Prediction of Critical Filling of a Storage Area Network by Machine Learning Methods

Abstract

The introduction of digital technologies into the activities of companies is based on software and hardware systems, which must function reliably and without interruption. The forecasting of the completion of storage area networks (SAN) is an essential tool for ensuring the smooth operation of such systems. The aim of this study is to develop a system of the modelling and simulation of the further loading of SAN on previously observed load measurements. The system is based on machine learning applied to the load prediction problem. Its novelty relates to the method used for forming input attributes to solve the machine learning problem. The proposed method is based on the aggregation of data on observed loading measurements and the formalization of the problem in the form of a regression analysis problem. The artificial dataset, synthesized stochastically according to the given parameter intervals and simulating SAN behavior, allowed for more extensive experimentation. The most effective algorithm is CatBoost (gradient boosting on decision trees), which surpasses other regression analysis algorithms in terms of R2 scores and MAE. The selection of the most significant features allows for the simplification of the prediction model with virtually no loss of accuracy, thereby reducing the number of confessions used. The experiments show that the proposed prediction model is adequate to the situation under consideration and allows for the prediction of the SAN load for the planning period under review with an R2 value greater than 0.9. The model has been validated on a series of real data on SAN.

1. Introduction

Storage area networks (SAN) constitute a software and hardware complex for organizing the reliable storage of various types of data and providing quick and guaranteed access to them. SAN are an essential component of information systems for organizations that process large volumes of data and use them to implement decision support systems. Each storage area network has a number of characteristics that affect its performance in a particular organization. One of the important characteristics is the size of the used volumes (memory capacity), which affects the cost of purchased and installed equipment. An organization implementing SAN in its information structure may not be able to install volumes large enough to suffice for long periods. In this case, to organize uninterrupted system functioning, it is necessary to know when volume filling of the system will be critical to the ability to complement the storage system with additional resources in advance. Thus, from a practical point of view, the task of predicting the filling or loading of SAN is very relevant.

In this work, the input data are observations (measurements) of the filling of the SAN, which contain the date and time, as well as the value of the degree of filling at a point in time. The task of predicting the loading of the SAN can be formulated in two ways: as a “Direct” question: what will the occupancy be at a given time interval in the future? Alternatively, the task can be approached from a practical point of view, wherein it is also interesting to answer the “dual” question: at what time will the SAN load reach a certain critical value?

This problem could be considered simply as a time series prediction problem. However, in the general case, the situation under consideration is of a more complex nature. The data series contains sections of loading, including growth, periods of idle time, and the short-term decline of loading. There are also areas of steep decreases in loading that appear due to memory clearing. This paper proposes that the entire time series of data be broken down into loading plots that form a subsample of the data. These sections can be viewed as complex observations from which the training and test datasets are composed. Each complex observation, in turn, represents a time series of data in which there is no volume cleaning procedure. The complex observations (segments) themselves have no order between them. Such a formulation of the problem does not correlate with the usual problem of time series prediction. In this paper, this problem is considered as a problem of regression analysis, in which it is necessary to predict the value of loading after a certain time interval (after a certain number of measurements). However, using solely loading values in past measurements (within the given loading phase) as input data sometimes leads to unsatisfactory results. To generate a predictive model, it is proposed to use the calculated indicators, considering the “velocity” of load growth and the “acceleration” of growth as input data. The effectiveness of the approach is confirmed by the results of the analysis of both real and specially generated synthetic data.

The load prediction problem is relevant for different areas, including energy systems [1]. So, the problem of load forecasting for power systems using a Bayesian approach is considered in [2].

2. Related Works

To solve such problems, we can observe the application of machine learning and data-mining methods. In addition, there are related problems in which the tasks of predicting the performance of servers and central processors are solved.

Server stability depends on various performance metrics, such as the processing capacity, random-access memory (RAM), storage, the network adapter’s characteristics (network operability), and network services. The AIOPS—Artificial Intelligence for IT Operations—approach is proposed in [3]. It is an approach that uses artificial intelligence to manage IT infrastructure based on a layered platform that automates data processing and decision making using machine learning and big data analytics stemming from various elements of the IT infrastructure in real time. AIOPS includes data collection, modeling, and forecasting processes. The paper proposes using an AIOPS-based platform to predict alerts for server stability. The platform includes data collection and preprocessing, time series modeling using ARIMA, and alert prediction. Central processing unit (CPU) utilization is considered as an indicator of server stability.

In the context of the growing importance of cloud-based IT solutions, companies are looking to increase flexibility and reduce costs. The workload in the form of CPU utilization often fluctuates. In [4], the prediction of future CPU workload using the Long Short-Term Memory Networks (LSTM) model is discussed. By predicting future workload, companies can accurately scale their capacity and avoid unnecessary costs and environmental damage. LSTM are compared to recurrent neural networks (RNN). Loads are predicted one step ahead and 30 min into the future. The results show that this approach can be a useful tool for business applications hosted in the public cloud.

Resource demand forecasting allows public cloud service providers to actively allocate or release resources for cloud services. In [5], the prediction of CPU utilization, both in the short and long terms, is discussed. To conceive of the model characteristics that are best-suited for specific types of prediction tasks, two different approaches are considered: the SARIMA time series prediction model as well as a neural network, namely, the LSTM model. These models are applied to data with a lag of 20 min in order to predict usage over the next hour for a short-term task and over the next three days for a long-term task. The SARIMA model outperformed the LSTM in the long-term prediction task but performed worse in the short-term task. In addition, the LSTM model was more robust, while SARIMA was superior in terms of data with a strong seasonal component.

In [6,7], which were devoted to load forecasting using artificial intelligence and machine learning, the authors propose the use of seasonal-trend decomposition using a LOESS (STL)—Local regressions—Local polynomial regressions method. STL allows one to study the distribution and degradation of memory, as well as analyze the comparison with the sample, as a result of which periodic changes in the configuration in the metric will be automatically corrected. Prediction requires algorithms that can analyze SAN load patterns and detect anomalies in daily usage trends.

Besides prediction, ML can also be used to improve anomaly detection. Here, adaptive thresholds for various indicators are set using ML and analyzing historical data, detecting anomalies and triggering appropriate alerts.

