Mathematical Modeling of Multiscale Network Traffic Combination Prediction Based on Fuzzy Support Vector Machine

Zhang, Feng

doi:https://doi.org/10.1155/2023/9972636

Mathematical Problems in Engineering

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Abstract Introduction Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 9972636 | https://doi.org/10.1155/2023/9972636

Mathematical Modeling of Multiscale Network Traffic Combination Prediction Based on Fuzzy Support Vector Machine

Feng Zhang¹

Academic Editor: Junwei Ma

Received04 Feb 2023

Revised25 Mar 2023

Accepted29 Mar 2023

Published17 Apr 2023

Abstract

In the process of multiscale network traffic prediction using a single model, the results are often single, resulting in a decline in the accuracy of multiscale network traffic prediction. In order to solve this problem effectively, a mathematical modeling method of multiscale network traffic combination prediction based on fuzzy SVM is proposed. Firstly, according to the multiscale network approximation signal, the multiscale network traffic feature function is constructed to complete the multiscale network traffic feature extraction. Secondly, according to the feature extraction results, the fuzzy membership function is introduced into the SVM, and the fuzzy SVM is used to classify the multiscale network traffic. Finally, based on the traffic classification results, the combination prediction of multiscale network traffic is completed by combining the grey Verhulst prediction model with the GNN model. The experimental results show that the prediction accuracy of this method for multiscale network traffic is higher, and the prediction accuracy can always maintain above 95%, and the MSE and MAE values are relatively low.

1. Introduction

Instant messaging software, high-definition video transmission, and other applications relying on high-speed networks are increasingly popular, which puts forward higher requirements for the Internet transmission capacity and information carrying capacity. At this stage, the network has become an inseparable part of people’s lives, and the network is an important foundation of the information society, constantly promoting economic development and social progress [1, 2]. As a special time series, network traffic has the characteristics of being multiscale, nonlinear, and scale-dependent [3]. Influenced by factors such as protocols and human behavior in the network, network traffic has multiscale characteristics. This multiscale performance is shown in low-level scale traffic that is affected by network protocols and high-level scale traffic that is periodically affected by human daily activities [4]. Influenced by user behavior and network environment at different times, network traffic is nonlinear. This kind of nonlinearity is manifested in as follows: with the change of time, the network traffic fluctuates and shows a nonlinear trend. Due to the correlation between different time scales, network traffic is scale-dependent [5]. This dependence is shown as follows: network traffic at different scales has different characteristics and laws, high-level scales have long-term laws, low-level scales have short-term laws, and high-level scale prediction needs to consider images of short-term laws [6]. Network traffic prediction needs to fully consider the complexity of network traffic. Accurate network traffic prediction not only helps to allocate network bandwidth resources reasonably and improve network service quality, but also helps to improve the security of network communication. Therefore, network traffic prediction has always been a research hotspot in the field of the network.

