The task of predicting internet traffic is challenging, particularly in multi-step forecasting due to the volatile and random nature of data. In addition, real-world traffic may contain outlier data points, so developing a prediction model that integrates anomaly detection and mitigation is necessary. This paper compares several deep sequence models, such as Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), LSTM Encoder-Decoder (LSTM En De), LSTM Encoder-Decoder with attention layer (LSTM En De Atn), and Gated Recurrent Unit (GRU), with our proposed methodology for single-step prediction. Our proposed LSTM En De model, integrated with outlier detection, outperforms traditional deep sequence models in single-step prediction, reducing the deviation between actual and predicted traffic by over 11%. We also apply our methodology to multi-step forecast analysis, using multiple output strategies for forecast horizons of 3, 6, 9, and 12 steps ahead. Experimental results demonstrate the effectiveness of our proposed methodology in improving the accuracy of singlestep prediction and multi-step forecasting tasks, especially when dealing with outlier data points that adversely affect model accuracy. In summary, this paper investigates the challenges of real-world internet traffic prediction, proposes a novel prediction model integrated with anomaly detection and mitigation, and compares different deep sequence models for single-step and multi-step forecasting tasks.