  Traffic learning and prediction is at the heart of the evaluation of the
performance of telecommunications networks and attracts a lot of attention in
wired broadband networks. Now, benefiting from the big data in cellular
networks, it becomes possible to make the analyses one step further into the
application level. In this paper, we firstly collect a significant amount of
application-level traffic data from cellular network operators. Afterwards,
with the aid of the traffic "big data", we make a comprehensive study over the
modeling and prediction framework of cellular network traffic. Our results
solidly demonstrate that there universally exist some traffic statistical
modeling characteristics, including ALPHA-stable modeled property in the
temporal domain and the sparsity in the spatial domain. Meanwhile, the results
also demonstrate the distinctions originated from the uniqueness of different
service types of applications. Furthermore, we propose a new traffic prediction
framework to encompass and explore these aforementioned characteristics and
then develop a dictionary learning-based alternating direction method to solve
it. Besides, we validate the prediction accuracy improvement and the robustness
of the proposed framework through extensive simulation results.
