurate and effective transmission of data packets. The simulation and verification platform in the vehicle networking generally include two parts: One is traffic simulation, which is mainly completed by some commonly used traffic simulators, while the network protocol simulation is mainly realized by some commonly used network simulators. When building the architecture of dynamic simulation experiment, the traffic simulator simulation of urban mobility is first used to configure the traffic scene needed in the simulation experiment, simulate the vehicle’s moving track and road topology, generate and record the Trace file generated in the process of vehicle driving, then import the Trace file into the NS network simulator (version 3.0). In the network simulator, the transmission protocol is designed, the simulation parameters are configured, and the dynamic vehicle network is simulated.

3.2 Preparing the transmission data of vehicle networking

In order to ensure the authenticity of the experimental results, the actual vehicle generated data are collected in the actual vehicle networking system as the preparation data to be transmitted in the test experiment. The communication management client of UA535 data acquisition card is installed in the PC. The client can directly set parameters such as the number of sampling channels, total sampling frequency, and total length. The collected signals can be displayed on the display in real time, or the user-defined file name collection disk can be stored in the computer hard disk for later viewing. The working mode of wireless AP is set as infrastructure wireless roaming mode, and the IP address of PC is set as 192.168.0.5, so that PC can be connected with UA535 data acquisition card. The experimental equipment, the signal generator, acceleration sensor, UA535 data acquisition card, and PC are, respectively, connected with the power supply, and the acquisition card collects the signal through the acceleration sensor and connects the data acquisition card with the PC with the network cable. The collected data will be stored in different files according to different types, as the data to be transmitted in the vehicle networking environment. Prepare the data transmission of vehicle networking to pave the way for setting data transmission test indicators.

3.3 Setting the test indexes of data transmission

Based on the above preparation of vehicle network transmission data, set the test index of data transmission. The purpose of this test experiment is to test the application performance of the designed data transmission mechanism of the vehicle networking and verify its transmission performance from the data transmission speed and reliability. The test indexes that determine the transmission speed are the actual transmission rate and the transmission delay of data. The experimental results can be obtained through the data transmission monitoring software. The security of data can count and calculate the packet loss rate of data to get the test results. The value of packet loss can be determined by comparing the data size before data transmission and the received data size.

3.4 Experimental process

In the experiment, the designed data transmission mechanism based on fuzzy comprehensive evaluation method and the traditional data transmission mechanism of the vehicle networking are set as the test methods, among which the designed transmission mechanism is the experimental method and the traditional transmission mechanism is the comparative method. The two data transmission methods are carried out in the same experimental environment, and the data type and data size are the same. According to the application sequence of data transmission method, the prepared data to be transmitted are input into the vehicle networking environment, to determine the data transmission vehicle and data receiving vehicle in the vehicle networking, and install the data receiving interface on the two experimental objects, which can directly count the data amount and data transmission speed. In addition, a certain degree of interference factors should be introduced into the experimental environment to simulate other vehicle interference in the real vehicle networking environment.

3.5 Analysis of experimental results

According to the set experimental process, the data transmission performance of the data transmission mechanism based on the fuzzy comprehensive evaluation method is analyzed from the data transmission rate and packet loss rate.

3.6 Data transmission rate

Through the third-party software connected to the vehicle networking, the real-time data transmission rate is directly output, as shown in Figure 10.

Figure 10 The detection interface of data transmission rate.
Figure 10

The detection interface of data transmission rate.

After statistics and comparison, it is found that the average transmission rate of the traditional data transmission mechanism is 1.86 Mb/s, while the average transmission rate of the designed data transmission mechanism based on the fuzzy comprehensive evaluation method is 5.44 MB/s, which is 3.58 MB/s higher than that of the traditional data transmission mechanism.

3.7 Packet loss performance

The statistics and calculation results of packet loss performance of the same data are shown in Table 1.

Table 1

Experimental results of packet loss rate

Number of data transfers Data transfer size (MB) Data reception under traditional data transmission mechanism (MB) Data reception under the design of data transmission mechanism (MB)
1 200 183.3 200
2 200 192.2 200
3 200 187.6 198.4
4 200 174.9 200
5 200 198.6 200
6 200 193.3 197.2
7 200 200 200
8 200 182.9 199.1

According to the calculation, the total packet loss of the traditional data transmission mechanism is 87.2 MB, while the data loss of the designed data transmission mechanism based on the fuzzy comprehensive evaluation method is 5.3 MB, and the corresponding packet loss rate is 43.6 and 2.6%, respectively, which saves 41% compared with the traditional one. The reason for the low packet loss rate of the studied method is that when the method is first connected to the network, all paths are selected for data transmission. At the same time, the link is evaluated, and the packet loss rate, delay, and other parameters of each path are calculated. Then, considering the packet loss rate of the path, traverse all paths and select the path with the packet loss rate below the average value. The path above the average value is not discarded and has been evaluated all the time, which is conducive to reducing the packet loss rate to a certain extent.