In [8,9], the researchers focused on collecting system resource data to predict usage levels in the near future so that the operating system could balance system resources. These studies showed that using data collected in fractions of a second accurately predicted the next step, but could not easily predict resource usage several steps ahead. The results of these attempts showed that the magnitude of the error increased with the number of steps and that the predictions were less effective. The researchers took the results of the short-term predictions and extended them to plan requests in web services. However, this study also showed that when planning was extended several steps into the future, the error rate was unacceptable. The levels of network usage were combined into ninety-minute cycles to reduce the fluctuations observed at shorter times. This study used simple moving averages (SMA), exponential moving averages (EMA), and cubic spline (CS) forecasts to examine the effectiveness of providing long-term forecasting. By creating aggregated data with coarser granularity, the predictability of the range of resource usage based on the seasonality of hours, days, and weeks was studied. The resources evaluated were CPU utilization, free memory, outbound/inbound network traffic, disk-writing time, and disk-reading time. The aggregated data were processed using SMA or EMA to generate a prediction and a confidence interval that matched the administrator’s needs. The actual data set was then compared to the prediction and confidence interval to determine whether the resource was still operating normally, and then the next prediction was generated for the next cycle.

Unpredictable user behavior causes variability in server workload distribution. This topic is addressed in [10,11], where server performance metrics are characterized and modeled using a fuzzy approach. A fuzzy inference system is generated using web server performance metrics and a server utilization index is derived to determine server utilization states for each time period. A fuzzy Markov mode is proposed to illustrate transitions of server resource utilization states based on experts’ linguistic estimation of the probability of a stationary transition. The steady-state algorithm is used to study the convergence of server resource utilization after a certain number of transition periods.

A semi-supervised learning approach can be used to predict extreme CPU utilization [12]. Semi-supervised learning for classification tasks is used in the cited paper to investigate a model for predicting an unpredictable load on IT systems and predicting extreme CPU utilization in a complex corporate environment with many applications running simultaneously. This proposed model predicts the probability of a scenario in which an extreme load affects IT systems, and this model predicts CPU utilization under extreme load conditions. An enterprise IT environment consists of many applications running in a real-time system. The characteristics of the workload patterns are hidden in the transactional data of the applications. This method simulates and generates synthetic server load patterns, runs the scenarios in a test environment, and uses the model to predict excessive CPU utilization under peak load conditions for validation. The expectation maximization classifier with forced learning attempts to extract and analyze parameters that can maximize the model’s chances after removing unknown labels. As a result of this model, the probability of excessive CPU utilization can be predicted in a short period of time compared to several days in a complex enterprise environment.

The authors of [13] propose a methodology for differentiated data storage capacity building based on a predictive model of time series incorporating an estimation of the volume of incoming traffic for storage. The influence of the structure of the incoming data flow on the choice of the prediction model is considered. The state of the SAN is represented in the form of patterns. The patterns are constructed using systematic slices of SAN load values. A periodic analysis of the patterns of the data storage state enables an estimation of the time to reach the limit value of the storage capacity. The predictive model underlying the methodology of the differentiated data storage capacity build-up considers the structure of the incoming data stream. If the incoming traffic possesses a self-similar structure, the predictive model of autoregressive and pro-integrated moving averages is implemented. For traffic without a self-similar structure, a general linear time series prediction model with known past values is implemented. The peculiarities of the structure of the stored traffic are given. The self-similarity properties are verified using LTE traffic as an example, demonstrating the presence of distributions with “heavy tails”. Using the autoregression model and the integrated moving average, the results of predicting the volume of incoming traffic for storage were obtained. The methodology of increasing data storage capacity considers the structure of the incoming data stream, allows for the organization of differentiated increases in storage capacity according to the characteristics of files, and ensures the requirements of guaranteed storage times.

In [14], the structure of a hardware–software complex of physical data storage management for systems that can be used by the owners of technological communication networks to store traffic is proposed. Management mechanisms are considered, such as the distribution of data across different carriers using Kohonen neural networks and the prediction of increases in storage capacity by means of a statistical model and machine learning methods.

In [15], an SAN utilization prediction model was proposed for the timely scaling of storage infrastructure based on predictive estimates of the moment when the storage medium reaches maximum capacity. An SAN capacity management model was developed based on the analysis of storage system state patterns. In the study, the representative pattern is a matrix in which each cell reflects the state of the storage medium’s occupancy at the corresponding level in the storage system’s hierarchical structure. Solving the scaling problem for a storage area network entails predicting the moments when the storage capacity limit and maximum storage capacity are reached. The difference between the predicted estimates is the time available to the administrator for connecting additional media. The research proposes the prediction of SAN utilization values by machine learning methods, namely, Decision trees, Random Forest, Feedforward neural networks, and SVM. It is shown that machine learning methods are less accurate than ARIMA in making short-term forecasts. However, for long-term forecasts, machine learning methods give results comparable to ARIMA results. The proposed SAN load prediction model automates the process of media connectivity, which helps to prevent the loss of data entering the system.

According to the relevant publications, tasks of this type are relevant. Some works estimate the volume of incoming data in storage systems based on the structure of the incoming data flow and on the loading patterns, which is unrealizable for the problem considered here since such information is missing.

However, of particular interest are the findings that the ARIMA method has an advantage only when making short-term forecasts. Machine-learning methods have more advantages when making some long-term forecasts. These conclusions are also confirmed by our studies on the comparative efficiency of different models.

There are also works on central processing unit load prediction [16], server load prediction [17], and cloud data centers [18,19] based on machine learning methods, including the use of artificial neural networks of various types [20] and fuzzy logic methods. However, these tasks, although similar, are different from the SAN load prediction problem solved herein.

Our experiments show that there are more efficient approaches besides neural networks. The approach we use is based on the application of machine learning methods to the regression problem on a transformed dataset consisting of integrated features of the loading history.

3. Materials and Methods

3.1. SAN Loading Simulation

The main task is to develop an algorithm that allows one to predict SAN load (volume), which can then be used in an organization’s information system.

The initial data are SAN fill observations which contain the date, time, and fill values at a given point in time. An example of the raw data (without preprocessing) is shown in Figure 1.

A typical SAN workload graph contains distinct periods of workload growth, periods of idle time, and periods of sharp decrease in workload. Due to the peculiarities of the practical applications of the proposed algorithm, it was decided to simulate only those parts of the dataset that contain periods of load growth. SAN downtimes, or periods in which there is no growth or decline in SAN workload, have been removed from the dataset. In addition, since it is the critical load growth that needs to be predicted, it is important to model only the periods of SAN load growth; accordingly, periods of decreasing load have been removed.

