# Short-Term Mobile Network Traffic Forecasting Using Seasonal ARIMA and Holt-Winters Models
## 1 Introduction
### Related Work  
Forecasting methods typically begin with statistical models, such as ARIMA (autoregressive integrated moving average) [18] and its seasonal variant SARIMA, exponential smoothing (Holt-Winters, extended Holt-Winters, etc.), and regression models (multiple, linear, etc.). In addition, ML and deep learning models, Gaussian models (Gaussian mixture model [19; 20], Gaussian process), random forests, and neural networks are also commonly used. While ML models generally outperform statistical models, there are instances where statistical models are applied for their faster processing capabilities. To achieve more accurate results, a combination of different approaches is often utilized [16]. The same applies to network traffic forecasting. LTE (long-term evolution) traffic is predicted by the ARIMA model [21], as well as bagging, random forest, and support vector machines [22]. In [23], the authors used ARIMA for post-processing the residuals of the ML algorithm, which improves the accuracy of traffic prediction. In [24], 5G traffic is forecasted by gated recurrent unit and long short-term memory (LSTM) networks. The authors of [25; 26] show that LSTM is good for online forecasting.  
Let us review selected papers on the subject of applying statistical models in network traffic forecasting. Table 1 provides a summary of these papers in terms of the tasks they address, the applications that generate traffic, the models used, and the metrics used to evaluate these models. Most of the papers focus on traffic forecasting, but the tasks of capacity planning [27] and resource optimization [28] are also addressed. The data are collected from several sources, including cells [29; 30; 31; 32], devices [33], switches [34], and servers [35]. The most commonly used statistical model is the ARIMA model [36; 37]. Moreover, combinations of statistical and machine learning methods are used to achieve more accurate results [38; 39]. The evaluation metrics help to determine which solutions are most suitable for the proposed model. The choice of metrics depends on the specific study, such as MAE and MSE [30; 31], or performance indicators [40].  
\begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Ref.** & **Task** & **Data Source/Application** & **Model** & **Evaluation Metric** \\ \hline
[30] & Traffic forecasting & Traffic from 2 cells & ARIMA & MAE, NMSE \\
[31] & Traffic forecasting & Traffic from 3 LTE cells & ARIMA, LSTM & MSE, MAE, \(R^{2}\) score \\
[34] & Network capacity forecasting & Circuit switch and packet switch 3G traffic & Exponential smoothing, ARIMA & RMSE, MAPE \\
[38] & Traffic forecasting & Traffic from 7160 LTE cells & SARIMA, Holt-Winters, Random Forest, SVM, ANN & MAPE, MAE \\
[28] & Recourse optimization & Traffic from the network with discontinuous reception (DRX) scheme & ARIMA, LSTM & RMSE \\
[39] & Traffic congestion forecasting & Traffic from 8 detectors of virtual reality railway & Random walk, Historical mean, ARIMA, LSTM, GRU, DCFCN & RMSE, MAE, MAPE \\
[36] & Traffic forecasting & Traffic from 470 access points of an enterprise network & Holt-Winters, SARIMA, LSTM, GRU, CNN & MAE, RMSE, NRMSE, \(R^{2}\) score \\
[40] & Throughput forecasting & Download traffic from HSPa network & ARIMA, FARIMA, ANN & Efficiency, switches per minute and buffering per minute \\
[35] & Traffic forecasting & WiFi and cellular download traffic from a server & ARIMA, FARIMA, SVR, RNN & MAE, RMSE, MAPE, MASE \\
[33] & Traffic forecasting & WiFi traffic from 15 protocols & ARIMA & Error rate, average absolute deviation, mean and variance of the error \\ \hline \end{tabular}
\end{table}
Table 1: Summary of selected works on statistical models for network traffic forecasting.