The structure of the mathematical model of computer network traffic data based on a periodically correlated stochastic process has been substantiated, which has become the basis for developing a method and a computer tool for predicting traffic load in order to optimize network functioning and improve the quality of providing Internet services to consumers. A method and algorithm for synphase processing of computer network traffic load data have been implemented, which made it possible to obtain predictive indicators in the form of 3D synphase components and their 2D averaged estimates. A computer (software) tool has been developed in the Matlab Guide environment for processing network traffic load data, which provides synphase load forecasting, in particular for individual elements of network equipment.
Today, most areas of human activity are closely interconnected with the use of modern Internet technologies. This creates the need to ensure the reliability and stability of the functioning of such technologies, in particular computer networks.
One of the key parameters of a computer network is traffic, which plays an important role in the processes of assessing user activity, monitoring network operation, as well as analyzing its functioning. These procedures are aimed at optimizing the use of network resources and managing under overload conditions.
Predicting network traffic load le vels in time space is one of the methods of avoiding congestion, which allows to increase the efficiency of network resource use and optimize its performance. For this purpose, various mathematical models and computational methods are used.
The application of methods for predicting the load on computer networks in telemedical systems is becoming particularly relevant, where biomedical data [6, 7, 10, 11, 13-17, 19, 20] processing requires a stable and predictable information transmission channel, which is critically important for ensuring continuous monitoring and diagnostics in real time.
Among the most well-known traffic models, one can distinguish the Poisson distribution [
Based on these models, various computational methods and computer (software) tools have been created for analyzing traffic data in order to predict its load. However, all of these models, with the exception of the PCSP, do not take into account the relationship between traffic values in different daily periods, which allows tracking the dynamics of traffic changes in time space. This is especially important for network load forecasting tasks.
The authors Khvostivskyi V.M., Osukhivska H.M. and Khvostovskyi M.O. used only the component method for processing traffic data, without revealing the full potential of ETSS. Therefore, the development of a method and a computer (software) tool for traffic forecasting based on the synphase method of a periodically correlated random process is an urgent task.
To substantiate the structure of the traffic load data model as the core of the method and computer forecasting tool, real data from the Internet provider UFONet in Ternopil was used. A graphical representation of computer network traffic registered for 7 days (from 01.07.2024 to 07.07.2024) within the Park Complex residential complex is presented in Figure 1.
During the day, for each implementation, clearly pronounced peaks in traffic load data are observed (Fig. 2), which demonstrate daily changes in amplitude, time, and phase values in time space (Fig. 3).
Due to the presence of variability (Fig. 2), a deterministic approach to describing traffic load data is not correct for mathematical description of traffic load data. In this case, it is necessary to use a stochastic approach to modeling traffic load data, and on its basis to create a method and computer tool for predicting network traffic load data.
The phase φn (Fig. 3) refers to a certain numerical value n, which quantitatively characterizes the measure of the time shift relative to the beginning of fluctuations in the values of traffic load data for the nth day relative to the previous days (n-1)T.
Based on the analysis of the time-phase structure of the traffic load data (Fig. 3), it was found that for the nth day, which is localized in the time intervals of the period T, there is a variability of the phase values φ1–φ10 for the data ξ1(t)–ξ10(t). The fact of such variability indicates that the mathematical model of traffic load data should provide the possibility of studying the variability of time dependencies for each of the nth days to provide a procedure for predicting the behavior of the network and its components in the future.
The model of network traffic load data behavior, presented as a PCSP, allows you to effectively take into account the daily repetition (periodicity) of the signal realization, its time-amplitude variability (stochasticity), and also provides the use of methods and algorithms to study their relationship using the following expression [9]: ξ (t )= ∑ ξk (t ) e− j 2 π k /T, k∈ Z (1) where ξk (t ) – stationary stochastic components of daily network traffic data;
e− j 2 π k /T – repeating component of network traffic data with an interval of T=24 hours.
The network traffic data model (1) provides extensive processing and analysis capabilities, including synphase, filtering, and component processing, to obtain quantitative and informative indicators. These indicators reflect the level of mutual correlation of the amplitude-time characteristics of traffic at different times of the day.