Initially, to select the best model, the target variable, which is the difference between data growth and the volume (the difference between the current value and the value for the previous period), was used. Then, based on the preliminary data estimation, the average period of a storage area network’s full load time is determined. The average period is equated to the planning horizon; in other words, it is the time period in which the full-load prediction of the SAN should be made.

After determining the best model, a prediction is made for the nearest future average period of the full utilization time of the SAN.

Based on the small number of data and large periods without SAN load, the most appropriate approach to this problem is the use of a regression model to predict the target variable Diff (the difference between the current and previous values of the SAN volume load) and exactly predict the load areas from the time when it is already known that the load has started.

The load prediction task can be divided into two stages:

• A binary classification task: it is necessary to predict whether there will be a significant increase in the volume of data at a future point in time.
• A regression task. If the forecast of task 1 will be positive, and thus there will be an increase in data, then it is necessary to forecast this volume (target variable). Otherwise, if there is no growth or it is insignificant (for example, in the normal operation of the system), the regression task will not be solved.

• To solve the regression problem, we pre-processed the data in two variants.
• The basic variant:
• Removing periods where there is no load, since there is no way to predict the time when the load will start from a small number of data (Figure 2);
• Calculating the Diff variable (Figure 3) and deleting sections that have large data deletions to convert the data into a single linear section (Figure 4).
• Addition to the basic variant:
• Converting the loading sections to fully linear sections by connecting the beginning and the end of the loading period (Figure 5 and Figure 6) using the averaged Diff value.

Figure 2. Dataset without “downtime” loading, where the measurement numbers are measured sequentially at a certain interval.

Figure 2. Dataset without “downtime” loading, where the measurement numbers are measured sequentially at a certain interval.

Figure 3. Diff field without areas with large data clearing, wherein measurement numbers are measured sequentially at a certain interval.

Figure 3. Diff field without areas with large data clearing, wherein measurement numbers are measured sequentially at a certain interval.

The following graph (Figure 4) visualizes the pre-processed dataset by the Value variable. It was further used to better visualize the estimation of the model’s quality. The information in the graph was obtained by aggregating the variable Diff with the cumulative total.

Figure 4. Value variable. The total linear section of the load, where measurement number is measured sequentially at a certain interval.

Figure 4. Value variable. The total linear section of the load, where measurement number is measured sequentially at a certain interval.

• Thus, the following actions with the original dataset were performed:
• The variable “Deviation” (diff) was added, which is the difference between the current SAN load value and the previous one;
• SAN downtimes were removed;
• All the sudden SAN load downturns (more than 10%) were removed, since only the SAN load growth prediction was consistent;
• The data were smoothed using a moving average (MA) with a period of 50.

As an additional variant of preprocessing, the dataset was converted into linear sections based on the minimum and maximum points of the SAN load value. This approach will hereinafter be referred to as “Smooth Trend”. The result of “Smooth Trend” preprocessing is shown in the graph below (Figure 5 and Figure 6), where the blue line denotes the original “Deviation” data, and the orange line denotes the “Deviation” after preprocessing.

Figure 5. Load plots converted to fully linear sections.

Figure 5. Load plots converted to fully linear sections.

Figure 6. Linear sections + removed “downtime” loading, where measurement number is measured sequentially at a certain interval.

Figure 6. Linear sections + removed “downtime” loading, where measurement number is measured sequentially at a certain interval.

Figure 7 shows the forecasts generated by the model. The target variable in this forecast is the variable Diff for one future period (not averaged, and exactly one record ahead). Once the predictions were obtained for all data, they were aggregated with cumulative totals to better visualize the error.

Figure 7. Forecast for 1 future period with subsequent aggregation to cumulative total, where measurement number is measured sequentially at a certain interval.

Figure 7. Forecast for 1 future period with subsequent aggregation to cumulative total, where measurement number is measured sequentially at a certain interval.

Figure 8 visualizes the prediction of each full loading step. For the prediction, 50 previous observations were taken; then, 1 loading step was calculated, and the grid of 50 observations was shifted +1, including 49 real values and 1 predicted value and so on until the end of the loading step (after predicting the 50th step, the model used only predicted values as inputs). The prediction was performed for the period of the real loading step in order to compare the difference between the real value and the predicted value. This graph shows what the prediction error can be depending on the period range.

Figure 8. Forecast for 1 period forward with subsequent aggregation to cumulative total, where measurement number is measured sequentially at a certain interval.

Figure 8. Forecast for 1 period forward with subsequent aggregation to cumulative total, where measurement number is measured sequentially at a certain interval.

• Here, we define the following notation:
• Diff—the difference between the current value and the previous value;
• MA—moving average;
• Lag—number of observations preceding the current one;
• Shift—shift from the beginning of the loading trend.
• Table 1 compares the results of SAN utilization prediction according to quality criteria.

Table 1. Comparison of forecasting results.

Model	Score Diff	MAPE Diff	MAPE Value	RMSE Diff	RMSE Value
NN_(162,512)_MA(50)_Diff Lag_50_Shift_50	0.916413	12.59	0.31	0.033401	0.950863
NN_(162,512)_MA(50)_Diff Lag_50_Shift_50_Even_trend	0.858994	0.19	0.06	0.012702	0.288143
CatBoost_MA(50)_Diff_Shift_50	0.573871	12.48	0.16	0.073646	0.480208
CatBoost_MA(50)_Diff Lag_50_Shift_50	0.573871	12.48	0.16	0.073646	0.480208
KNN_MA(50)_Diff Lag_50_Even_trend	0.953349	0.04	0.00	0.006142	0.084444
KNN_MA(50)_Diff Lag_50_Shift_50_Even_trend	0.953349	0.04	0.00	0.006142	0.084444

Table 1. Comparison of forecasting results.