4 Conclusions

Considering the three-layer network composed of vehicle nodes, relay nodes, and sink nodes, the driving conditions of vehicles in three different road scenarios are analyzed: straight roads, T-junctions, and intersections. The nodes are classified and different channels are allocated according to the driving direction of the vehicle. Vehicle node and relay node only communicate in the allocated channel to reduce the interference of data transmission. On this basis, the fast diffusion method of relay node information and the priority transmission method of emergency traffic information are proposed. Compared with the traditional data transmission mechanism of Internet of Vehicles, the following conclusions are drawn:

  1. The method designed in this article not only ensures the reliability of data transmission but also improves the efficiency of data transmission.

  2. The data transmission rate of the vehicle network under the data transmission mechanism of the Internet of Vehicles based on the fuzzy comprehensive evaluation method is increased by 3.58 MB/s, and the packet loss rate is reduced by 41%.

The data transmission method designed in this article can be used to design a message-type recognition algorithm in subsequent research, classify the messages to be transmitted according to their importance, determine the transmission order, and prioritize more urgent messages such as security messages. Massive traffic data of the Internet of Vehicles are constantly generated. These data have important reference value for analyzing and solving current traffic problems. It believes that in the near future, when the data transmission technology of the Internet of Vehicles is perfect, the development of the Internet of Things will reach a certain level. In the initial stage, this method can be widely used in practice to reflect the actual value.

Acknowledgments

This work was funded by National Natural Science Foundation of China (61402526, 61402525, 61502528).

  1. Funding information: This work was funded by National Natural Science Foundation of China (61402526, 61402525, and 61502528).

  2. Author contributions: In this paper, based on the traditional data transmission mechanism, the fuzzy comprehensive evaluation method is used to achieve the optimal design of the data transmission mechanism of the Internet of Vehicles. Hongtao Zhang according to the operation mechanism of the Internet of Vehicles, build the Internet of Vehicles model. Yi Guo, and Zhenxing Wang using this model, the fuzzy comprehensive evaluation is used to analyze the data transmission characteristics of the Internet of Vehicles, and the characteristics evaluation results of data transmission are obtained. Liancheng Zhang set the data transmission protocol of the Internet of Vehicles, select the appropriate data transmission path, allocate the data transmission load, and realize the data transmission of the Internet of Vehicles. Hongtao Zhang, Liancheng Zhang, Yi Guo, and Zhenxing Wang made a great contribution to the preparation of the manuscript.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: All data generated or analysed during this study are included in this published article.

References

[1] D. Wu, J. J. Xu, X. Z. Gao, and H. M. Zhao, An Enhanced MSIQDE Algorithm With Novel Multiple Strategies for Global Optimization Problems, IEEE. Trans. Syst. 3 (2022), no. 52, 1578–1587.10.1109/TSMC.2020.3030792Search in Google Scholar

[2] Y. B. Bang, Multi-speed transmission mechanism using a compound planetary gear set and brakes, Int. J. Automot. Technol. 4 (2019), no. 20, 739–748.10.1007/s12239-019-0069-9Search in Google Scholar

[3] Y. Jin and K. J. Xia, Intelligent location and recognition mechanism of abnormal point of medical image based on reliable transmission in medial CT scanner local big data networks, J. Med. Imaging & Health Inform. 3 (2018), no. 8, 609–617.10.1166/jmihi.2018.2321Search in Google Scholar

[4] X. Peng, Q. Deng, and S. Tian, Multi-channel vehicle networking V2R/V2V data transmission scheduling algorithm, J. Commun. 3 (2019), no. 40, 96–105.Search in Google Scholar

[5] Y. Han, B. Wang, T. Guan, D. Tian, G. Yang, W. Wei, et al. Research on road environmental sense method of intelligent vehicle based on tracking check, IEEE. Trans. Intell. Transp. Syst. 2022 (2022), 1–15.10.1109/TITS.2022.3183893Search in Google Scholar

[6] A. Fj, A. Mc, A. Wz, Y. A. Ye, and A. Sw, Intrusion detection on internet of vehicles via combining log-ratio oversampling, outlier detection and metric learning, Inform. Sci. 1 (2021), no. 579, 814–831.10.1016/j.ins.2021.08.010Search in Google Scholar

