This paper compares four different artificial neural network approaches for computer network traffic forecast, such as: 1) multilayer perceptron (MLP) using the backpropagation as training algorithm; 2) MLP with resilient backpropagation (Rprop); (3) recurrent neural network (RNN); 4) deep learning stacked autoencoder (SAE). The computer network traffic is sampled from the traffic of the network devices that are connected to the internet. It is shown herein how a simpler neural network model, such as the RNN and MLP, can work even better than a more complex model, such as the SAE. Internet traffic prediction is an important task for many applications, such as adaptive applications, congestion control, admission control, anomaly detection and bandwidth allocation. In addition, efficient methods of resource management, such as the bandwidth, can be used to gain performance and reduce costs, improving the quality of service (QoS). The popularity of the newest deep learning methods have been increasing in several areas, but there is a lack of studies concerning time series prediction, such as internet traffic.