Model	Score Diff	MAPE Diff	MAPE Value	RMSE Diff	RMSE Value
NN_(162,512)_MA(50)_Diff Lag_50_Shift_50	0.916413	12.59	0.31	0.033401	0.950863
NN_(162,512)_MA(50)_Diff Lag_50_Shift_50_Even_trend	0.858994	0.19	0.06	0.012702	0.288143
CatBoost_MA(50)_Diff_Shift_50	0.573871	12.48	0.16	0.073646	0.480208
CatBoost_MA(50)_Diff Lag_50_Shift_50	0.573871	12.48	0.16	0.073646	0.480208
KNN_MA(50)_Diff Lag_50_Even_trend	0.953349	0.04	0.00	0.006142	0.084444
KNN_MA(50)_Diff Lag_50_Shift_50_Even_trend	0.953349	0.04	0.00	0.006142	0.084444

List of the models used:

• NN_(162,512)_MA(50)_Diff_Lag_50_Shift_50:

  ○

  Multilayer Perspectron Neural Network;

  ○

  Architecture: 2 hidden layers, namely, 1-162 and 2-512;

  ○

  Input parameters:

  ■

  MA (50);

  ■

  Diff (50)—50 observations back from the current value.

  ○

  From the starting point of the loading stage, 50 observations were “waited out” and the forecast was performed based on their values (this stage was performed only for the graph in Figure 8).

• NN_(162,512)_MA(50)_Diff_Lag_50_Shift_50_Even_trend:

  ○

  Multilayer Perspectron Neural Network;

  ○

  Architecture—2 hidden layers: 1-162 and 2-512;

  ○

  The dataset for training was preprocessed to fully linear loading plots;

  ○

  Input data:

  ■

  MA (50);

  ■

  Diff (50)—50 observations back from the current value.

  ○

  From the starting point of the loading stage 50 observations were “waited out” and the forecast was performed based on their values (this stage was performed only for the graph in Figure 8).

• CatBoost_MA(50)_Diff_Shift_50:

  ○

  CatBoostRegressor model;

  ○

  Hyperparameters by default;

  ○

  Input data:

  ■

  MA (50);

  ■

  Diff;

  ○

  From the starting point of the loading stage 50 observations were “waited out” and the forecast was performed based on their values (this stage was performed only for the graph in Figure 8).

• CatBoost_MA(50)_Diff_Lag_50_Shift_50:

  ○

  CatBoostRegressor model;

  ○

  Hyperparameters by default;

  ○

  Input data:

  ■

  MA (50);

  ■

  Diff (50)—50 observations back from the current value.

  ○

  From the starting point of the loading stage 50 observations were “waited out” and the forecast was performed based on their values (this stage was performed only for the graph in Figure 8).

• KNN_MA(50)_Diff_Lag_50_Even_trend:

  ○

  KNeighborsClassifier model;

  ○

  Hyperparameters:

  ■

  metric = ‘cityblock’;

  ■

  weights = ‘distance’.

  ○

  The dataset for training was preprocessed into fully linear loading sections;

  ○

  Input data:

  ■

  MA (50);

  ■

  Diff (50)—50 observations back from the current value.

• KNN_MA(50)_Lag_50_Shift_50_Even_trend:

  ○

  KNeighborsClassifier model;

  ○

  Hyperparameters:

  ■

  metric = ‘cityblock’;

  ■

  weights = ‘distance’.

  ○

  The dataset for training was preprocessed into fully linear loading sections;

  ○

  Input data:

  ■

  MA (50);

  ■

  Diff (50)—50 observations back from the current value.

  ○

  From the starting point of the loading stage 50 observations were “waited out” and the forecast was performed based on their values (this stage was performed only for the graph in Figure 8).

After a comparative results analysis, we can conclude that the best result for the forecast of the full loading phase is the KNN_MA(50)_Diff_Lag_50_Even_trend model, shown in Figure 9.

Figure 9. The best model. KNN_MA(50)_Diff_Lag_50_Even_trend.

Figure 9. The best model. KNN_MA(50)_Diff_Lag_50_Even_trend.

3.2. CatBoost Description

The CatBoost algorithm developed by Yandex is available through open access and is an algorithm consisting of gradient boosting applied to decision trees [21]. It is widely used in prediction tasks, such as weather forecasting or driving an unmanned car. Another example of the use of this algorithm is the prediction of the bankruptcy of a company; accordingly, the authors of [22] used CatBoost with only financial or qualitative variables for prediction and training, which were performed using a sample of data from about 90,000 organizations. This library implements a learning algorithm on the GPU and a scoring algorithm on the CPU, which greatly accelerates its performance; thus, the authors of article [23] conducted a direct comparison of other algorithms with CatBoost. The test was performed as follows: for each algorithm, a python test dataset was loaded; then, it was converted to the internal representation of the algorithm and the simulation time of the predictions was measured. The results showed that with the same ensemble size, CatBoost could run about 25 times faster than XGBoost and about 60 times faster than LightGBM.

In their work, Jabeur S. B. et al. [24] use gradient enhancement method to predict the bankruptcy of firms, which is a fundamental factor regarding banks’ decisions to lend money to organizations. The method used showed its high efficiency, which was proven by conducting a comparison with eight benchmark machine learning models one, two, and three years before the failure.

In [25], algorithms were proposed to solve the problem of prediction bias caused by a special kind of target leakage. These algorithms, implemented via CatBoost, include an implementation of ordered boosting, a permutation-based alternative to the classical algorithm, and an innovative algorithm for processing categorical features. The results show that the proposed algorithms solve the prediction shift problem efficiently, which leads to excellent empirical results.

The authors of [26] conducted a study on the sentimental analysis of social network messages on COVID-19 data using the CatBoost algorithm. The main purpose of this study was to determine the messages’ emotional tone and classify the messages. There was also a comparative study of different machine learning algorithms, and the results of performance indicators were illustrated graphically.

The CatBoost algorithm has gained wide applicability in medicine as well, as the authors of [27] developed their own methodology for the self-treatment of obesity, which allows one to create a personalized, optimal life plan that is easy to implement and adhere to, thereby reducing the incidence of obesity and obesity-related diseases.

Thus, it seems possible to judge the applicability of this algorithm for the task of SAN prediction.

4. Results

4.1. Initial Data Synthesis

In order to conduct broader research on SAN load prediction, the selection of models and methods and parameter tuning were conducted, and an artificial dataset implementation method was used, on which further experiments were subsequently conducted.

In addition, when applying the SAN load prediction system to real processes, the problem of raw data scarcity is encountered. This may arise due to the upgrade or implementation of a new storage area network or simply a lack of records for past periods of system operation. In such cases, it is proposed to use a prediction system pre-trained on artificial data and to then conduct additional training procedures on the observed data.

