Long-Term Data Traffic Forecasting for Network Dimensioning in LTE with Short Time Series
Abstract
:1. Introduction
- The first comprehensive comparison of the performance of SL algorithms against classical time series analysis in long-term data traffic forecasting on a cell basis, relying on short and noisy time series. Algorithms are compared in terms of accuracy and computational complexity.
- A detailed analysis of the impact of key design parameters, namely the observation window, the prediction horizon and the number of models to be created (one per cell or one for the whole network).
2. Related Work
3. Problem Formulation
4. Dataset
- The average DL traffic volume (in kbps) and the average number of active users (i.e., those users demanding resources) are measured and collected per cell c and hour.
- The weekly busy-hour is selected per cell as the hour with the highest number of active users in week w. Each week belongs to a month m. The DL traffic volume (in kbps) during that busy-hour is selected as the weekly DL traffic volume per cell, week and month, (in kbps).
- Finally, the monthly busy-hour DL traffic volume per cell and month, , is computed as the average of across weeks in month m, as
5. Traffic Forecasting Methods
- SARIMA computes the current value of a time series difference as the combination of previous difference values and the present and previous values of the series. As detailed in [41], a SARIMA process is described as SARIMA(p,d,q)(P,D,Q). (p,d,q) describe the non-seasonal part of the model, where p is the auto-regressive order, d is the level of difference and q is the moving average order, with p, d and q non-negative integers. (P,D,Q) describe the seasonal part of the model, where P, D and Q are similar to p, d and q, but with backshifts of the seasonal period m (e.g., for monthly data, ).
- AHW calculates the future value of a time series with recursive equations by aggregating its typical level (average), trend (slope) and seasonality (cyclical pattern) [42]. These three components are expressed as three types of exponential smoothing, with smoothing parameters , and , respectively. As in SARIMA, the seasonal period is denoted as m (for monthly data, ). In this work, Additive Holt–Winters (AHW) is chosen, since, as shown in Figure 1, the seasonal effect is nearly constant through the time series (i.e., it does not increase with the level).
- RF is an ensemble learning method where several decision trees are created with different subsets of the training data (also known as aggregating or bagging). To reduce the correlation among trees, a different random subset of input attributes is selected at each candidate split in the learning process (feature bagging) [43]. To avoid model overfitting, trees are pruned. Then, predictions obtained from different trees are averaged to perform a robust regression [44].
- ANN is a statistical learning method inspired by the structure of a human brain. In ANN, entities called nodes act as neurons, performing non-linear computations by means of activation functions [45]. Two ANNs are considered in this work. The first one, denoted as ANN–MLP, is a feed-forward network (i.e., without memory) consisting on a Multi-Layer Perceptron (MLP) [46]. The second one, denoted as ANN–LSTM, is a deep recurrent network (i.e., with memory) based on LSTM units capable of capturing long-term dependencies thanks to the use of information control gates [47]. The architectures of such networks (number of layers, number of neurons per layer, activation functions, etc.) are detailed in Section 6.1.
- SVR maps a set of inputs into a higher dimensional feature space to find the regression hyperplane that best fits every sample in the dataset. For this purpose, a linear or non-linear (also known as kernel) mapping function can be used. Unlike traditional multiple linear regression, SVR neglects all deviations below an error sensitivity parameter, . Moreover, the regularization parameter, C, restricts the absolute value of regression coefficients. Both parameters control the trade-off between regression accuracy and model complexity (i.e., the smaller and larger C, the better the model fits the training data, but overfitting is more likely) [44].
- Observation window: time series corresponding to recently deployed cells may not have many historical measurements. Thus, it is important to check the capability of the methods to work with small observation windows. Such a feature is especially critical during the network deployment stage, when network structure is constantly evolving (e.g., new cells are activated every month). At this early stage, robust traffic forecasting is crucial to avoid under-/over-estimating traffic in the new cells.
