# Internet Traffic Prediction with Distributed Multi-Agent Learning
###### Abstract  
Internet traffic prediction has been considered a research topic and the basis for intelligent network management and planning, e.g., elastic network service provision and content delivery optimization. Various methods have been proposed in the literature for Internet traffic prediction, including statistical, machine learning and deep learning methods. However, most of the existing approaches are trained and deployed in a centralized approach, without considering the realistic scenario in which multiple parties are concerned about the prediction process and the prediction model can be trained in a distributed approach. In this study, a distributed multi-agent learning framework is proposed to fill the research gap and predict Internet traffic in a distributed approach, in which each agent trains a base prediction model and the individual models are further aggregated with the cooperative interaction process. In the numerical experiments, two sophisticated deep learning models are chosen as the base prediction model, namely, long short-term memory (LSTM) and gated recurrent unit (GRU). The numerical experiments demonstrate that the GRU model trained with five agents achieves state-of-the-art performance on a real-world Internet traffic dataset collected in a campus backbone network in terms of root mean square error (RMSE) and mean absolute error (MAE). internet traffic prediction; distributed multi-agent learning; long short-term memory; gated recurrent unit +
Footnote †: journal:  
0000-0001-1999-22000/0000-0000-0000-0000-0000-0000-00000-0000-00000-0000-0000  
recurrent neural networks for time series-format prediction [6; 7], convolutional neural networks for grid-based prediction [8; 9] and graph neural networks for graph-format prediction [10; 11]. However, most of the existing studies for Internet traffic prediction focus on the centralized approach, in which the prediction models are trained and deployed in a centralized server, neglecting the case that multiple parties are concerned about the prediction process and want to be involved in the training process in a distributed approach. In reality, multiple parties would be interested in the prediction result of Internet traffic usages. For example, for the campus backbone network considered in this paper, the involved parties include the university network management department, the Internet service provider and the Internet content provider. All these parties behave as an intelligent agent with their own computation and communication facilities that can be leveraged in the traffic prediction task. On the other hand, distributed multi-agent learning has been proven more efficient than training a deep learning model on a single agent [12]. However, few previous discussed whether better performance can be achieved with such settings in the problem of Internet traffic prediction. To the best of our knowledge, this paper presents a pioneer work which predicts Internet traffic with a distributed multi-agent learning approach when Internet traffic prediction is modeled as a supervised learning problem. For this paper, the research motivation is to validate the marginal benefit of the distributed multi-agent learning approach over traditional centralized learning and initiate the research direction of a potential further performance improvement in follow-up studies. Two recurrent neural networks, namely, long short-term memory (LSTM) [13] and gated recurrent unit (GRU) [14], are adopted as the base prediction model and compared on a real-world Internet traffic dataset. The numerical experiments show that the GRU-based distributed multi-agent learning approach achieves state-of-the-art performance, outperforming both the LSTM-based multi-agent learning approach and the centralized learning approach in a previous study [15]. The contributions of this paper are summarized as follows:  
1.