Multi-Step Internet Traffic Forecasting Models with Variable Forecast Horizons for Proactive Network Management †
Abstract
:1. Introduction
- Our study involves a comparative analysis of machine learning models belonging to the gradient descent and gradient boosting categories for the purpose of predicting traffic in a single step. Additionally, we evaluate the performance of conventional machine learning models in comparison to our novel traffic prediction framework, which incorporates an anomaly detection and mitigation module.
- Our investigation involves the examination of actual traffic data to detect anomalous data points, utilizing both statistical and unsupervised machine learning models. Furthermore, we conduct a thorough analysis to effectively manage these outlier observations prior to incorporating them into our training models for prediction.
- Our study entails a thorough multi-step analysis of forecasting, wherein we assess the performance of different classical gradient descent and boosting algorithms based on their prediction accuracy and execution time. Furthermore, we evaluate the efficacy of our proposed framework across three distinct forecast lengths.
- Our research delves into the exploration of various feature sets for the purpose of traffic prediction. Specifically, we examine five distinct time-lagged feature subsets for predicting traffic volume in the subsequent timestamp in the context of single-step prediction. Additionally, we train our multi-step forecasting models using multiple feature sets to identify the optimal inputs that offer improved prediction accuracy and execution time.
2. Literature Review
- While several works have been carried out in traffic prediction, most of them have overlooked the importance of outlier detection in their methodology, which can hinder the generalization of the model. The sudden changes in traffic patterns due to several factors, such as ISP companies or external events, can create outliers that affect the reliability of the model. The proposed model integrates an anomaly detection and mitigation module to address this issue, which can enhance the generalization of the model and improve the accuracy of the traffic prediction. The use of outlier detection and mitigation can help capture the underlying patterns and trends in the data and lead to more reliable and precise predictions, particularly in real-world scenarios where traffic patterns can be unpredictable and subject to sudden changes.
- Most existing research in the field of traffic prediction has focused on single-step forecasting and has not undertaken a comprehensive analysis of multi-step forecasting. However, multi-step forecasting is more challenging yet more practical for businesses than single-step forecasting. In our study, we addressed this limitation by considering several forecast horizons for multi-step traffic prediction tasks, in contrast to most existing works that only consider a single horizon. This approach can improve the accuracy and practicality of multi-step traffic prediction tasks, which are crucial in real-world traffic scenarios.
- Existing studies typically compare the performance of various machine learning models, including statistical, deep, and machine learning. However, we noticed a lack of comparative analysis between gradient boosting and gradient descent algorithms, despite their effectiveness in modeling complex data for regression problems. To address this gap, we selected several algorithms from the gradient boosting and gradient descent categories and conducted a comparative performance analysis for both single-step and multi-step traffic forecasting in our study. This approach can help identify the most efficient and accurate algorithms for traffic prediction tasks, especially in scenarios where data complexity is a challenge.
- Unlike most existing studies that rely on synthetic traffic datasets for their analysis, we utilized a real-world traffic dataset in our experiment. This approach can enhance the practicality and relevance of our findings and provide a more accurate representation of real-world traffic scenarios.Table 1. Summary of internet traffic forecasting techniques: a comparative analysis.
Ref. Methodology Data Preprocessing Forecast
HorizonDataset Outlier
DetectionEvaluation Metric [7] Gaussian processes Based stations are grouped based on geographical location Single-Step and multi-step Univariate, temporal N/A Mean Absolute Percentage Error (MAPE) [9] linear regression, Passive Aggressive Regressor, k neighbors regressor, and multi-layer perceptron regressor N/A Single-Step Univariate, temporal N/A TLPQ (Traffic Level Prediction Quality), Root Mean Square Percentage Error (RMSPE) [11] RNN and CNN N/A Single-Step Multi-variate, temporal, and spatial N/A MAE (Mean Absolute Error), RMSE (Root Mean Square Error), MAPE, and MA (Mean Accuracy) [12] ARIMA and RNN Discrete wavelet transform DWT) decomposes a given discrete signal into orthogonal wavelet functions. Single-Step Univariate, temporal N/A NRMSE (Normalized Root Mean Square Error) [13] LSTM, Seq2SeqLSTM, ConvLSTM reordering of flow streams, window-based value aggregation, and harmonization Multi-step Multi-variate, temporal N/A RMSPE [14] Stacked Denoising Autoencoders and MLP Min-Max Normalization, handling missing value Single-Step Univariate, temporal N/A MAE, RMSE, MRE (Mean Relative Error) [17] echo state network Phase-space reconstruction has been used to reconstruct the original network traffic data series Multi-step Univariate, temporal N/A RMSE, MAE [18] LA-Resnet missing data were replaced and filled to the average of nearby values. Single-step Univariate, temporal, spatial N/A RMSE, MA [19] LSTM and Online-Sequential Extreme Learning Machine (OS-ELM) Data transformation for supervised learning, data differencing, and normalization Single-step Univariate, temporal N/A MSE [20] TTGCN (Temporal–Topological Graph Convolutional Neural Network), N/A Multi-step Univariate, temporal, spatial N/A MAE, RMSE [21] LSTM encoder–decoder Min-Max Normalization Multi-step Univariate, temporal N/A RMSE, R2 (R Squared) [22] Linear Regression, KNN, and Random Forest Seasonality feature extraction Single-Step Univariate N/A RMSPE Table 2. Comparison of core contributions against existing works.Key Contribution Existing Works Proposed Work Outlier Detection and Mitigation Lacks comprehensive methods for identifying and mitigating outliers, potentially leading to inaccurate traffic forecasting. Employs empirical analysis and unsupervised learning for robust outlier management, enhancing forecasting accuracy. Forecast Horizon Primarily focuses on short-term predictions, with minimal exploration of long-term forecasting challenges. Includes both short-term and long-term forecasts, examining the impact of forecast horizon on accuracy. Feature Optimization Limited investigation into the optimal selection of features for improving model performance. Conducts experiments with various feature subsets to identify the most effective inputs for forecasting. Model Selection Comparisons often span across broad categories, lacking depth within specific model types for traffic forecasting. Provides a detailed analysis within the boosting model category, offering insights into achieving superior prediction accuracy.