Studying the level of stochasticity of mutual correlation between network traffic data indicators at different times of the day allows for load forecasting, determining in advance the optimal operating modes of network equipment. This helps ensure stable and high-quality provision of communication and information services to network users.
The methods (tools) of the PCSP are distinguished by high efficiency, as they implement three key approaches to processing network traffic data: synphase, component and filter. The main difference between synphase and component processing is the processing sequence: synphase processing, the traffic covariance is first determined, after which the corresponding frequency components are calculated using the Fourier transform. In contrast, component and filter processing immediately perform an estimate of the covariance in the frequency domain.
Synphase processing of network traffic data is based on the assumption that informative traffic features can be represented as functions with recurring, time-dependent characteristics in the form of synphase components:
B^k (u)= 1 ∫T b^ξ (t , u) e− j 2 π k /T, T 0 (2)
N−1 0 0 where b^ξ (t , u)=l i m ∑ ξ (t +u+ k T ) ξ (t + k T ) - parametric covariance;
k=0 Т — period of load traffic data equal to the duration of a day; u — time shift.
Synphase components allow us to isolate characteristic features of network traffic data, which helps to increase the accuracy of predicting its load in the general context.
The main stages of synphase traffic forecasting include the following structural elements: - Synphase processing of computer network traffic data according to expression (2), which calculates an informative forecast indicator in the form of synphase components.
- Evaluation of the synphase components calculated at the previous stage, the form and value of which make it possible to forecast the traffic load of a computer network.
- The process of making a decision based on the shape and indicators of the estimated synphase components regarding the forecast of computer network traffic load.
The foundation of synphase processing is: the procedure of centering relative to the mean; the formation of stationary components; the calculation of synphase components by correlation and Fourier transformation. These operations determine the computational complexity of the synphase processing process, which is illustrated in Fig. 4.
Given the complexity of the expression characterizing the synphase method of processing computer network traffic data, a sequence of synphase processing was developed, which is presented in Fig. 5.
5 – calculation of synphase components B^k (u ) as Fourier transforms of the covariance b^ξ (t , u );
7 – making a decision on the level of computer network traffic load forecasting based on the estimated B^k (u ).
The sequence shown in Fig. 5 provides the possibility of developing an algorithm for synphase processing of traffic data for the further development of a computer tool for predicting the traffic load of a computer network.
Fig. 6 presents an algorithm for synphase processing (synphase prediction core) of computer network traffic data.
The implemented algorithm (Fig. 6) allows you to programmatically create a computer system for synphase processing of network traffic, focused on calculating synphase components, which act as indicators for effective prediction of computer network traffic load.
The GUIDE utility, as a component of the MATLAB environment, allows you to programmatically implement a computer system with a graphical interface for predicting computer network traffic according to the developed algorithm (Fig. 6).
Fig. 7. shows the appearance of the computer system and the result of predicting computer network traffic load.
An enlarged fragment of the averaged synphase 3D components is shown in Fig. 9.
According to the synphase components of the traffic data, which are shown in Fig. 8-10, it was found that in the period from 03:00 to 05:00 and from 17:00 to 22:00, an increase in the traffic load by consumers is observed. At these times, provider should activate the operation of most of the network equipment to avoid overload modes on their functioning. At other times, providers should transfer a significant part of the network equipment to the economical consumption mode in order to save electricity and increase the resource of equipment operation. In order to verify the correctness of the decision made, test data of unchanged traffic was created within 7 days, the results of its synphase processing were obtained using the implemented program (Fig. 10).
Based on the processing of stable traffic data (Fig. 1 0), it was ascertained that the synphase components are at zero level both in the 3D representation and in their averaged form.
In the case of variable computer network traffic data (Fig. 8-10), an increase in the power level of synphase components is observed depending on time (an increase in traffic consumption by consumers), with the main localization on 3D components and in their averaged implementation.
Such variability of the characteristics of synphase components reflects the dynamics of the traffic load of the computer network in the future, which is relevant for the forecasting problem.
The calculated synphase components of computer network traffic data submitted via the PC SP numerically reflect the future behavior of network load by consumers, thereby providing a clear solution to the problem of predicting network traffic load in order to optimize the functioning of network equipment based on the power of synphase components.
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