Reference [7] proposes a network traffic prediction method based on local mean decomposition (LMD) improved Gaussian process regression (GPR) optimization. LMD is used to decompose the network traffic to obtain subsequences of multiple traffic data. The network traffic subsequence is modeled and analyzed by GPR. The scope of vision in the process of ant search is optimized to improve the comprehensive performance and solving ability of ants in the process of optimization. On this basis, Levy flight is used to update the step size of ant search to ensure that the ants have better global search performance, and then the ant colony algorithm is used to optimize the parameters to obtain the relevant network traffic prediction results. This method considers relatively few factors in the process of network traffic prediction, resulting in higher prediction MAE values and reduced prediction accuracy. Reference [8] proposes a network traffic prediction method based on the two-way gated recurrent unit (GRU) model. Based on the GRU neural network, a network model of the bidirectional GRU neural network and artificial neural network stack is designed, with multidimensional vectors such as flow characteristics, time characteristics, and event characteristics as the input of the model. In order to improve the accuracy of traffic peak prediction, the sample rebalancing method and self-defined loss function are used to realize network traffic prediction by using the artificial neural network stack network model. However, in the actual application process, there is a problem of low prediction accuracy, and there is still a certain gap with the ideal application effect. Reference [9] proposes a network traffic prediction method based on generating confrontation networks. Firstly, the generated network captures the spatiotemporal characteristics of traffic and the type characteristics of base stations, inputs the splicing features into the composite residual module to generate the predicted traffic, and inputs the generated traffic into the discrimination network. Then, judge whether the generated traffic is real traffic or predicted traffic by judging the network. Finally, through the game confrontation between the generating network and the discriminating network, the generating network generates high-precision traffic prediction results. Although this method can complete the prediction of network traffic, it constructs a single prediction model that considers fewer traffic influencing factors, resulting in poor accuracy in the final traffic prediction. Reference [10] proposes a simple Gaussian kernel width estimation method for network traffic prediction based on least squares support vector machines. In order to improve the accuracy of network traffic prediction and overcome the shortcomings of least square support vector machine (LSSVM) in the process of network traffic prediction, such as slow convergence speed and being prone to falling into local minima, a network traffic security prediction model based on LSSVM with a simple estimation of Gaussian kernel width was proposed. The model assigns different Gaussian kernel widths to each sampling point based on the local density of the sampling points and inputs the data from the sampling points into the model to obtain relevant prediction results. However, this method has the problem of high MSE values and large prediction errors. Reference [11] proposes a traffic prediction method for artificial intelligence 6G spatiotemporal cellular networks based on multitask deep learning. A new multitask deep learning framework has been developed for urban cellular network traffic prediction. Functionally, the framework is mainly composed of a dual module feature sharing layer and a multitask learning layer. The former aims to mine long-term spatiotemporal correlations and local spatiotemporal fluctuations in data, respectively, through a new combination of ConvGRU and the 3D-convolutional neural network. For the latter, each task is to predict traffic data for a specific service based on a fully connected network and obtain relevant traffic prediction results. However, this method has the problem of low prediction accuracy, and there is still a certain gap with the ideal application effect.

In order to solve the problems of low prediction accuracy and high MSE and MAE values in the above methods, this study proposes a mathematical modeling method of multiscale network traffic combination prediction based on fuzzy support vector machine. This method can help operators cope with upcoming congestion as early as possible and carry out network expansion, adjustment, and optimization in advance. Not only that, but also it can improve communication network efficiency and customize and expand network value-added services, which is of great significance in network management, network planning and design, and improving network application performance.

2. Mathematical Modeling Method for Multiscale Network Traffic Combination Prediction

2.1. Multiscale Network Traffic Feature Extraction

Multiscale network traffic has the characteristics of multilevel, long correlation, and strong similarity, so the prediction of multiscale network traffic is difficult [10–12]. Therefore, before the prediction of multiscale network traffic, it is necessary to extract the characteristics of multiscale network traffic, so that the characteristic details of multiscale network traffic can be better described [13].

In order to achieve the important goal of accurate extraction of multiscale network traffic characteristics, we assume that the approximation signal in the traffic is , where is the multiscale parameter of the signal and is the detailed signal in the multiscale network traffic. The calculation formula for constructing the multiscale network traffic approximation signal based on the above signals is as follows:

There is a subspace in the multiscale network. Mapping multiscale network traffic to subspace can describe the relationship between traffic approximation signal and traffic :

With the support of the mapping relation factor and scale function [14–16], the relationship shown in formula (2) can be rewritten as

The expression of the mapping relation factor is

According to the above principles, the detailed signal in multiscale network traffic can be calculated, and the results are as follows:

In the formula, represents the mapping relation function [17], whose expression can be written as

According to the above multiscale network traffic characteristic function, we complete the extraction of multiscale network traffic characteristics, and the results are as follows:

In the discrete information with a relatively single variable, the construction of a traffic feature extraction function can complete the feature extraction of multiscale network traffic and ensure the accuracy.

2.2. Multiscale Network Traffic Classification Based on Fuzzy Support Vector Machine

After the feature extraction of multiscale network traffic is completed, in order to improve the authenticity and reliability of multiscale network traffic combination prediction results, fuzzy support vector machine is used for traffic classification. Multiscale network traffic can reflect the operation status of the network, especially the defect location and status of the network. The basis for realizing the above functions is the classification of multiscale network traffic [18–20].