3. Methodology
3.1. Handling Missing Value
3.2. Autocorrelation Function (ACF) Analysis
3.3. Anomaly Detection and Mitigation
3.4. Feature Extraction
3.4.1. Feature Extraction for Single-Step Prediction
3.4.2. Feature Extraction for Multi-Step Prediction
3.5. Regression Models for Single- and Multi-Step Forecasting
3.6. Proposed Model’s Algorithmic Analysis
Algorithm 1: Traffic prediction integrated with anomaly detection and mitigation. |
4. Experimental Detail
4.1. Dataset Description
4.2. Time Series Cross-Validation
4.3. Evaluation Metrics
4.4. Software and Hardware Preliminaries
5. Result and Discussion
5.1. Outlier Mitigation Impact Analysis
- The ECDF plot suggests that the range of values is narrower after outlier replacement, indicating a reduction in variability.
- The statistical tests indicate that there is no significant difference in the standard deviation of the two groups, suggesting that the difference in range is not likely to be due to chance.
- Taken together, these results suggest that the removal of the outliers has resulted in a reduction in the range of values, even though the standard deviation of the two groups is similar.
5.2. Single-Step Traffic Prediction
5.3. Multi-Step Traffic Prediction
- Improved Accuracy with Outlier Removal: The results highlighted that models trained without outlier data generally performed better than their counterparts trained with outliers. This emphasizes the importance of data preprocessing and outlier removal in enhancing model performance.
- Prediction Challenges in Multi-Step Forecasting: The study pointed out the increased complexity and challenges associated with multi-step forecasting as compared to single-step forecasting. This is due to the accumulative error in the current steps, which impacts the next step prediction.
- Impact of Feature Selection: The study found that the number of input features used can significantly influence model performance. This signifies the importance of feature selection and dimensionality reduction techniques in predictive modeling.
- Trade-off between Accuracy and Execution Time: Different models exhibited trade-offs between prediction accuracy and execution time. High-performing models like CBR were found to take the longest execution time. This highlights the need for balanced optimization between model accuracy and computational efficiency.
- Gradient Boosting vs. Gradient Descent: The study underlined a fundamental difference between gradient boosting and gradient descent approaches, which led to better prediction accuracy with gradient boosting models. This could inspire further research into model architectures and algorithmic design.
- Role of Regularization in Overfitting Control: The improved performance of the XGB model was attributed to its ability to control overfitting through a more regularized model formalization. This showcases the importance of proper regularization techniques in model development to prevent overfitting.