[7] N. Kumar, R. Chaudhry, O. Kaiwartya, N. Kumar, and S. H. Ahmed, Green computing in software defined social internet of vehicles, IEEE. Trans. Intell. Transp. Syst. 6 (2020), no. 22, 3644–3653.10.1109/TITS.2020.3028695Search in Google Scholar

[8] G. Rathee, F. Ahmad, F. Kurugollu, M. A. Azad, and M. Imran, Crt-biov: A cognitive radio technique for blockchain-enabled internet of vehicles, IEEE. Trans. Intell. Transp. Syst. 7 (2020), no. 22, 4005–4015.10.1109/TITS.2020.3004718Search in Google Scholar

[9] C. Liu, D. Wu, Y. Li, and Y. Du, Large-scale pavement roughness measurements with vehicle crowdsourced data using semi-supervised learning, Transportation Research, C-Emerg. Technol. 2021 (2021), no. 125, 103048.10.1016/j.trc.2021.103048Search in Google Scholar

[10] J. Wang, C. Jiang, and Z. Han, Vehicle networking: sensing-aided transportation information collection and diffusion, IEEE. Trans. Veh. Technol. 5 (2018), no. 67, 3813–3825.10.1109/TVT.2018.2796443Search in Google Scholar

[11] H. M. Zhao, J. Li, H. Y. Chen, J. Chen, Y. Li, J. J. Xu, et al. Intelligent diagnosis using continuous wavelet transform and gauss convolutional deep belief network, IEEE. Trans. Rel. 6 (2022), no. 13, 1–11.10.1109/TR.2022.3180273Search in Google Scholar

[12] Q. L. Zhang, Fully discrete convergence analysis of non-linear hyperbolic equations based on finite element analysis, Appl. Math. Nonlinear. Sci. 2 (2019), no. 4, 433–444.10.2478/AMNS.2019.2.00041Search in Google Scholar

[13] J. Z. Wu, J. B. Yuan, and W. Gao, Analysis of fractional factor system for data transmission in SDN, Appl. Math. Nonlinear. Sci. 1 (2019), no. 4, 191–196.10.2478/AMNS.2019.1.00025Search in Google Scholar

[14] M. S. M. Selvi, and L. Rajendran, Application of modified wavelet and homotopy perturbation methods to nonlinear oscillation problems, Appl. Math. Nonlinear. Sci. 2 (2019), no. 4, 351–364.10.2478/AMNS.2019.2.00030Search in Google Scholar

[15] B. Cao, W. Zhang, X. Wang, J. Zhao, Y. Gu, and Y. Zhang, A memetic algorithm based on two_Arch2 for multi-depot heterogeneous-vehicle capacitated arc routing problem, Swarm. Evol. Computat. 2021 (2021), no. 63, 100864.10.1016/j.swevo.2021.100864Search in Google Scholar

[16] H. Yuan, and Z. Y. Zha, Optimized monitoring network measurement point data transmission efficiency mathematical modeling simulation, Comput. Simul. 5 (2019), no. 36, 218–221.Search in Google Scholar

[17] Z. Xiong, Y. Wu, C. H. Ye, X. M. Zhang, and F. Xu, Color image chaos encryption algorithm combining crc and nine palace map, Multimed. Tools. Appl. 22 (2019), no. 78, 31035–31055.10.1007/s11042-018-7081-3Search in Google Scholar

[18] M. Medvedeva, T. E. Simos, C. Tsitouras, and V. Katsikis, Randomized time‐varying knapsack problems via binary beetle antennae search algorithm: Emphasis on applications in portfolio insurance, Math. Methods Appl. Sci. 2 (2021), no. 44, 2002–2012.10.1002/mma.6904Search in Google Scholar

[19] T. M. Ni, Y. Yao, H. Chang, L. Lu, H. G. Liang, A. B. Yan, et al. LCHR-TSV: Novel low cost and highly repairable honeycomb-based TSV redundancy architecture for clustered faults, IEEE. Trans. Comput. Aid. Des. Int. 10 (2020), no. 39, 2938–2951.10.1109/TCAD.2019.2946243Search in Google Scholar

[20] Y. Fang, H. Min, X. Wu, W. Wang, X. Zhao, and G. Mao, On-ramp merging strategies of connected and automated vehicles considering communication delay, IEEE. Trans. Intell. Transp. Syst. 2022 (2022), 1–15.10.1109/TITS.2022.3140219Search in Google Scholar

[21] S. Muhammad, Analytic approximate solution of rabies transmission dynamics using homotopy perturbation method, Matrix. Sci. Math. 1 (2020), no. 4, 1–5.Search in Google Scholar