Traditional support vector machines divide samples into two opposing classes through an optimal hyperplane. However, in practical applications, it is generally necessary to solve the problem of multiclass recognition, and in some cases, each sample may not be fully classified into a certain class, that is, there is a certain fuzzy membership relationship between the samples and the class [21]. The combination of the fuzzy support vector machine algorithm and fuzzy mathematics method can adjust the optimal plane by increasing the membership value based on the basic support vector machine algorithm, which can reduce the impact of noise or outliers and improve classification accuracy. Applying it to the process of multiscale network traffic classification can improve the accuracy of multiscale network traffic classification, thereby laying a solid foundation for subsequent multiscale network traffic prediction. There are no other viable alternatives.

The classification principle of support vector machine is to divide the optimal classification plane, so as to classify different types of traffic [22]. Assuming that multiscale network traffic samples are represented by , the classification hyperplane of traffic samples is . The support vector machine optimal classification hyperplane diagram is shown in Figure 1.

To ensure the classification effect of multiscale network traffic, the following constraints are set:where represents relaxation variables and and represent different support vector machine parameters.

Under the above constraints, the constraint expression of the maximum classification interval can be constructed when the classification interval is .where represents the constraint constant, represents the penalty term, and represents the optimized support vector machine parameters [23–25].

The dual algorithm is used to transform the solving problem under the above constraints into a dual problem, and the calculation expression iswhere represents different Lagrange multipliers.

The above calculation results are more applicable to the classification of linear data, but the multiscale network traffic data contains a large number of nonlinear data. Therefore, it is necessary to construct the objective function of multiscale network traffic data classification with the support of kernel function. The specific description of this function is as follows:where represents the kernel function.

In order to further improve the classification effect of multiscale network traffic, fuzzy membership is introduced into support vector machine to calculate the fuzzy form of multiscale network traffic, where represents fuzzy membership and . Therefore, the constraint conditions of the hyperplane can be transformed into the following forms:

According to the fuzzy membership , the weight of different traffic points can be adjusted, mainly by adjusting the fuzzy membership to increase the gap between different traffic types, so as to improve the accuracy of multiscale network traffic classification. However, when calculating the fuzzy membership degree, it is necessary to consider the characteristics and imbalance of multiscale network traffic [26, 27]. The calculation process of fuzzy membership is as follows:

The number of samples in the multiscale network traffic training set is , . Assume that the fuzzy membership functions of the two multiscale network traffic categories are and respectively, and the expression of the two is

In the formula, represents the importance of in this category.

is defined as follows:

In the formula, represents the Euclidean distance between and the class center [28] and represents the farthest distance from the class center in the sample class.

According to the above calculation results, the calculation of fuzzy membership degree in fuzzy support vector machine is completed. Through the fuzzy membership degree, the special points and category imbalance problems in multiscale network traffic classification can be solved. The calculated fuzzy membership degree can be substituted into formula (12) to complete the classification of multiscale network traffic.

2.3. Mathematical Modeling of Multiscale Network Traffic Combination Prediction

Firstly, the grey system theory and Verhulst model are combined to build the grey Verhulst prediction model. Then, the classified scale network traffic non-negative original data sequence can be expressed as

For the data sequence shown in formula (15), the following sequence can be obtained by replacing each element with the preceding element:

Then, the ^th data sequence is expressed by the following formula:

is set as the sequence formed by the mean value of the elements adjacent to :

Then, the sequence formed by the mean value of the ^th neighboring element is expressed by the following formula:

In the formula, .

is the original multiscale network traffic, is the cumulative sequence of and is the adjacent mean sequence of , so the grey Verhulst prediction model can be constructed.where and represent different grey parameters.

The whitening equation of grey Verhulst prediction model is as follows:

The parameters in formula (21) are calculated using the least square principle [29, 30], and the parameter adjustment term is expressed by the following formula:

Including

With as the initial condition, build the time function of the grey Verhulst prediction model:

The sequence obtained from the above functions is subtracted to obtain the fitting results of the original multiscale network traffic sequence.

In order to ensure the accuracy of multiscale network traffic prediction, a grey neural network prediction model is built based on the grey system. The grey system can improve the prediction ability of regular cross data, get a strong relationship sequence from the random data, and establish the corresponding mathematical model. The structure of the series grey neural network model is shown in Figure 2.

Multiscale network traffic is affected by many factors, resulting in its overall regular intersection. In order to prevent the problem of large traffic deviation in the grey prediction process, the neural network is used to correct the residual between the results of the grey Verhulst prediction model and the actual results, so that the prediction results of multiscale network traffic are closer to the actual value.