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Miguel, M.; Penna, M.; Nievola, J.; Pellenz, M. New models for long-term Internet traffic forecasting using artificial neural networks and flow based information. In Proceedings of the 2012 IEEE Network Operations and Management Symposium, Maui, HI, USA, 16–20 April 2012; pp. 1082–1088. [Google Scholar]
- Zeng, Q.; Sun, Q.; Chen, G.; Duan, H.; Li, C.; Song, G. Traffic prediction of wireless cellular networks based on deep transfer learning and cross-domain data. IEEE Access 2020, 8, 172387–172397. [Google Scholar] [CrossRef]
- Wilmet, A.; Viard, T.; Latapy, M.; Lamarche-Perrin, R. Outlier detection in IP traffic modelled as a link stream using the stability of degree distributions over time. Comput. Netw. 2019, 161, 197–209. [Google Scholar] [CrossRef]
- Li, N.; Hu, L.; Deng, Z.; Su, T.; Liu, J. Research on GRU neural network Satellite traffic prediction based on transfer learning. Wirel. Pers. Commun. 2021, 118, 815–827. [Google Scholar] [CrossRef]
- Abdellah, A.; Mahmood, O.; Paramonov, A.; Koucheryavy, A. IoT traffic prediction using multi-step ahead prediction with neural network. In Proceedings of the 2019 11th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Dublin, Ireland, 28–30 October 2019; pp. 1–4. [Google Scholar]
- Saha, S.; Haque, A.; Sidebottom, G. Towards an Ensemble Regressor Model for ISP Traffic Prediction with Anomaly Detection and Mitigation. In Proceedings of the 2022 International Symposium on Networks, Computers and Communications (ISNCC), Shenzhen, China, 19–22 July 2022; pp. 1–6. [Google Scholar]
- Xu, Y.; Xu, W.; Yin, F.; Lin, J.; Cui, S. High-accuracy wireless traffic prediction: A GP-based machine learning approach. In Proceedings of the GLOBECOM 2017-2017 IEEE Global Communications Conference, Singapore, 4–8 December 2017; pp. 1–6. [Google Scholar]
- Bayati, A.; Nguyen, K.; Cheriet, M. Multiple-step-ahead traffic prediction in high-speed networks. IEEE Commun. Lett. 2018, 22, 2447–2450. [Google Scholar] [CrossRef]
- Szostak, D.; Włodarczyk, A.; Walkowiak, K. Machine learning classification and regression approaches for optical network traffic prediction. Electronics 2021, 10, 1578. [Google Scholar] [CrossRef]
- Szostak, D.; Walkowiak, K.; Włodarczyk, A. Short-Term Traffic Forecasting in Optical Network using Linear Discriminant Analysis Machine Learning Classifier. In Proceedings of the 2020 22nd International Conference On Transparent Optical Networks (ICTON), Bari, Italy, 19–23 July 2020; pp. 1–4. [Google Scholar]
- Huang, C.; Chiang, C.; Li, Q. A study of deep learning networks on mobile traffic forecasting. In Proceedings of the 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), Montreal, QC, Canada, 1–8 October 2017; pp. 1–6. [Google Scholar]
- Madan, R.; Mangipudi, P. Predicting computer network traffic: A time series forecasting approach using DWT, ARIMA and RNN. In Proceedings of the 2018 Eleventh International Conference on Contemporary Computing (IC3), Noida, India, 2–4 August 2018; pp. 1–5. [Google Scholar]
- Fischer, S.; Katsarou, K.; Holschke, O. DeepFlow: Towards Network-Wide Ingress Traffic Prediction Using Machine Learning At Large Scale. In Proceedings of the 2020 International Symposium on Networks, Computers and Communications (ISNCC), Online, 3–6 August 2020; pp. 1–8. [Google Scholar]