- Number of models: recursive models such as SARIMA, AHW and ANN–LSTM are conceived to build a different model per cell based on historical data of that particular cell. Thus, the short period available in data warehouse systems for long-term forecasting (typically, less than 24 months) may jeopardize prediction capability in these methods, since it is always necessary to have more observations than model parameters [40]. In contrast, in RF, ANN–MLP and SVR, a single model can be derived for the whole network from historical data of all the cells. The latter ensures that enough training data are available to adjust model parameters, avoiding model overfitting. Likewise, sharing past knowledge across cells in the system increases the robustness of predictions in cells with limited data or abnormal events.
- Time horizon: The earlier a capacity bottleneck can be predicted, the more likely the problem will be fixed without any service degradation, since some network re-planning actions (e.g., build a new site) may take several months. Such a delay forces operators to foresee traffic demand several months in advance (referred to as multi-step prediction). In classical time series analysis methods, such as SARIMA and AHW, multi-step prediction is carried out recursively by using a one-step model multiple times (i.e., the prediction for the previous month is used as an input for predicting the following month). Such a recursive approach reduces the number of models needed, but quickly increases prediction errors originated by the use of predictions instead of observations as inputs [48]. This is a critical issue when using recursive methods for series with large random components, as those used in long-term forecasting. In contrast, SL algorithms have the ability to directly train a separate model for each future step. Such an approach does not entail an increase of computational load if the set of steps predicted is small (e.g., 3 and 6 months ahead).
- Interpretability: Ideally, prediction models should be simple enough to have an intuitive explanation of their output values [49]. Models built with SARIMA and AHW are easier to understand, since their behavior is described by a simple closed-form expression, whereas models built with RF, ANN and SVR cannot be explained intuitively. In long-term traffic forecasting, interpretability is not an issue, and is thus neglected in this work.
6. Performance Assessment
6.1. Model Construction
6.2. Assessment Methodology
6.2.1. Experiment 1—Selection of the Observation Window
6.2.2. Experiment 2—Method Comparison
6.2.3. Experiment 3—Creation of Specific Models for High-Traffic Cells
- The Mean Absolute Error () computed as
- The Mean Absolute Percentage Error () computed as
6.3. Results
6.3.1. Experiment 1
6.3.2. Experiment 2
6.3.3. Experiment 3
6.4. Computational Complexity
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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SARIMA | |
---|---|
p, d, q, P, D, Q | Automatically set by Expert mode |
m | 12 |
AHW | |
, , | Automatically set by Expert mode |
m | 12 |
RF | |
No. of trees | 10 |
Maximum depth | Until leaves have 10 samples |
No. of predictors per tree | (: total number of predictors) |
ANN–MLP | |
No. of layers | 3 (1 hidden layer) |
No. neurons in hidden layer | Automatically set by Expert mode |
Activation function | Hyperbolic tangent |
Error function | Sum of squares |
Training algorithm | Gradient descend |
Training data split | 70% for training/30% for validation |