The SAN performance observations for various organizations show different schedules regarding storage occupancy over time. Some are linear, while others are more variable and less predictable. As mentioned above, a typical SAN utilization schedule contains distinct periods of increased utilization, periods of downtime, and periods of dramatic decreases in utilization. In general, a period of load growth consists of smaller characteristic areas, as illustrated in Figure 10.

The symbols on the graph in Figure 10:

• A large loading section (or large loading stage) is a storage area network loading from 0 to some limit value. In the case of the current data synthesis, the limit value is in the range of 60 to 90% of the total volume. In the current example, the volume is set to 1 Tb. After each large loading step, there is a complete deletion of records to 0 with no small deletion steps. Since the data are generated, the large loading steps are not related to each other, and this deletion is performed only to start a new loading step from a point at 0.
• Short loading section (or small loading stage)—this is a local loading stage, similar to the large one, only inside of it. It is loaded at a smaller percentage, and after stage-by-stage deletion occurs with a simulation of the real values, it obtains one record of removal in the range from 10 Gb to 50 Gb; the range of the limits of removal are from 5 to 25% of the total volume.
• No-load—this is the point at which nothing happens; the value is the same throughout several records.
• Linear section—this is the section that is very close to the linear load, wherein the values of the increment at each step are in the range of ±5% of the average value given for this linear section to move from point A to point B.

Figure 11 shows a block diagram of the algorithm that allowed for the formation of a synthetic dataset for its further use in SAN load prediction. At the first stage, the algorithm is called through the configuration function, which contains a valid range of values, and through the number of examples function, which implies one large loading step.

Next, the condition is fulfilled if the number of examples is greater than zero; if so, the following information is determined:

• The value and duration of one large loading step (LLS);
• The number of small loading steps (SLS), inside of the large one.

If this condition is not satisfied, the function with parameters is called:

• An array of diff values (delta function);
• An array of values of the boundaries between the examples;
• The completion of the algorithm.

Then, in the case of a cycle, another cycle is started, as long as the value of the large loading step is greater than zero. At each iteration, the loading value is adjusted (if the loading increases, it decreases; if data are deleted, it increases), until this value is not equal to zero. In addition, the duration of loading is decreased.

Afterwards, the cycle is executed until the number of small loading steps is greater than zero or equals. The cycle determines the value and duration of the small loading step.

Then, the cycle is executed until the value of the small loading step is greater than zero. At the current stage, the loading value of each iteration is adjusted (if loading increases, then it decreases; if data are deleted, then it increases) until this value is 0, or until the value of the large stage is 0. In addition, the loading duration is decreased.

If the value of a large loading step or a small loading step is greater than zero, it is checked whether the section will be linear, that is, its probability of occurrence. The chance constant is set in the configuration; then, the value of the linear section is determined until it is less than zero, and the following steps are performed:

• The operation of determining a single loading step is performed;
• The obtained value is added to the array;
• The values of the large loading step, the small loading step, and the linear section are decreased by this value;
• The durations of the large loading step and the small loading step are decreased.

This cycle is performed as long as the section is linear. If the section is not linear, then it is checked whether there will be idle loading and its duration, and the following steps are performed as long as the available number of idle periods is less than or equal to zero:

• the value of the large loading step, small loading step, and linear section are decreased by that value;
• The durations of the large loading step and the small loading step are decreased.

Note that random selection is used. The chance constant for downtime is set in the configuration.

Provided that there is no idle time, the plot is not linear, and the small loading step is zero, an exit from the loop is performed and the loop is continued when the value of the large loading step is greater than zero and the small loading step is equal to zero. Then, the cycle is started while the idle time is greater than 0 and it is checked for the last stage of the small loading stage; consequently, the idle time of the loading stage is determined. Then, the cycle number of idle periods greater than zero is executed, where the available number of periods is reduced.

When the number of idle periods is less than or equal to zero, the cycle is exited. When the small loading stage has exhausted the value limit, the degree of data deletion is determined.

Then, if the limit of the large loading step is exhausted, the cycle is exited. After that, the cycle is executed until the deletion value is greater than zero, in which case the available value decreases.

The next step executes the cycle until the last step of the small loading step. This step determines the idle duration of the load, and then executes the cycle until the idle duration is greater than zero. In this case, it is determined whether there will be idle loading (no increment) after deleting the data in the small stage. Random selection is used. The chance constant, i.e., that there will be downtime, is set in the configuration. It is worth undoing this step when the small loading stage has exhausted the value limit, then the degree of data deletion is determined.

When the deletion value is greater than zero and the limit of the small loading step is exhausted, then the transition to the loop execution step is finished, while the number of examples is greater than 0.

If this condition is not met, the function returns two data arrays:

• An array of delta values;
• An array of boundary values between examples.

The values of the parameters used in the formation of synthetic data are shown in

Table 2. Parameters for synthetic data generation.

Parameters	Min. Value	Max. Value
Limit value range of one large loading step (% of volume filling)	60	90
The duration of one large loading step (number of hours)	192	384
Range of values, i.e., the number of small loading steps within a large one	0	7
Limit value range of one small loading step within a large one (% of volume filling)	10	50
Duration of one small download step within a large one (number of hours)	8	48
Value range of one download record (5 min/Mb)	100	3500
One deletion record. Only considered when downloading (5 min/Mb)	500	1000
Probability of a deletion record appearing only when downloading (%)	1
Limit value range of one deletion step. Follows a small loading step (% volume filling)	5	25
Range of values of one deletion record. Only considered at the moment of large data cleaning (5 min/Mb)	10,000	50,000
Probability of a linear section appearing (approximation to the average value of the loading section) at a small loading step (%)	1
Percentage of available values from the average in a linear segment	5
Distance of a linear section in a small loading stage (ratio to the remaining value of a small loading stage) (%)	10	30
Length of time of no-volume loading after a small loading step (number of hours)	1	30
Probability of occurrence of downtime after a small loading step (%)	20
Duration of volume unloading absence at the moment of loading a small stage (number of hours)	1	3
Probability of the absence of volume unloading at the time of downloading a small stage (%)	1

.

Examples of the resulting synthetic data are shown in Figure 12.

4.2. Formation of a Set of Essential Features for Predicting SAN Utilization

A simulation of the dataset sections that contain periods of loading, deleting data, and downtime was performed. The time interval in the original data is 5 min.