- Wang, W.; Bai, Y.; Yu, C.; Gu, Y.; Feng, P.; Wang, X.; Wang, R. A network traffic flow prediction with deep learning approach for large-scale metropolitan area network. In Proceedings of the NOMS 2018-2018 IEEE/IFIP Network Operations and Management Symposium, Taipei, Taiwan, 23–27 April 2018; pp. 1–9. [Google Scholar]
- Oliveira, T.; Barbar, J.; Soares, A. Multilayer perceptron and stacked autoencoder for Internet traffic prediction. In Proceedings of the IFIP International Conference on Network and Parallel Computing, Ilan, Taiwan, 18–20 September 2014; pp. 61–71. [Google Scholar]
- Theodoropoulos, T.; Maroudis, A.; Violos, J.; Tserpes, K. An Encoder-Decoder Deep Learning Approach for Multistep Service Traffic Prediction. In Proceedings of the 2021 IEEE Seventh International Conference on Big Data Computing Service and Applications (BigDataService), Online, 23–26 August 2021; pp. 33–40. [Google Scholar]
- Han, Y.; Jing, Y.; Li, K. Multi-step prediction for the network traffic based on echo state network optimized by quantum-behaved fruit fly optimization algorithm. In Proceedings of the 2017 29th Chinese Control and Decision Conference (CCDC), Chongqing, China, 28–30 May 2017; pp. 2270–2274. [Google Scholar]
- Li, M.; Wang, Y.; Wang, Z.; Zheng, H. A deep learning method based on an attention mechanism for wireless network traffic prediction. Ad Hoc Netw. 2020, 107, 102258. [Google Scholar] [CrossRef]
- Rau, F.; Soto, I.; Adasme, P.; Zabala-Blanco, D.; Azurdia-Meza, C. Network Traffic Prediction Using Online-Sequential Extreme Learning Machine. In Proceedings of the 2021 Third South American Colloquium on Visible Light Communications (SACVLC), Online, 11–12 November 2021; pp. 1–6. [Google Scholar]
- Yao, Z.; Xu, Q.; Chen, Y.; Tu, Y.; Zhang, H.; Chen, Y. Internet Traffic Forecasting using Temporal-Topological Graph Convolutional Networks. In Proceedings of the 2021 International Joint Conference on Neural Networks (IJCNN), Virtual, 18–22 July 2021; pp. 1–8. [Google Scholar]
- Zeb, S.; Rathore, M.; Mahmood, A.; Hassan, S.; Kim, J.; Gidlund, M. Edge intelligence in softwarized 6G: Deep learning-enabled network traffic predictions. In Proceedings of the 2021 IEEE Globecom Workshops (GC Wkshps), Madrid, Spain, 7–11 December 2021; pp. 1–6. [Google Scholar]
- Knapińska, A.; Lechowicz, P.; Walkowiak, K. Machine-learning based prediction of multiple types of network traffic. In Proceedings of the International Conference on Computational Science, Las Vegas, NV, USA, 15–17 December 2021; pp. 122–136. [Google Scholar]
- Molnar, F.; Hutton, B.; Fergusson, D. Does analysis using “last observation carried forward” introduce bias in dementia research? Can. Med. Assoc. J. 2008, 179, 751–753. [Google Scholar] [CrossRef] [PubMed]
- Chernick, M. The Essentials of Biostatistics for Physicians, Nurses, and Clinicians; John Wiley & Sons: Hoboken, NJ, USA, 2011. [Google Scholar]
- Kvanli, A.; Pavur, R.; Keeling, K. Concise Managerial Statistics; Cengage Learning: Boston, MA, USA, 2005. [Google Scholar]
