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Recovery and forecast of network traffic data from incomplete observed data is an important issue in internet engineering and management. In this paper, by fully considering the temporal stability and periodicity features in internet traffic data, a novel optimization model for internet data recovery and forecast is proposed, which is based upon the newly introduced higher order tensor decomposition form called tubal tensor train decomposition. Moreover, by introducing auxiliary variables and penalty techniques, a relaxation of the proposed model is obtained. Then, an easy-to-operate and effective algorithm for solving the relaxation model is proposed. We prove that the sequence generated by the proposed algorithm converges to a stationary point of the established relaxation model. A series of numerical experiments about the recovery of structurally missing traffic data and the traffic data prediction on the widely used real-world datasets demonstrate that our approach have favorable performance than some state-of-the-art tensor/matrix based approaches.

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