[22] W. Zou, Y. Sun, Y. Zhou, Q. Lu, Y. Nie, T. Sun, et al. Limited sensing and deep data mining: a new exploration of developing city-wide parking guidance systems, IEEE Intel. Transp. Syst. Mag. 1 (2022), no. 14, 198–215.10.1109/MITS.2020.2970185Search in Google Scholar

[23] J. H. Wang, Y. C. Huang, T. Wang, C. L. Zhang, and Y. H. Liu, Fuzzy finite-time stable compensation control for a building structural vibration system with actuator failures, Appl. Soft. Comput. 2020 (2020), no. 93, 106372.10.1016/j.asoc.2020.106372Search in Google Scholar
Received: 2021-05-04
Revised: 2022-11-23
Accepted: 2022-11-25
Published Online: 2022-12-31

© 2022 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

  1. Regular Articles
  2. A random von Neumann theorem for uniformly distributed sequences of partitions
  3. Note on structural properties of graphs
  4. Mean-field formulation for mean-variance asset-liability management with cash flow under an uncertain exit time
  5. The family of random attractors for nonautonomous stochastic higher-order Kirchhoff equations with variable coefficients
  6. The intersection graph of graded submodules of a graded module
  7. Isoperimetric and Brunn-Minkowski inequalities for the (p, q)-mixed geominimal surface areas
  8. On second-order fuzzy discrete population model
  9. On certain functional equation in prime rings
  10. General complex Lp projection bodies and complex Lp mixed projection bodies
  11. Some results on the total proper k-connection number
  12. The stability with general decay rate of hybrid stochastic fractional differential equations driven by Lévy noise with impulsive effects
  13. Well posedness of magnetohydrodynamic equations in 3D mixed-norm Lebesgue space
  14. Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems
  15. Generic uniqueness of saddle point for two-person zero-sum differential games
  16. Relational representations of algebraic lattices and their applications
  17. Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms
  18. The equivalent condition of G-asymptotic tracking property and G-Lipschitz tracking property
  19. Arithmetic convolution sums derived from eta quotients related to divisors of 6
  20. Dynamical behaviors of a k-order fuzzy difference equation
  21. The transfer ideal under the action of orthogonal group in modular case
  22. The multinomial convolution sum of a generalized divisor function
  23. Extensions of Gronwall-Bellman type integral inequalities with two independent variables
  24. Unicity of meromorphic functions concerning differences and small functions
  25. Solutions to problems about potentially Ks,t-bigraphic pair
  26. Monotonicity of solutions for fractional p-equations with a gradient term
  27. Data smoothing with applications to edge detection
  28. An ℋ-tensor-based criteria for testing the positive definiteness of multivariate homogeneous forms
  29. Characterizations of *-antiderivable mappings on operator algebras
  30. Initial-boundary value problem of fifth-order Korteweg-de Vries equation posed on half line with nonlinear boundary values
  31. On a more accurate half-discrete Hilbert-type inequality involving hyperbolic functions
  32. On split twisted inner derivation triple systems with no restrictions on their 0-root spaces
  33. Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry
  34. Bifurcation and chaos in a discrete predator-prey system of Leslie type with Michaelis-Menten prey harvesting
  35. A posteriori error estimates of characteristic mixed finite elements for convection-diffusion control problems
  36. Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect
  37. An efficient finite element method based on dimension reduction scheme for a fourth-order Steklov eigenvalue problem
  38. Connectivity with respect to α-discrete closure operators
  39. Khasminskii-type theorem for a class of stochastic functional differential equations
  40. On some new Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in (p, q)-calculus with applications
  41. New properties for the Ramanujan R-function
  42. Shooting method in the application of boundary value problems for differential equations with sign-changing weight function
  43. Ground state solution for some new Kirchhoff-type equations with Hartree-type nonlinearities and critical or supercritical growth
  44. Existence and uniqueness of solutions for the stochastic Volterra-Levin equation with variable delays
  45. Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign
  46. Research of cooperation strategy of government-enterprise digital transformation based on differential game
  47. Malmquist-type theorems on some complex differential-difference equations
  48. Disjoint diskcyclicity of weighted shifts
  49. Construction of special soliton solutions to the stochastic Riccati equation
  50. Remarks on the generalized interpolative contractions and some fixed-point theorems with application
  51. Analysis of a deteriorating system with delayed repair and unreliable repair equipment
  52. On the critical fractional Schrödinger-Kirchhoff-Poisson equations with electromagnetic fields
  53. The exact solutions of generalized Davey-Stewartson equations with arbitrary power nonlinearities using the dynamical system and the first integral methods