- Kordos, M.; Arnaiz-Gonzalez, A.; Garcia-Osorio, C. Evolutionary prototype selection for multi-output regression. Neurocomputing 2019, 358, 309–320. [Google Scholar] [CrossRef]
- Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; et al. Scikit-learn: Machine Learning in Python. J. Mach. Learn. Res. 2011, 12, 2825–2830. [Google Scholar]
- Dorogush, A.; Ershov, V.; Gulin, A. CatBoost: Gradient boosting with categorical features support. arXiv 2018, arXiv:1810.11363. [Google Scholar]
- Dhananjay, B.; Sivaraman, J. Analysis and classification of heart rate using CatBoost feature ranking model. Biomed. Signal Process. Control. 2021, 68, 102610. [Google Scholar] [CrossRef]
- Reddy, D.; Behera, H. CatBoosting Approach for Anomaly Detection in IoT-Based Smart Home Environment. Comput. Intell. Data Min. 2022, 281, 753–764. [Google Scholar]
- Zhou, F.; Yang, Q.; Zhang, K.; Trajcevski, G.; Zhong, T.; Khokhar, A. Reinforced spatiotemporal attentive graph neural networks for traffic forecasting. IEEE Internet Things J. 2020, 7, 6414–6428. [Google Scholar] [CrossRef]
- Wang, Y.; Jiang, D.; Huo, L.; Zhao, Y. A new traffic prediction algorithm to software defined networking. Mob. Netw. Appl. 2021, 26, 716–725. [Google Scholar] [CrossRef]
Data Samples Statistics | ||
Statistics | Before | After |
Mean | 8,364,742,790 | 8,344,127,355 |
SD | 4,096,690,529 | 4,013,117,118 |
Statistical Test Results Summary | ||
Test | Test statistic | p-value |
Two-sample t-test | 0.328505869 | 0.742533327 |
Wilcoxon Rank-sum test | 0.015409873 | 0.987705187 |
Kolmogorov–Smirnov test | 0.005148467 | 0.999891457 |
Input | Classical Model (With Outlier) | Proposed Model (Without Outlier) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Model | 6 | 9 | 12 | 15 | 18 | 6 | 9 | 12 | 15 | 18 | |
GBR | 7.47 | 7.74 | 7.57 | 7.60 | 7.76 | 5.20 | 5.31 | 5.24 | 5.26 | 5.25 | |
XGB | 7.65 | 7.69 | 7.47 | 7.59 | 7.60 | 5.16 | 5.20 | 5.19 | 5.15 | 5.17 | |
LGB | 8.51 | 8.47 | 8.47 | 8.47 | 8.53 | 5.11 | 5.09 | 5.13 | 5.14 | 5.10 | |
CBR | 7.56 | 7.58 | 7.64 | 7.78 | 8.12 | 5.10 | 5.08 | 5.20 | 5.32 | 5.44 | |
SGD | 12.80 | 10.51 | 10.44 | 11.13 | 12.16 | 6.10 | 7.27 | 8.01 | 8.50 | 8.23 |
Model | GBR | XGB | LGB | CBR | SGD | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Classical Model | Prop. Model | Classical Model | Prop. Model | Classical Model | Prop. Model | Classical Model | Prop. Model | Classical Model | Prop. Model | ||
6 | Step 1 | 3.80 | 3.76 | 3.78 | 3.75 | 3.68 | 3.63 | 3.65 | 3.61 | 6.41 | 5.23 |
Step 2 | 4.95 | 4.84 | 4.85 | 4.85 | 4.71 | 4.63 | 4.55 | 4.54 | 7.45 | 6.46 | |
Step 3 | 5.93 | 5.85 | 5.88 | 5.84 | 5.53 | 5.44 | 5.44 | 5.38 | 8.62 | 7.57 | |
Step 4 | 6.85 | 6.78 | 6.84 | 6.80 | 6.26 | 6.22 | 6.21 | 6.16 | 9.72 | 8.71 | |
Step 5 | 7.74 | 7.58 | 7.76 | 7.63 | 7.02 | 6.96 | 6.90 | 6.91 | 10.85 | 9.81 | |
Step 6 | 8.66 | 8.46 | 8.68 | 8.62 | 7.77 | 7.76 | 7.70 | 7.68 | 11.80 | 10.92 | |
9 | Step 1 | 3.79 | 3.70 | 3.75 | 3.71 | 3.67 | 3.60 | 3.64 | 3.60 | 7.36 | 5.61 |
Step 2 | 4.82 | 4.73 | 4.75 | 4.71 | 4.61 | 4.52 | 4.55 | 4.46 | 8.54 | 6.71 | |
Step 3 | 5.70 | 5.54 | 5.71 | 5.63 | 5.44 | 5.31 | 5.27 | 5.24 | 9.76 | 7.77 | |
Step 4 | 6.60 | 6.42 | 6.59 | 6.51 | 6.08 | 5.98 | 5.99 | 5.94 | 10.75 | 8.83 | |