Training stop rule | Accuracy in the validation dataset is higher than 90% or does not improve across iterations |
ANN–LSTM | |
No. of layers | 3 (2 LSTM layers + 1 output layer) |
No. LSTM units per layer | 10 |
Activation function | Rectified Linear Unit |
Error function | Mean average error |
Training algorithm | Adaptive Moment Estimation (Adam) |
Training data split | 70% for training/30% for validation |
Training stop rule | 100 epochs or accuracy in the validation dataset does not improve in 3 consecutive epochs |
Batch size | 64 |
SVR | |
Error sensitivity parameter, | 0.1 |
Regularization parameter, C | 10 |
Kernel | Linear |
Training algorithm | Sequential minimal optimization |
Window | 12 Months | 18 Months | 24 Months | |||
---|---|---|---|---|---|---|
Indicator | [%] | [kbps] | [%] | [kbps] | [%] | [kbps] |
SARIMA | - | - | - | - | 43.25 | 2069.72 |
AHW | - | - | - | - | 29.28 | 1780.71 |
RF | 23.75 | 1017.55 | 24.25 | 1027.20 | 23.29 | 1236.44 |
ANN–MLP | 24.28 | 1023.55 | 25.33 | 1046.25 | 24.90 | 1339.91 |
ANN–LSTM | 22.65 | 976.69 | 25.61 | 1076.16 | 23.38 | 999.15 |
SVR | 25.78 | 1070.03 | 24.70 | 1020.59 | 27.86 | 1572.81 |
Window | 12 Months | 18 Months | 24 Months | |||
---|---|---|---|---|---|---|
Indicator | [%] | [kbps] | [%] | [kbps] | [%] | [kbps] |
SARIMA | - | - | - | - | 590.17 | 16,708.55 |
AHW | - | - | - | - | 30.88 | 1902.44 |
RF | 23.94 | 1048.63 | 25.14 | 1053.56 | 22.76 | 1199.32 |
ANN–MLP | 24.23 | 1055.93 | 27.46 | 1277.13 | 23.58 | 1250.32 |
ANN–LSTM | 22.23 | 1034.30 | 24.59 | 1041.39 | 29.55 | 1253.69 |
SVR | 30.81 | 1372.89 | 27.59 | 1163.40 | 37.66 | 2517.43 |
Case | 12-3 | 12-6 | ||||
---|---|---|---|---|---|---|
Indicator | [%] | [kbps] | [kbps] | [%] | [kbps] | [kbps] |
RF | 27.63 | 994.21 | 160.51 | 40.09 | 1329.31 | 719.20 |
ANN–MLP | 27.73 | 987.28 | 134.61 | 38.71 | 1256.40 | 572.46 |
ANN–LSTM | 26.37 | 986.88 | 134.27 | 31.87 | 1173.39 | 287.73 |
SVR | 30.26 | 1059.86 | −251.32 | 36.71 | 1327.15 | −531.02 |
Model | Network-Wide | Specific | ||
---|---|---|---|---|
Indicator | [%] | [kbps] | [%] | [kbps] |
RF | 12.46 | 1339.88 | 11.26 | 1212.18 |
ANN–MLP | 12.31 | 1374.55 | 11.35 | 1232.98 |
ANN–LSTM | 12.21 | 1311.72 | 13.27 | 1356.13 |
SVR | 20.44 | 2223.88 | 14.49 | 1725.20 |
Case | 12-3 | 12-6 | 24-3 | 24-6 |
---|---|---|---|---|
Number of predictors | ||||
SARIMA and AHW | - | - | 24 | 24 |
SL algorithms | 9 | 6 | 21 | 18 |
Execution times [s] | ||||
SARIMA (per cell) | - | - | 0.56 | 0.61 |
AHW (per cell) | - | - | 0.65 | 0.72 |
RF (entire network) | 5 | 4 | 8 | 6 |
ANN–MLP (entire network) | 3 | 2 | 6 | 4 |
ANN–LSTM (entire network) | 140 | 98 | 313 | 245 |
SVR (entire network) | 12 | 10 | 14 | 13 |
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Gijón, C.; Toril, M.; Luna-Ramírez, S.; Marí-Altozano, M.L.; Ruiz-Avilés, J.M. Long-Term Data Traffic Forecasting for Network Dimensioning in LTE with Short Time Series. Electronics 2021, 10, 1151. https://doi.org/10.3390/electronics10101151
Gijón C, Toril M, Luna-Ramírez S, Marí-Altozano ML, Ruiz-Avilés JM. Long-Term Data Traffic Forecasting for Network Dimensioning in LTE with Short Time Series. Electronics. 2021; 10(10):1151. https://doi.org/10.3390/electronics10101151
Chicago/Turabian StyleGijón, Carolina, Matías Toril, Salvador Luna-Ramírez, María Luisa Marí-Altozano, and José María Ruiz-Avilés. 2021. "Long-Term Data Traffic Forecasting for Network Dimensioning in LTE with Short Time Series" Electronics 10, no. 10: 1151. https://doi.org/10.3390/electronics10101151