The specific steps of the multiscale network traffic prediction combination model based on the grey neural network are as follows:

Step 1. Calculate the original restoration sequence of the multiscale network traffic Verhulst model through formula (24), and compare the difference between the fitting result and the actual result.

Step 2. Subtract the fitting result and the actual result to build the residual sequence model.

Step 3. Take the output result of the residual sequence model as the input value of the artificial neural network and use the artificial neural network to predict the residual result to obtain the residual prediction result .

Step 4. Build a multiscale network traffic correction prediction model.Among them, is the multiscale network traffic prediction result obtained from the multiscale network traffic combination model.

3. Experimental Verification

In order to verify the practical application effect of the proposed mathematical modeling method of multiscale network traffic combination prediction based on fuzzy support vector machine, relevant experimental tests are carried out.

3.1. Experimental Data

Multiscale network traffic prediction is based on network traffic. In this experiment, the NetFlow method is used to collect network traffic. The NetFlow method can judge whether the network traffic of the traffic router enters a known flow and update the cache flow record if it is determined to be a known flow. If it is determined that the flow is not known, the new flow will be recorded in the cache. The cache record is saved and deleted. The NetFlow collection model is shown in Figure 3.

As can be seen from Figure 3, the work of the NetFlow collection model mainly includes data export, data collection, and data analysis. The collected traffic data is output in the format of NetFlow.

In order to obtain sufficient and effective network traffic, a NetFlow collection model is used to collect traffic within the network for 50 days, with a collection interval of 1 hour. 24 traffic data are obtained within a day, and a total of 1200 traffic data are collected within 50 days. Part of the flow data is shown in Figure 4.

3.2. Experimental Scheme

The experimental scheme is set before the experiment, and the parameter settings are as follows:

Taking the multiscale network traffic feature extraction accuracy, classification accuracy, prediction accuracy, root mean square error (MSE), and mean absolute error (MAE) as experimental comparison indicators, the method in this article is compared with the method in [8] and [9].

The calculation formula of the root mean square error (MSE) and mean absolute error (MAE) is

In the formula, represents the actual value of multiscale network traffic, and represents the predicted value of traffic.

3.3. Analysis of Experimental Results

After the collection of experimental flow samples and the setting of the experimental scheme, the comparative experiments of the method in this article and the methods in different literatures are carried out according to different test indicators, so as to obtain the relevant experimental results.

3.3.1. Accuracy of Multiscale Network Traffic Feature Extraction

Since the collected network traffic contains many types, in order to ensure the prediction effect of multiscale network traffic, multiscale network traffic should be screened out from the collected network traffic. This operation is based on the characteristics of multiscale network traffic, which can improve the screening accuracy of multiscale network traffic and help to improve the accuracy of multiscale network traffic prediction. Therefore, the accuracy of multiscale network traffic feature extraction is taken as the index to compare and verify the practical application effect of the proposed method with the method in [8] and [9]. The precision results of multiscale network traffic feature extraction by the three methods are shown in Figure 5.

From the comparison results of multiscale network traffic feature extraction accuracy shown in Figure 5, it can be seen that with the increase of traffic, the feature extraction accuracy of the three methods has a significant difference, in which the feature extraction accuracy curve of the reference [8] method shows a gradual declining trend, while the feature extraction accuracy curve of the reference [9] method shows a trend of rising first and then falling, but the overall feature extraction accuracy level still needs to be improved. On the whole, the feature accuracy of the method in [8] and [9] is not more than 80%. Compared to the two literature comparison methods, the accuracy of multiscale network traffic feature extraction in this method has always been maintained at over 90%, and the fluctuation range of the feature extraction accuracy curve in this method is small, indicating that the accuracy of feature extraction in this method is high and relatively stable. The reason is that this method builds a multiscale network traffic feature function based on the multiscale network approximation signal to complete the multiscale network traffic feature extraction. Therefore, this method has high accuracy in multiscale network traffic feature extraction.

3.3.2. Classification Accuracy of Multiscale Network Traffic

Taking the flow classification as the test index, the comparative test experiments of different methods are carried out. The multiscale network traffic data classification accuracy test results of the method in this article and the method in [8] and [9] are shown in Figure 6.