Initially, to select the best model, the difference between the data growth and volume was used to determine attributes; thus, the variable “Deviation” (diff) is the difference between the current value of SAN loading and the previous one. The planning horizon (the period of time for which SAN utilization should be predicted) takes values of 1 h, 2 h, 4 h, 8 h, 24 h, and 48 h.

The input data in the problem under consideration are the volume load values at different moments of time, where the time interval of records is 5 min.

v₀, v₁, v₂, …, where v₀ is the workload at the present moment of time for which further workload is predicted, and v_i is the known workload at moment t_i units of time earlier.

As it was described earlier, this study’s problem is considered as the problem of predicting the load increase from the current moment of time to some period in the future, diff* = v* − v₀, where v^* is the predicted load at moment t^*.

As inputs we also used the load increases in the previous time periods t_i calculated on the basis of the initial data: diff_i = v_i − v_i−1.

As the experiments show, the influence of the diff_i attributes turns out to be insignificant, especially when i increases.

The following hypotheses were formulated in order to ascertain the set of significant attributes and to build a prediction model.

• The value of load increase in the next period of time is close to the current value of load increase diff₁ (the principle of “inertia” or stable load increase);
• In the case when the change of the diff value at the current moment is temporary, and when the value of diff was higher or lower during the entirety of the earlier operation, then the average value of loading change at time periods (t_j, t_j−1, …, t₁), j = 1, …, n) should be considered (the principle of the “average speed” of loading corresponds to Equation (1)):

$$ve{l}_j=\frac{1}{j}{\sum }_{i=1}^j dif{f}_i,$$

(1)

3.

In the case when the loading rate (vel) increases (or decreases) in the process, then this tendency to increase (decrease) should be considered with respect to the values of the change in diff (the principle of accounting for the “acceleration” of the loading is given in Equation (2)):

$$ac{c}_j=\frac{1}{j}{\sum }_{i=1}^j \left(dif{f}_i-dif{f}_{i+1}\right),$$

(2)

Thus, it is proposed to use the values vel_j and acc_j as input attributes (Figure 13).

Table 3. Processed dataset.

Index	Value	Diff	Diff_Pred	Vel_1	Vel_2	Vel_4	Acc_1	Vel_3	Vel_37	Acc_3	Acc_2
0	2.88 × 108	2.88 × 108	7.84 × 108	287,595,427	1.44 × 108	7.18 × 107	2.88 × 108	95,865,142	26,145,039	95,865,142	1.44 × 108
1	4.6 × 108	1.73 × 108	8.52 × 108	172,849,937	2.3 × 108	1.15 × 108	−1.1 × 108	1.53 × 108	38,370,447	57,616,646	86,424,969
2	1.46 × 109	109	8.74 × 108	1,000,166,779	5.87 × 108	3.65 × 108	8.27 × 108	4.87 × 108	1.12 × 108	3.33 × 108	3.56 × 108
3	1.69 × 109	2.32 × 108	9.11 × 108	231,652,134	6.16 × 108	4.23 × 108	−7.7 × 108	4.68 × 108	1.21 × 108	−1.9 × 107	29,401,099
4	1.93 × 109	2.34 × 108	9.47 × 108	233,602,912	2.33 × 108	4.1 × 108	1,950,778	4.88 × 108	1.28 × 108	20,250,992	−3.8 × 108
5	3.09 × 109	1.16 × 109	8.87 × 108	1,163,185,905	6.98 × 108	6.57 × 108	9.3 × 108	5.43 × 108	1.93 × 108	54,339,709	4.66 × 108
6	4.23 × 109	1.14 × 109	8.45 × 108	1,139,444,841	1.15 × 109	6.92 × 108	−2.4 × 107	8.45 × 108	2.49 × 108	3.03 × 108	4.53 × 108
7	5.25 × 109	1.02 × 109	8.65 × 108	1,022,942,872	1.08 × 109	8.9 × 108	−1.2 × 108	1.11 × 109	2.92 × 108	2.63 × 108	−7 × 107
8	6.23 × 109	9.81 × 108	8.04 × 108	980,959,592	109	1.08 × 109	−4.2 × 107	1.05 × 109	3.28 × 108	−6.1 × 107	−7.9 × 107
9	7.49 × 109	1.26 × 109	7.38 × 108	1,258,057,292	1.12 × 109	1.1 × 109	2.77 × 108	1.09 × 109	3.75 × 108	39,537,484	1.18 × 108
10	8.46 × 109	9.65 × 108	7.09 × 108	964,858,193	1.11 × 109	1.06 × 109	−2.9 × 108	1.07 × 109	4.03 × 108	−1.9 × 107	−8,050,700

shows a fragment of the preprocessed dataset. Only the most important fields are shown.

4.3. Experimental Results

All experiments were performed on the CatBoostRegressor model with basic settings.

Experiment No. 1 (

Table 4. Comparison table of the results of test #1 sorted by MAE.

Feature	R2_Score	MAE (5 min/Mb)
top_3_diff	0.141	245.3
top_5_diff	0.136	245.518
top_10_diff	0.118	250.166
diff—diff575	0.095	251.993
top_1_diff	0.141	245.3

).

• The model was tested on 576 incoming diff properties.
• The 10 best properties were selected by the CatBoost model function “get_feature_importance”. Testing was conducted on these properties.
• The five best properties were selected by the CatBoost model function “get_feature_importance”. Testing was conducted on these properties.
• The three best properties were selected by the function of the CatBoost model “get_feature_importance”. Testing was conducted on these properties.
• A single best property was selected by the CatBoost model function “get_feature_importance”. Testing was conducted on these properties.

Definition of the variable diff:

Diff is the difference between the current value and the previous value. For example, if line number 10 is selected, then let us assume that diff₅ is equal to the value of line 5 minus the value of line 4, that is, the values of the previous entries. For instance, if it is now 13:00, then we know the values for 12:00, 11:00, 10:00, and so on. These functions are fed to the input of the model.

Based on the results of this test, we can conclude that the three incoming diff properties give the best results on the MAE metric.

Experiment No. 2 (

Table 5. Comparison table of the results of experiment #2 sorted by MAE.

Feature	R2_Score	MAE (5 min/Mb)
vel576_acc_575	0.158	241.16
top_20	0.164	243.976
top_10	0.166	244.427
top_5	0.157	245.122

).