Step 5 | 7.31 | 7.22 | 7.34 | 7.21 | 6.69 | 6.55 | 6.56 | 6.51 | 11.79 | 9.92 | |
Step 6 | 8.15 | 7.99 | 8.14 | 8.10 | 7.31 | 7.25 | 7.17 | 7.19 | 12.99 | 10.96 | |
12 | Step 1 | 3.92 | 3.68 | 3.78 | 3.69 | 3.72 | 3.58 | 3.60 | 3.55 | 8.40 | 5.38 |
Step 2 | 4.73 | 4.58 | 4.62 | 4.55 | 4.59 | 4.43 | 4.43 | 4.43 | 9.49 | 6.39 | |
Step 3 | 5.51 | 5.36 | 5.57 | 5.37 | 5.31 | 5.21 | 5.18 | 5.12 | 10.67 | 7.35 | |
Step 4 | 6.29 | 6.13 | 6.24 | 6.13 | 5.94 | 5.89 | 5.74 | 5.74 | 11.65 | 8.31 | |
Step 5 | 6.85 | 6.75 | 7.00 | 6.79 | 6.52 | 6.45 | 6.35 | 6.33 | 12.86 | 9.22 | |
Step 6 | 7.63 | 7.45 | 7.60 | 7.50 | 7.08 | 7.01 | 6.91 | 6.92 | 13.92 | 10.10 | |
15 | Step 1 | 3.69 | 3.59 | 3.71 | 3.60 | 3.68 | 3.60 | 3.66 | 3.62 | 9.15 | 4.87 |
Step 2 | 4.53 | 4.46 | 4.53 | 4.43 | 4.57 | 4.43 | 4.44 | 4.39 | 10.82 | 5.73 | |
Step 3 | 5.26 | 5.19 | 5.26 | 5.16 | 5.26 | 5.14 | 5.14 | 5.09 | 11.39 | 6.59 | |
Step 4 | 5.89 | 5.81 | 5.91 | 5.76 | 5.87 | 5.79 | 5.66 | 5.68 | 12.24 | 7.36 | |
Step 5 | 6.57 | 6.38 | 6.59 | 6.46 | 6.45 | 6.41 | 6.27 | 6.21 | 13.31 | 8.15 | |
Step 6 | 7.23 | 7.06 | 7.16 | 7.12 | 7.03 | 7.01 | 6.76 | 6.85 | 14.71 | 8.90 | |
18 | Step 1 | 3.68 | 3.55 | 3.67 | 3.55 | 3.60 | 3.53 | 3.64 | 3.62 | 9.48 | 4.36 |
Step 2 | 4.45 | 4.40 | 4.46 | 4.39 | 4.54 | 4.43 | 4.48 | 4.42 | 10.50 | 5.12 | |
Step 3 | 5.19 | 5.08 | 5.17 | 5.08 | 5.21 | 5.09 | 5.12 | 5.07 | 11.50 | 5.87 | |
Step 4 | 5.81 | 5.73 | 5.82 | 5.72 | 5.81 | 5.76 | 5.71 | 5.67 | 12.72 | 6.59 | |
Step 5 | 6.51 | 6.38 | 6.51 | 6.39 | 6.40 | 6.35 | 6.35 | 6.31 | 13.34 | 7.25 | |
Step 6 | 7.08 | 7.03 | 7.10 | 6.99 | 7.04 | 7.02 | 6.93 | 6.96 | 14.31 | 7.94 |
Model | GBR | XGB | LGB | CAB | SGD | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Classical Model | Prop. Model | Classical Model | Prop. Model | Classical Model | Prop. Model | Classical Model | Prop. Model | Classical Model | Prop. Model | ||
9 | Step 1 | 3.78 | 3.71 | 3.76 | 3.69 | 3.66 | 3.60 | 3.67 | 3.60 | 7.40 | 5.64 |
Step 2 | 4.83 | 4.67 | 4.76 | 4.74 | 4.61 | 4.54 | 4.60 | 4.52 | 8.56 | 6.73 | |
Step 3 | 5.73 | 5.55 | 5.69 | 5.59 | 5.42 | 5.33 | 5.28 | 5.25 | 9.66 | 7.80 | |
Step 4 | 6.69 | 6.40 | 6.58 | 6.42 | 6.07 | 6.03 | 5.98 | 5.91 | 10.74 | 8.90 | |
Step 5 | 7.35 | 7.20 | 7.37 | 7.15 | 6.65 | 6.56 | 6.58 | 6.53 | 11.90 | 9.90 | |
Step 6 | 8.12 | 7.94 | 8.10 | 8.03 | 7.29 | 7.24 | 7.23 | 7.20 | 13.22 | 10.96 | |
Step 7 | 8.97 | 8.77 | 9.01 | 8.79 | 7.98 | 7.92 | 7.96 | 7.88 | 14.15 | 11.98 | |
Step 8 | 9.66 | 9.43 | 9.65 | 9.48 | 8.55 | 8.51 | 8.53 | 8.50 | 15.49 | 12.91 | |
Step 9 | 10.41 | 10.15 | 10.49 | 10.17 | 9.17 | 9.17 | 9.08 | 9.02 | 16.26 | 13.84 | |
12 | Step 1 | 3.84 | 3.66 | 3.82 | 3.64 | 3.70 | 3.58 | 3.59 | 3.56 | 8.47 | 5.37 |
Step 2 | 4.68 | 4.58 | 4.65 | 4.56 | 4.57 | 4.44 | 4.43 | 4.41 | 9.51 | 6.42 | |
Step 3 | 5.53 | 5.40 | 5.51 | 5.39 | 5.31 | 5.22 | 5.18 | 5.14 | 10.56 | 7.36 | |
Step 4 | 6.26 | 6.10 | 6.20 | 6.16 | 5.97 | 5.84 | 5.76 | 5.77 | 11.74 | 8.31 | |
Step 5 | 6.91 | 6.77 | 7.05 | 6.80 | 6.57 | 6.41 | 6.43 | 6.36 | 12.77 | 9.22 | |
Step 6 | 7.63 | 7.56 | 7.60 | 7.52 | 7.09 | 6.99 | 6.96 | 6.95 | 13.97 | 10.12 | |
Step 7 | 8.28 | 8.16 | 8.34 | 8.18 | 7.73 | 7.69 | 7.57 | 7.53 | 14.92 | 10.97 | |