  54. Regularity of models associated with Markov jump processes
  55. Multiplicity solutions for a class of p-Laplacian fractional differential equations via variational methods
  56. Minimal period problem for second-order Hamiltonian systems with asymptotically linear nonlinearities
  57. Convergence rate of the modified Levenberg-Marquardt method under Hölderian local error bound
  58. Non-binary quantum codes from constacyclic codes over 𝔽q[u1, u2,…,uk]/⟨ui3 = ui, uiuj = ujui⟩
  59. On the general position number of two classes of graphs
  60. A posteriori regularization method for the two-dimensional inverse heat conduction problem
  61. Orbital stability and Zhukovskiǐ quasi-stability in impulsive dynamical systems
  62. Approximations related to the complete p-elliptic integrals
  63. A note on commutators of strongly singular Calderón-Zygmund operators
  64. Generalized Munn rings
  65. Double domination in maximal outerplanar graphs
  66. Existence and uniqueness of solutions to the norm minimum problem on digraphs
  67. On the p-integrable trajectories of the nonlinear control system described by the Urysohn-type integral equation
  68. Robust estimation for varying coefficient partially functional linear regression models based on exponential squared loss function
  69. Hessian equations of Krylov type on compact Hermitian manifolds
  70. Class fields generated by coordinates of elliptic curves
  71. The lattice of (2, 1)-congruences on a left restriction semigroup
  72. A numerical solution of problem for essentially loaded differential equations with an integro-multipoint condition
  73. On stochastic accelerated gradient with convergence rate
  74. Displacement structure of the DMP inverse
  75. Dependence of eigenvalues of Sturm-Liouville problems on time scales with eigenparameter-dependent boundary conditions
  76. Existence of positive solutions of discrete third-order three-point BVP with sign-changing Green's function
  77. Some new fixed point theorems for nonexpansive-type mappings in geodesic spaces
  78. Generalized 4-connectivity of hierarchical star networks
  79. Spectra and reticulation of semihoops
  80. Stein-Weiss inequality for local mixed radial-angular Morrey spaces
  81. Eigenvalues of transition weight matrix for a family of weighted networks
  82. A modified Tikhonov regularization for unknown source in space fractional diffusion equation
  83. Modular forms of half-integral weight on Γ0(4) with few nonvanishing coefficients modulo ℓ
  84. Some estimates for commutators of bilinear pseudo-differential operators
  85. Extension of isometries in real Hilbert spaces
  86. Existence of positive periodic solutions for first-order nonlinear differential equations with multiple time-varying delays
  87. B-Fredholm elements in primitive C*-algebras
  88. Unique solvability for an inverse problem of a nonlinear parabolic PDE with nonlocal integral overdetermination condition
  89. An algebraic semigroup method for discovering maximal frequent itemsets
  90. Class-preserving Coleman automorphisms of some classes of finite groups
  91. Exponential stability of traveling waves for a nonlocal dispersal SIR model with delay
  92. Existence and multiplicity of solutions for second-order Dirichlet problems with nonlinear impulses
  93. The transitivity of primary conjugacy in regular ω-semigroups
  94. Stability estimation of some Markov controlled processes
  95. On nonnil-coherent modules and nonnil-Noetherian modules
  96. N-Tuples of weighted noncommutative Orlicz space and some geometrical properties
  97. The dimension-free estimate for the truncated maximal operator
  98. A human error risk priority number calculation methodology using fuzzy and TOPSIS grey
  99. Compact mappings and s-mappings at subsets
  100. The structural properties of the Gompertz-two-parameter-Lindley distribution and associated inference
  101. A monotone iteration for a nonlinear Euler-Bernoulli beam equation with indefinite weight and Neumann boundary conditions
  102. Delta waves of the isentropic relativistic Euler system coupled with an advection equation for Chaplygin gas
  103. Multiplicity and minimality of periodic solutions to fourth-order super-quadratic difference systems
  104. On the reciprocal sum of the fourth power of Fibonacci numbers
  105. Averaging principle for two-time-scale stochastic differential equations with correlated noise
  106. Phragmén-Lindelöf alternative results and structural stability for Brinkman fluid in porous media in a semi-infinite cylinder
  107. Study on r-truncated degenerate Stirling numbers of the second kind
  108. On 7-valent symmetric graphs of order 2pq and 11-valent symmetric graphs of order 4pq
  109. Some new characterizations of finite p-nilpotent groups
  110. A Billingsley type theorem for Bowen topological entropy of nonautonomous dynamical systems
  111. F4 and PSp (8, ℂ)-Higgs pairs understood as fixed points of the moduli space of E6-Higgs bundles over a compact Riemann surface
  112. On modules related to McCoy modules
  113. On generalized extragradient implicit method for systems of variational inequalities with constraints of variational inclusion and fixed point problems
  114. Solvability for a nonlocal dispersal model governed by time and space integrals