From the multiscale network traffic classification accuracy results shown in Figure 6, it can be seen that with the increase of experimental time, the classification accuracy curves of the reference [8] method and reference [9] method show a significant fluctuation. The fluctuation range of the traffic classification accuracy of the method in [8] is 11%–75%, and the fluctuation range of the traffic classification accuracy of the method in [9] is 17%–64%, indicating that the classification accuracy of these two methods is relatively low and unstable, and it is difficult to meet practical application requirements. However, the accuracy of traffic classification in this method varies between 92% and 97%, indicating that this method has a high accuracy of multiscale network traffic classification and can still maintain a high classification quality despite continuous increase in time. The reason is that this method introduces a fuzzy membership function into support vector machines based on the feature extraction results and uses fuzzy support vector machines for multiscale network traffic classification processing. Therefore, this method has high classification accuracy.

3.3.3. Multiscale Network Traffic Prediction Accuracy

The prediction accuracy is the most intuitive performance of the multiscale network traffic prediction method. The higher the prediction accuracy is, the stronger the performance of the prediction method is. In order to fully verify the prediction accuracy performance of the method in this article, the actual effect of the method in this article and the two methods in the literature are compared and verified. The comparison results of multiscale network traffic prediction accuracy of the three methods are shown in Figure 7.

Figure 7 intuitively presents the precision results of multiscale network traffic prediction using the method in this article and the methods in [8] and [9]. The multiscale network traffic prediction accuracy of the method in [8] is always between 21% and 79%, and the multiscale network traffic prediction accuracy of the method in [9] is always between 24% and 70%. However, the multiscale traffic prediction accuracy of the method in this article is stable at about 95%, and there is no significant fluctuation. It is said that this method has high prediction accuracy. The reason is that this method is based on traffic classification results and uses a combination of the grey Verhulst prediction model and grey neural network model to complete the combined prediction of multiscale network traffic. Therefore, the prediction accuracy of this method has always maintained a high level.

3.3.4. Predicted MSE and MAE

In order to further verify the multiscale network traffic prediction performance of this method, the root mean square error (MSE) and mean absolute error (MAE) are used as the relevant indicators to verify the prediction performance of the three methods. The method in this article, in [8], and in [9] are repeated for 50 times for multiscale network traffic prediction. The MSE and MAE results are shown in Table 1.

The MSE and MAE in Table 1 show that the root mean square error (MSE) and mean absolute error (MAE) of the method in this article are significantly lower than those in the reference [8] method and reference [9] method. From the average results, the mean MSE and MAE of the method in this article are 0.013094 and 0.09435, respectively, the mean MSE and MAE of the reference [8] method are 0.191732 and 0.141872, respectively, and the mean MSE and MAE of the reference [9] method are 0.08570 and 0.128146, respectively. Therefore, the traffic prediction performance of this method has been improved. The reason is that this method uses fuzzy support vector machines to classify and process multiscale network traffic by extracting multiscale network traffic characteristics. The method of combining the grey Verhulst prediction model and grey neural network model is used to complete the combined prediction of multiscale network traffic, in order to maximize the performance of network traffic prediction.

4. Conclusion

In the process of using a single model to predict multiscale network traffic, the results often have a single nature, resulting in a decline in the accuracy of multiscale network traffic prediction. Therefore, a method for constructing a multiscale network traffic combination prediction mathematical model based on fuzzy support vector machine is proposed. This method mainly extracts multiscale network traffic characteristics and uses fuzzy support vector machines to classify multiscale network traffic. The method of combining the grey Verhulst prediction model and grey neural network model is used to complete the combined prediction of multiscale network traffic. The experimental results show that the accuracy of multiscale network traffic feature extraction is always above 90%, the accuracy of traffic classification varies between 92% and 97%, and the accuracy of multiscale traffic prediction is stable at about 95%. The accuracy of feature extraction, traffic classification, and traffic prediction is high, and the MSE and MAE values are low, indicating that the prediction effect of this method is better. The future research direction is to explore the application of this method in other fields, so as to further expand the application scope of this method and promote the further development of research in the field of network traffic prediction.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This research was supported by the Key Natural Science Research Projects in Anhui Province (no. 2022AH052453).

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Copyright © 2023 Feng Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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