Step 8 | 8.98 | 8.84 | 8.96 | 8.78 | 8.24 | 8.25 | 8.08 | 8.06 | 16.03 | 11.74 | |
Step 9 | 9.64 | 9.50 | 9.56 | 9.40 | 8.78 | 8.77 | 8.60 | 8.69 | 17.62 | 12.59 | |
15 | Step 1 | 3.73 | 3.59 | 3.68 | 3.57 | 3.64 | 3.58 | 3.67 | 3.64 | 9.12 | 4.88 |
Step 2 | 4.57 | 4.42 | 4.52 | 4.43 | 4.54 | 4.42 | 4.51 | 4.41 | 10.37 | 5.74 | |
Step 3 | 5.26 | 5.16 | 5.23 | 5.15 | 5.27 | 5.15 | 5.10 | 5.08 | 11.28 | 6.55 | |
Step 4 | 5.89 | 5.86 | 5.90 | 5.84 | 5.86 | 5.77 | 5.69 | 5.67 | 12.28 | 7.36 | |
Step 5 | 6.60 | 6.46 | 6.63 | 6.48 | 6.46 | 6.41 | 6.28 | 6.23 | 13.36 | 8.19 | |
Step 6 | 7.22 | 7.15 | 7.19 | 7.10 | 7.09 | 6.99 | 6.76 | 6.90 | 14.46 | 8.90 | |
Step 7 | 7.89 | 7.77 | 7.91 | 7.77 | 7.71 | 7.63 | 7.40 | 7.42 | 15.44 | 9.37 | |
Step 8 | 8.54 | 8.41 | 8.52 | 8.39 | 8.09 | 8.13 | 7.93 | 8.04 | 16.33 | 10.05 | |
Step 9 | 9.14 | 9.07 | 9.19 | 8.99 | 8.73 | 8.65 | 8.53 | 8.61 | 17.24 | 10.72 | |
18 | Step 1 | 3.66 | 3.54 | 3.68 | 3.54 | 3.61 | 3.55 | 3.61 | 3.63 | 9.68 | 4.36 |
Step 2 | 4.45 | 4.43 | 4.46 | 4.39 | 4.52 | 4.43 | 4.49 | 4.44 | 10.60 | 5.12 | |
Step 3 | 5.19 | 5.06 | 5.19 | 5.10 | 5.21 | 5.11 | 5.13 | 5.09 | 11.39 | 5.87 | |
Step 4 | 5.79 | 5.76 | 5.84 | 5.74 | 5.85 | 5.75 | 5.73 | 5.66 | 12.42 | 6.59 | |
Step 5 | 6.59 | 6.40 | 6.52 | 6.37 | 6.47 | 6.35 | 6.33 | 6.28 | 13.34 | 7.27 | |
Step 6 | 7.12 | 7.00 | 7.10 | 6.97 | 6.98 | 7.03 | 6.95 | 6.94 | 14.40 | 7.91 | |
Step 7 | 7.80 | 7.66 | 7.88 | 7.67 | 7.63 | 7.57 | 7.52 | 7.52 | 15.24 | 8.43 | |
Step 8 | 8.33 | 8.27 | 8.34 | 8.24 | 8.15 | 8.16 | 8.11 | 8.16 | 16.12 | 9.06 | |
Step 9 | 8.98 | 8.88 | 8.97 | 8.90 | 8.74 | 8.72 | 8.70 | 8.75 | 17.10 | 9.69 |
Model | GBR | XGB | LGB | CBR | SGD | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Classical Model |
Prop. Model |
Classical Model |
Prop. Model |
Classical Model |
Prop. Model |
Classical Model |
Prop. Model |
Classical Model |
Prop. Model | ||
12 | Step 1 | 3.92 | 3.67 | 3.82 | 3.65 | 3.70 | 3.58 | 3.59 | 3.56 | 8.42 | 5.36 |
Step 2 | 4.75 | 4.57 | 4.69 | 4.54 | 4.56 | 4.46 | 4.44 | 4.42 | 9.47 | 6.40 | |
Step 3 | 5.52 | 5.38 | 5.52 | 5.42 | 5.30 | 5.23 | 5.17 | 5.12 | 10.59 | 7.36 | |
Step 4 | 6.24 | 6.11 | 6.26 | 6.11 | 5.92 | 5.85 | 5.77 | 5.76 | 11.75 | 8.35 | |
Step 5 | 6.91 | 6.80 | 7.00 | 6.84 | 6.55 | 6.47 | 6.42 | 6.34 | 12.85 | 9.23 | |
Step 6 | 7.62 | 7.48 | 7.61 | 7.41 | 7.11 | 6.95 | 6.94 | 6.99 | 13.82 | 10.15 | |
Step 7 | 8.26 | 8.16 | 8.34 | 8.17 | 7.73 | 7.66 | 7.50 | 7.55 | 15.05 | 11.02 | |
Step 8 | 8.94 | 8.80 | 8.94 | 8.71 | 8.31 | 8.21 | 8.05 | 8.11 | 15.91 | 11.78 | |
Step 9 | 9.56 | 9.50 | 9.56 | 9.40 | 8.84 | 8.84 | 8.63 | 8.74 | 17.03 | 12.58 | |
Step 10 | 10.22 | 10.11 | 10.20 | 10.03 | 9.35 | 9.31 | 9.18 | 9.25 | 18.15 | 13.41 | |
Step 11 | 10.81 | 10.68 | 10.88 | 10.63 | 9.96 | 9.90 | 9.79 | 9.87 | 19.16 | 13.86 | |
Step 12 | 11.46 | 11.39 | 11.43 | 11.27 | 10.52 | 10.52 | 10.50 | 10.48 | 20.11 | 14.69 | |
15 | Step 1 | 3.68 | 3.61 | 3.70 | 3.60 | 3.66 | 3.57 | 3.68 | 3.63 | 9.12 | 4.84 |
Step 2 | 4.57 | 4.48 | 4.52 | 4.44 | 4.54 | 4.43 | 4.51 | 4.42 | 10.23 | 5.74 | |
Step 3 | 5.28 | 5.23 | 5.29 | 5.15 | 5.22 | 5.16 | 5.11 | 5.10 | 11.32 | 6.61 | |
Step 4 | 5.99 | 5.81 | 5.95 | 5.83 | 5.84 | 5.75 | 5.73 | 5.70 | 12.50 | 7.44 | |