  115. Finite groups whose maximal subgroups of even order are MSN-groups
  116. Symmetric results of a Hénon-type elliptic system with coupled linear part
  117. On the connection between Sp-almost periodic functions defined on time scales and ℝ
  118. On a class of Harada rings
  119. On regular subgroup functors of finite groups
  120. Fast iterative solutions of Riccati and Lyapunov equations
  121. Weak measure expansivity of C2 dynamics
  122. Admissible congruences on type B semigroups
  123. Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions
  124. Inverse eigenvalue problems for rank one perturbations of the Sturm-Liouville operator
  125. Data transmission mechanism of vehicle networking based on fuzzy comprehensive evaluation
  126. Dual uniformities in function spaces over uniform continuity
  127. Review Article
  128. On Hahn-Banach theorem and some of its applications
  129. Rapid Communication
  130. Discussion of foundation of mathematics and quantum theory
  131. Special Issue on Boundary Value Problems and their Applications on Biosciences and Engineering (Part II)
  132. A study of minimax shrinkage estimators dominating the James-Stein estimator under the balanced loss function
  133. Representations by degenerate Daehee polynomials
  134. Multilevel MC method for weak approximation of stochastic differential equation with the exact coupling scheme
  135. Multiple periodic solutions for discrete boundary value problem involving the mean curvature operator
  136. Special Issue on Evolution Equations, Theory and Applications (Part II)
  137. Coupled measure of noncompactness and functional integral equations
  138. Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator
  139. Global weak solution of 3D-NSE with exponential damping
  140. Special Issue on Fractional Problems with Variable-Order or Variable Exponents (Part I)
  141. Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells
  142. A class of p1(x, ⋅) & p2(x, ⋅)-fractional Kirchhoff-type problem with variable s(x, ⋅)-order and without the Ambrosetti-Rabinowitz condition in ℝN
  143. Jensen-type inequalities for m-convex functions
  144. Special Issue on Problems, Methods and Applications of Nonlinear Analysis (Part III)
  145. The influence of the noise on the exact solutions of a Kuramoto-Sivashinsky equation
  146. Basic inequalities for statistical submanifolds in Golden-like statistical manifolds
  147. Global existence and blow up of the solution for nonlinear Klein-Gordon equation with variable coefficient nonlinear source term
  148. Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation
  149. Efficient fixed-point iteration for generalized nonexpansive mappings and its stability in Banach spaces
https://doi.org/10.1515/math-2022-0537
Keywords for this article
fuzzy comprehensive evaluation method; vehicle networking; data transmission; transmission mechanism; transport protocol; transmission path switching
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. A random von Neumann theorem for uniformly distributed sequences of partitions
  3. Note on structural properties of graphs
  4. Mean-field formulation for mean-variance asset-liability management with cash flow under an uncertain exit time
  5. The family of random attractors for nonautonomous stochastic higher-order Kirchhoff equations with variable coefficients
  6. The intersection graph of graded submodules of a graded module
  7. Isoperimetric and Brunn-Minkowski inequalities for the (p, q)-mixed geominimal surface areas
  8. On second-order fuzzy discrete population model
  9. On certain functional equation in prime rings
  10. General complex Lp projection bodies and complex Lp mixed projection bodies
  11. Some results on the total proper k-connection number
  12. The stability with general decay rate of hybrid stochastic fractional differential equations driven by Lévy noise with impulsive effects
  13. Well posedness of magnetohydrodynamic equations in 3D mixed-norm Lebesgue space
  14. Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems
  15. Generic uniqueness of saddle point for two-person zero-sum differential games
  16. Relational representations of algebraic lattices and their applications
  17. Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms
  18. The equivalent condition of G-asymptotic tracking property and G-Lipschitz tracking property
  19. Arithmetic convolution sums derived from eta quotients related to divisors of 6
  20. Dynamical behaviors of a k-order fuzzy difference equation
  21. The transfer ideal under the action of orthogonal group in modular case
  22. The multinomial convolution sum of a generalized divisor function
  23. Extensions of Gronwall-Bellman type integral inequalities with two independent variables
  24. Unicity of meromorphic functions concerning differences and small functions
  25. Solutions to problems about potentially Ks,t-bigraphic pair
  26. Monotonicity of solutions for fractional p-equations with a gradient term
  27. Data smoothing with applications to edge detection
  28. An ℋ-tensor-based criteria for testing the positive definiteness of multivariate homogeneous forms
  29. Characterizations of *-antiderivable mappings on operator algebras
