There is a lack of research on the analysis of peruser traffic in cellular networks, for deriving and following traffic-aware network management. In fact, the legacy design approach, in which resource provisioning and operation control are performed based on the cell-aggregated traffic scenarios, are not so energy- and cost-efficient and need to be substituted with user-centric predictive analysis of mobile network traffic and proactive network resource management. Here, we shed light on this problem by designing traffic prediction tools that utilize standard machine learning (ML) tools, including long shortterm memory (LSTM) and autoregressive integrated moving average (ARIMA) on top of per-user data. We present an expansive empirical evaluation of the designed solutions over a real network traffic dataset. Within this analysis, the impact of different parameters, such as the time granularity, the length of future predictions, and feature selection are investigated. As a potential application of these solutions, we present an ML-powered Discontinuous reception (DRX) scheme for energy saving. Towards this end, we leverage the derived ML models for dynamic DRX parameter adaptation to user traffic. The performance evaluation results demonstrate the superiority of LSTM over ARIMA in general, especially when the length of the training time series is high enough, and it is augmented by a wisely-selected set of features. Furthermore, the results show that adaptation of DRX parameters by online prediction of future traffic provides much more energy-saving at low latency cost in comparison with the legacy cell-wide DRX parameter adaptation.