Recently, deep learning, an emerging machine learning technique, is garnering a lot of research attention in several computer science areas. However, to the best of our knowledge, its application to improve heterogeneous network traffic control (which is an important and challenging area by its own merit) has yet to appear because of the difficult challenge in characterizing the appropriate input and output patterns for a deep learning system to correctly reflect the highly dynamic nature of large-scale heterogeneous networks. In this vein, in this article, we propose appropriate input and output characterizations of heterogeneous network traffic and propose a supervised deep neural network system. We describe how our proposed system works and how it differs from traditional neural networks. Also, preliminary results are reported that demonstrate the encouraging performance of our proposed deep learning system compared to a benchmark routing strategy (Open Shortest Path First (OSPF)) in terms of significantly better signaling overhead, throughput, and delay.