Traffic prediction represents one of the crucial tasks for smartly optimizing the mobile network. The research in this topic concentrated in making predictions in a centralized fashion, i.e., by collecting data from the different network elements. This translates to a considerable amount of energy for data transmission and processing. In this work, we propose a novel prediction framework based on edge computing which uses datasets obtained on the edge through a large measurement campaign. Two main Deep Learning architectures are designed, based on Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), and tested under different training conditions. In addition, Knowledge Transfer Learning (KTL) techniques are employed to improve the performance of the models while reducing the required computational resources. Simulation results show that the CNN architectures outperform the RNNs. An estimation for the needed training energy is provided, highlighting KTL ability to reduce the energy footprint of the models of 60% and 90% for CNNs and RNNs, respectively. Finally, two cutting-edge explainable Artificial Intelligence techniques are employed to interpret the derived learning models.