  30. Initial-boundary value problem of fifth-order Korteweg-de Vries equation posed on half line with nonlinear boundary values
  31. On a more accurate half-discrete Hilbert-type inequality involving hyperbolic functions
  32. On split twisted inner derivation triple systems with no restrictions on their 0-root spaces
  33. Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry
  34. Bifurcation and chaos in a discrete predator-prey system of Leslie type with Michaelis-Menten prey harvesting
  35. A posteriori error estimates of characteristic mixed finite elements for convection-diffusion control problems
  36. Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect
  37. An efficient finite element method based on dimension reduction scheme for a fourth-order Steklov eigenvalue problem
  38. Connectivity with respect to α-discrete closure operators
  39. Khasminskii-type theorem for a class of stochastic functional differential equations
  40. On some new Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in (p, q)-calculus with applications
  41. New properties for the Ramanujan R-function
  42. Shooting method in the application of boundary value problems for differential equations with sign-changing weight function
  43. Ground state solution for some new Kirchhoff-type equations with Hartree-type nonlinearities and critical or supercritical growth
  44. Existence and uniqueness of solutions for the stochastic Volterra-Levin equation with variable delays
  45. Ambrosetti-Prodi-type results for a class of difference equations with nonlinearities indefinite in sign
  46. Research of cooperation strategy of government-enterprise digital transformation based on differential game
  47. Malmquist-type theorems on some complex differential-difference equations
  48. Disjoint diskcyclicity of weighted shifts
  49. Construction of special soliton solutions to the stochastic Riccati equation
  50. Remarks on the generalized interpolative contractions and some fixed-point theorems with application
  51. Analysis of a deteriorating system with delayed repair and unreliable repair equipment
  52. On the critical fractional Schrödinger-Kirchhoff-Poisson equations with electromagnetic fields
  53. The exact solutions of generalized Davey-Stewartson equations with arbitrary power nonlinearities using the dynamical system and the first integral methods
  54. Regularity of models associated with Markov jump processes
  55. Multiplicity solutions for a class of p-Laplacian fractional differential equations via variational methods
  56. Minimal period problem for second-order Hamiltonian systems with asymptotically linear nonlinearities
  57. Convergence rate of the modified Levenberg-Marquardt method under Hölderian local error bound
  58. Non-binary quantum codes from constacyclic codes over 𝔽q[u1, u2,…,uk]/⟨ui3 = ui, uiuj = ujui⟩
  59. On the general position number of two classes of graphs
  60. A posteriori regularization method for the two-dimensional inverse heat conduction problem
  61. Orbital stability and Zhukovskiǐ quasi-stability in impulsive dynamical systems
  62. Approximations related to the complete p-elliptic integrals
  63. A note on commutators of strongly singular Calderón-Zygmund operators
  64. Generalized Munn rings
  65. Double domination in maximal outerplanar graphs
  66. Existence and uniqueness of solutions to the norm minimum problem on digraphs
  67. On the p-integrable trajectories of the nonlinear control system described by the Urysohn-type integral equation
  68. Robust estimation for varying coefficient partially functional linear regression models based on exponential squared loss function
  69. Hessian equations of Krylov type on compact Hermitian manifolds
  70. Class fields generated by coordinates of elliptic curves
  71. The lattice of (2, 1)-congruences on a left restriction semigroup
  72. A numerical solution of problem for essentially loaded differential equations with an integro-multipoint condition
  73. On stochastic accelerated gradient with convergence rate
  74. Displacement structure of the DMP inverse
  75. Dependence of eigenvalues of Sturm-Liouville problems on time scales with eigenparameter-dependent boundary conditions
  76. Existence of positive solutions of discrete third-order three-point BVP with sign-changing Green's function
  77. Some new fixed point theorems for nonexpansive-type mappings in geodesic spaces
  78. Generalized 4-connectivity of hierarchical star networks
  79. Spectra and reticulation of semihoops
  80. Stein-Weiss inequality for local mixed radial-angular Morrey spaces
  81. Eigenvalues of transition weight matrix for a family of weighted networks
  82. A modified Tikhonov regularization for unknown source in space fractional diffusion equation
  83. Modular forms of half-integral weight on Γ0(4) with few nonvanishing coefficients modulo ℓ
  84. Some estimates for commutators of bilinear pseudo-differential operators
  85. Extension of isometries in real Hilbert spaces
  86. Existence of positive periodic solutions for first-order nonlinear differential equations with multiple time-varying delays
  87. B-Fredholm elements in primitive C*-algebras
  88. Unique solvability for an inverse problem of a nonlinear parabolic PDE with nonlocal integral overdetermination condition