• Testing was performed on 1151 incoming properties. Of these:
  • Average velocity (vel)—576;
  • Average acceleration (acc)—575.
• The 20 best properties were selected by the CatBoost model function “get_feature_importance”. Tests were conducted on these properties.
• The 10 best properties were selected by function of the CatBoost model “get_feature_importance”. Tests were conducted on these properties.
• The five best properties were selected by the function of the CatBoost model “get_feature_importance”. Tests were conducted on these properties.

From the results of this experiment, we can conclude that the best results were obtained for 1151 incoming properties, but this requires a long learning curve for the model. This option is not suitable for finding the optimal model. It is better to search for the optimal model applied to the top 20 properties. However, the optimal model can already be trained on all properties.

The following conclusions have been drawn from these studies:

• Changing the feature space by introducing the generalizing features vel_j and acc_j leads to improved prediction;
• A truncated feature set simplifies the model and accelerates training without incurring a significant loss (or improvement) of prediction accuracy.

Subsequently, the most significant 20 attributes consisting of the average rates and acceleration rates of load growth were used to build the forecasting model.

A general block diagram of the prediction algorithm is shown in Figure 14.

5. Experimental Studies on Predicting SAN Loading Using Regression

5.1. Predicting SAN Utilization by Regression One Hour Ahead

The following models and parameters were used for the regression task:

• CatBoostRegressor and CatBoost Library;
• KNeighborsRegressor, using the k-nearest neighbor method;
• LinearRegression, linear regression.
• CatBoost model hyperparameter grid search:
• Loss-function MAE average absolute error;
• A test sample size of 20%.
• The following is a list of CatBoost model hyperparameters:

‘learning_rate’: [0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09],

‘depth’: [10, 11, 12],

‘l2_leaf_reg’: [2, 3, 4, 5, 6, 7, 8],

‘bootstrap_type’: [‘Bernoulli’, ‘Bayesian’, ‘MVS’, ‘No’]

• The best hyperparameters of the CatBoost model are as follows:

‘iterations’: 1000,

‘loss_function’: ‘MAE’,

‘random_seed’: 42,

‘verbose’: False,

‘boosting_type’: ‘Plain’,

‘task_type’: ‘CPU’,

‘depth’: 9,

‘l2_leaf_reg’: 2,

‘learning_rate’: 0.09,

‘bootstrap_type’: ‘Bernoulli’}

LinearRegression model on the top 20 attributes, with a test sample size of 20%:

DIFF train:

R2 0.11759055044319466

mean_absolute_error 368.54792226600927 5 min/Mb

DIFF test:

R2 0.1032108082741724

mean_absolute_error 391.8978915286052 5 min/Mb

Value train:

R2 0.9953090618853814

mean_absolute_percentage_error 48.447349557246284%

Value test:

R2 0.994880793879479

mean_absolute_percentage_error 57.711763654202244%

KNeighborsRegressor model hyperparameter grid search on top-20 features

• The best hyperparameters of the KneighborsRegressor model are as follows:

‘metric’: ‘cityblock’,

‘n_neighbors’: 110,

‘weights’: ‘uniform’}

The results of different variants of the test sample size are as follows:

DIFF train:

R2 0.21459744816203896

mean_absolute_error 332.0943812516901 5 min/Mb

DIFF test:

R2 0.1768628775777361

mean_absolute_error 296.16665025915586 5 min/Mb

Summary results of the regression models are shown in

Table 6. Ranking of the best regression models.

	Feature	R2_Score_Test	MAE (5 min/Mb) Test	R2_Score_Train	MAE (5 min/Mb) Train	R2_Score_Value_Train	MAPE Train	R2_Score_Test	MAPE_Test	Time
0	CatBoost	0.170824	278.800098	0.208604	246.253602	0.995776	41.662629	0.995247	47.190251	60 s
1	LinearRegression	0.103211	391.897892	0.117591	368.547922	0.995309	48.447350	0.994881	57.711764	1 s
2	KNeighborsRegressor	0.181701	316.129383	0.215314	290.157608	0.995814	41.746353	0.995302	47.815941	240 s

.

We can conclude the following findings on forecasting with regression models: according to the MAE metric, which provided the average absolute error, the best regression model is CatBoost.

5.2. Predicting SAN Load Using Neural Networks

Table 7. The architecture and metrics of the first neural network.

Layer (Type)	Output Shape	Param #
dense_28 (Dense)	(None, 256)	5376
dense_29 (Dense)	(None, 256)	5376
dense_30 (Dense)	(None, 256)	65,792
dense_31 (Dense)	(None, 256)	65,792
dense_32 (Dense)	(None, 256)	65,792
dense_33 (Dense)	(None, 256)	65,792
dense_34 (Dense)	(None, 256)	65,792
dense_35 (Dense)	(None, 256)	65,792
dense_36 (Dense)	(None, 256)	65,792
dense_37 (Dense)	(None, 256)	65,792
dense_38 (Dense)	(None, 1)	257
Total params: 597,761 Trainable params: 597,761 Non-trainable params: 0

(Model: “sequential_5”) shows the structures of the neural networks used.

The results of applying the neural network are presented below.

DIFF train:

R2 0.09572336879029608

mean_absolute_error 267.88508843588266 5 min/Mb

DIFF test:

R2 0.0715112658919046

mean_absolute_error 293.7732381006516 5 min/Mb

Value train:

R2 0.9951645323227666

mean_absolute_percentage_error 48.22053331531325%

Value test:

R2 0.9946512741134749

mean_absolute_percentage_error 56.9436754761519%

A summary of the results of the neural network application is shown in

Table 8. Summary results of the application of neural networks.

	feature	R2_Score_Test	MAE (5 min/Mb) Test	R2_Score_Train	MAE (5 min/Mb) Train	R2_Score_Value_Train	MAPE Train	R2_Score_Test	пpost	Time
0	NN (30)	0.145156	296.460396	0.169836	272.314980	0.995568	43.799124	0.995092	52.625168	85 s
1	NN 10 layers of 30 neurons	0.132219	291.138713	0.165863	265.017411	0.995561	40.682488	0.995079	50.087625	100 s
2	NN (256)	0.143416	300.917126	0.166495	277.047718	0.995546	46.452904	0.995072	55.716560	80 s
3	NN 10 layers of 256 neurons	0.076478	297.920565	0.098162	273.298865	0.995178	48.149521	0.994680	56.919627	130 s

.