Step 5 | 6.55 | 6.50 | 6.62 | 6.48 | 6.45 | 6.39 | 6.28 | 6.19 | 13.43 | 8.19 | |
Step 6 | 7.23 | 7.12 | 7.25 | 7.03 | 7.09 | 7.02 | 6.84 | 6.82 | 14.30 | 8.91 | |
Step 7 | 7.86 | 7.73 | 7.91 | 7.81 | 7.74 | 7.66 | 7.48 | 7.45 | 15.37 | 9.61 | |
Step 8 | 8.51 | 8.41 | 8.50 | 8.39 | 8.08 | 8.14 | 7.99 | 7.99 | 16.46 | 10.03 | |
Step 9 | 9.16 | 9.03 | 9.14 | 9.01 | 8.73 | 8.72 | 8.53 | 8.62 | 17.36 | 10.71 | |
Step 10 | 9.65 | 9.66 | 9.72 | 9.64 | 9.25 | 9.26 | 9.16 | 9.17 | 18.32 | 11.43 | |
Step 11 | 10.26 | 10.19 | 10.30 | 10.14 | 9.80 | 9.86 | 9.82 | 9.80 | 19.24 | 12.13 | |
Step 12 | 10.90 | 10.79 | 10.94 | 10.78 | 10.43 | 10.40 | 10.36 | 10.47 | 20.27 | 12.80 | |
18 | Step 1 | 3.68 | 3.55 | 3.65 | 3.53 | 3.63 | 3.53 | 3.68 | 3.61 | 9.51 | 4.35 |
Step 2 | 4.46 | 4.41 | 4.46 | 4.38 | 4.58 | 4.42 | 4.51 | 4.40 | 10.43 | 5.15 | |
Step 3 | 5.20 | 5.10 | 5.20 | 5.09 | 5.21 | 5.12 | 5.16 | 5.10 | 11.48 | 5.87 | |
Step 4 | 5.84 | 5.74 | 5.83 | 5.74 | 5.91 | 5.73 | 5.76 | 5.69 | 12.43 | 6.57 | |
Step 5 | 6.49 | 6.40 | 6.57 | 6.40 | 6.47 | 6.36 | 6.36 | 6.28 | 13.66 | 7.27 | |
Step 6 | 7.12 | 6.97 | 7.15 | 6.99 | 7.06 | 7.01 | 6.93 | 6.95 | 14.47 | 7.96 | |
Step 7 | 7.84 | 7.69 | 7.80 | 7.66 | 7.76 | 7.67 | 7.58 | 7.52 | 15.32 | 8.47 | |
Step 8 | 8.31 | 8.27 | 8.35 | 8.21 | 8.19 | 8.10 | 8.14 | 8.15 | 16.14 | 9.04 | |
Step 9 | 8.96 | 8.97 | 9.02 | 8.92 | 8.70 | 8.74 | 8.68 | 8.73 | 17.18 | 9.72 | |
Step 10 | 9.49 | 9.42 | 9.45 | 9.43 | 9.20 | 9.28 | 9.18 | 9.19 | 18.20 | 10.31 | |
Step 11 | 10.03 | 10.02 | 10.06 | 10.06 | 9.78 | 9.81 | 9.74 | 9.77 | 19.82 | 10.89 | |
Step 12 | 10.71 | 10.60 | 10.72 | 10.57 | 10.35 | 10.36 | 10.42 | 10.38 | 20.28 | 11.58 |
Ref. | Dataset | Method | Forecast Length | Outlier Detection and Mitigation | Mean Accuracy |
---|---|---|---|---|---|
[18] | temporal and spatial | convolutional neural network | single-step | no | 91.05% |
[31] | temporal and spatial | reinforcement learning | multi-step | no | 93.12% (15 min), 91.68% (30 min), 90.03% (60 min) |
[32] | temporal | statistical technique | single-step and multi-step | no | 90% (1 min), 70% (5 min), 53% (10 min) |
Proposed | temporal | boosting algorithms | single-step and multi-step | yes | 4.92% (5 min), 94.70% (30 min), 93.78% (45 min), 92.89% (60 min) |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Saha, S.; Haque, A.; Sidebottom, G. Multi-Step Internet Traffic Forecasting Models with Variable Forecast Horizons for Proactive Network Management. Sensors 2024, 24, 1871. https://doi.org/10.3390/s24061871
Saha S, Haque A, Sidebottom G. Multi-Step Internet Traffic Forecasting Models with Variable Forecast Horizons for Proactive Network Management. Sensors. 2024; 24(6):1871. https://doi.org/10.3390/s24061871
Chicago/Turabian StyleSaha, Sajal, Anwar Haque, and Greg Sidebottom. 2024. "Multi-Step Internet Traffic Forecasting Models with Variable Forecast Horizons for Proactive Network Management" Sensors 24, no. 6: 1871. https://doi.org/10.3390/s24061871
APA StyleSaha, S., Haque, A., & Sidebottom, G. (2024). Multi-Step Internet Traffic Forecasting Models with Variable Forecast Horizons for Proactive Network Management. Sensors, 24(6), 1871. https://doi.org/10.3390/s24061871