  89. An algebraic semigroup method for discovering maximal frequent itemsets
  90. Class-preserving Coleman automorphisms of some classes of finite groups
  91. Exponential stability of traveling waves for a nonlocal dispersal SIR model with delay
  92. Existence and multiplicity of solutions for second-order Dirichlet problems with nonlinear impulses
  93. The transitivity of primary conjugacy in regular ω-semigroups
  94. Stability estimation of some Markov controlled processes
  95. On nonnil-coherent modules and nonnil-Noetherian modules
  96. N-Tuples of weighted noncommutative Orlicz space and some geometrical properties
  97. The dimension-free estimate for the truncated maximal operator
  98. A human error risk priority number calculation methodology using fuzzy and TOPSIS grey
  99. Compact mappings and s-mappings at subsets
  100. The structural properties of the Gompertz-two-parameter-Lindley distribution and associated inference
  101. A monotone iteration for a nonlinear Euler-Bernoulli beam equation with indefinite weight and Neumann boundary conditions
  102. Delta waves of the isentropic relativistic Euler system coupled with an advection equation for Chaplygin gas
  103. Multiplicity and minimality of periodic solutions to fourth-order super-quadratic difference systems
  104. On the reciprocal sum of the fourth power of Fibonacci numbers
  105. Averaging principle for two-time-scale stochastic differential equations with correlated noise
  106. Phragmén-Lindelöf alternative results and structural stability for Brinkman fluid in porous media in a semi-infinite cylinder
  107. Study on r-truncated degenerate Stirling numbers of the second kind
  108. On 7-valent symmetric graphs of order 2pq and 11-valent symmetric graphs of order 4pq
  109. Some new characterizations of finite p-nilpotent groups
  110. A Billingsley type theorem for Bowen topological entropy of nonautonomous dynamical systems
  111. F4 and PSp (8, ℂ)-Higgs pairs understood as fixed points of the moduli space of E6-Higgs bundles over a compact Riemann surface
  112. On modules related to McCoy modules
  113. On generalized extragradient implicit method for systems of variational inequalities with constraints of variational inclusion and fixed point problems
  114. Solvability for a nonlocal dispersal model governed by time and space integrals
  115. Finite groups whose maximal subgroups of even order are MSN-groups
  116. Symmetric results of a Hénon-type elliptic system with coupled linear part
  117. On the connection between Sp-almost periodic functions defined on time scales and ℝ
  118. On a class of Harada rings
  119. On regular subgroup functors of finite groups
  120. Fast iterative solutions of Riccati and Lyapunov equations
  121. Weak measure expansivity of C2 dynamics
  122. Admissible congruences on type B semigroups
  123. Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions
  124. Inverse eigenvalue problems for rank one perturbations of the Sturm-Liouville operator
  125. Data transmission mechanism of vehicle networking based on fuzzy comprehensive evaluation
  126. Dual uniformities in function spaces over uniform continuity
  127. Review Article
  128. On Hahn-Banach theorem and some of its applications
  129. Rapid Communication
  130. Discussion of foundation of mathematics and quantum theory
  131. Special Issue on Boundary Value Problems and their Applications on Biosciences and Engineering (Part II)
  132. A study of minimax shrinkage estimators dominating the James-Stein estimator under the balanced loss function
  133. Representations by degenerate Daehee polynomials
  134. Multilevel MC method for weak approximation of stochastic differential equation with the exact coupling scheme
  135. Multiple periodic solutions for discrete boundary value problem involving the mean curvature operator
  136. Special Issue on Evolution Equations, Theory and Applications (Part II)
  137. Coupled measure of noncompactness and functional integral equations
  138. Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator
  139. Global weak solution of 3D-NSE with exponential damping
  140. Special Issue on Fractional Problems with Variable-Order or Variable Exponents (Part I)
  141. Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells
  142. A class of p1(x, ⋅) & p2(x, ⋅)-fractional Kirchhoff-type problem with variable s(x, ⋅)-order and without the Ambrosetti-Rabinowitz condition in ℝN
  143. Jensen-type inequalities for m-convex functions
  144. Special Issue on Problems, Methods and Applications of Nonlinear Analysis (Part III)
  145. The influence of the noise on the exact solutions of a Kuramoto-Sivashinsky equation
  146. Basic inequalities for statistical submanifolds in Golden-like statistical manifolds
  147. Global existence and blow up of the solution for nonlinear Klein-Gordon equation with variable coefficient nonlinear source term
  148. Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation
  149. Efficient fixed-point iteration for generalized nonexpansive mappings and its stability in Banach spaces
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 26.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/math-2022-0537/html
Scroll to top button