According to the MAE, i.e., the average absolute error metric, the best neural network architecture is 10 hidden layers with 30 neurons each. However, the metrics of this neural network are worse than those of the CatBoost model.

A visualization of the forecast for 1 h and real data on the graph of the CatBoost model are shown in Figure 15.

The graph (Figure 15) was constructed from one large loading stage. The graph (Figure 14) shows the entire loading step; the next graph (Figure 16) shows one part of it with a larger scale.

The formula for calculating the predicted values on the graph:

Value_predicti = valuei-12 + diff_predicti-12 * 12

where value_predict is the point to be predicted (the value in 12 records from the current time or 1 h).

Value is the current volume load value.

Diff_predict is the predicted average value of the load gain or loss, which must be added to the current value 12 times to predict the load value in 1 h.

Note: The model predicts only 1 point in 1 h, wherein the way to this point is a straight line from the average diff. The curvature of the forecast on the graph was already verified from the previous forecasts.

5.3. Predicting SAN Load Using Regression for 24 h Ahead

Using the conclusions of Section 6and Section 7 concerning the choice of the best model for predicting SAN utilization one hour ahead, let us consider the use of CatBoost for a 24 h forward forecast.

• CatBoost hyperparameter grid search on top—20 parameters.
• The list of hyperparameters of the CatBoost model:

‘learning_rate’: [0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09],

‘depth’: [1, 2, 3, 4, 5, 6, 7, 8, 9],

‘l2_leaf_reg’: [2, 3, 4, 5, 6, 7, 8],

‘bootstrap_type’: [‘Bernoulli’, ‘Bayesian’, ‘MVS’, ‘No’

• The best hyperparameters of the CatBoost model:

‘iterations’: 200,

‘loss_function’: ‘MAE’,

‘random_seed’: 42,

‘verbose’: False,

‘boosting_type’: ‘Plain’,

‘task_type’: ‘CPU’,

‘depth’: 9,

‘l2_leaf_reg’: 6,

‘learning_rate’: 0.05,

‘bootstrap_type’: ‘Bernoulli’

• The best results of the CatBoost model prediction:

DIFF train:

R2 0.3517532239354847

mean_absolute_error 160.15495056506484 5 min/Mb

DIFF test:

R2 0.19196146687069315

mean_absolute_error 194.37242886618847 5 min/Mb

Value train:

R2 0.8578543459067921

mean_absolute_percentage_error 807.5265537419783%

Value test:

R2 0.8113079668072851

mean_absolute_percentage_error 682.4150839712811%

The CatBoost model is shown in Figure 17 in a visualization of the 24 h forecast and real data on a graph.

The graph (Figure 17) is built from one large loading stage. The graph (Figure 17) shows the whole loading phase, while the next graph (Figure 18) shows one part of it at a larger scale.

The formula for calculating the predicted values on the graph:

Value_predicti = valuei-288 + diff_predicti-288 * 288

where value_predict is the point to predict (value in 288 records from the current time or 24 h).

Value is the current value of volume load.

Diff_predict is the predicted average value of the load gain or loss, which must be added to the current value 288 times to predict the load value in 24 h.

Note: The model predicts only 1 point in 24 h; the way to this point is a straight line from the average diff. The curvature of the forecast on the graph is already a fact of previous forecasts.

Table 9. Comparison table for predicting all target variables 1, 2, 4, 8, 24, 48 h.

Model	Diff Train MAE	Diff Test MAE	Diff Train R2	Diff Test R2	Value Train MAPE	Value Test MAPE	Value Train R2	Value Test R2
1 h	246.25	277.8	0.21	0.17	41.66	47.19	0.996	0.995
2 h	275.22	307.0	0.17	0.12	90.63	102.5	0.989	0.988
4 h	275.2	300.62	0.18	0.12	178.67	217.26	0.976	0.973
8 h	240.15	266.05	0.24	0.15	348.02	458.5	0.948	0.943
24 h	160.15	194.37	0.35	0.19	807.53	682.42	0.858	0.811
48 h	106.91	129.48	0.25	0.11	921.97	270.47	0.748	0.656

presents comparisons of the predictions of all target variables.

6. Discussion

To perform detailed experiments on the considered problem of SAN load prediction, an artificial data set was generated, which corresponds to the real data on SAN load measurements, including periods of growth, idle time, and volume cleaning.

The CatBoost algorithm (decision-tree gradient binning) showed a higher efficiency compared to other regression analysis algorithms (linear regression, nearest neighbor, and artificial neural networks) in terms of the R2_score and MAE.

The use of generalizing features—such as the “average loading speed” and “average loading acceleration”, which were introduced in accordance with the hypotheses of their influence on further growth—in the CatBoost algorithm for regression led to an increase in the prediction accuracy by 30% on average. The identification and selection of the most significant attributes in the CatBoost algorithm allows for the simplification of the forecast model almost without a loss (and, in some cases, producing an increase) in the forecast’s accuracy, thereby reducing the number of used attributes to 20.

The prediction accuracy decreases slightly when the planning horizon increases. Thus, when planning for 1 h, the R2 is close to 1; when planning for 8 h, the R2 is approximately equal to 0.95; but when planning for 24 h and more, the R2 decreases to 0.9 and lower. Nevertheless, the proposed approach is quite applicable for practical SAN utilization prediction based on the records of previous utilization states.

7. Conclusions

The artificial data set synthesized stochastically according to the specified parameter intervals allowed us to conduct more extensive experiments. In general, the synthesized data correspond to real data, which allows for the generalization of the results of the experimental studies. In addition, the pre-trained model can be applied in cases where historical data are extremely scarce. In this case, the use of a pre-trained model on synthetic data is a useful technique. In further SAN work, this model will be further trained according to real measurements.

The best model for prediction is the CatBoost model. Adding generalizable features, such as the SAN load speed (vel) and the SAN load acceleration (acc), improves its prediction. A truncated set of features consisting of up to 20 attributes simplifies the model and accelerates training without a significant loss of prediction accuracy. The best results are obtained when predicting up to about 100 records ahead, and then the accuracy decreases. However, the results can be improved by training the model on real data concerning specific equipment.

For practical applications, a graphical user interface (GUI) application for SAN utilization prediction based on the best-trained CatBoost model has been developed based on this research.