The internet traffic data completion is an important and challenging task in network engineering. Due to the multi-dimensionality of internet traffic data, we introduce two tensor train (TT) based optimization models with temporal regularization to recover the data from an incomplete observation. Moreover, we propose two easily implementable algorithms by following the spirit of alternating minimization. It is remarkable that our algorithms have closed-form solutions and one algorithm can be implemented in a parallel way for large-scale problems. Some numerical experiments on real-world datasets show that our approaches perform better than some existing state-of-the-art matrix- and tensor-based completion methods in terms of achieving higher accuracy and taking much less computing time for some datasets.

互联网流量数据补全是网络工程中一项重要且具有挑战性的任务。由于互联网流量数据的多维性，我们引入了两个基于张量训练 (TT) 的优化模型和时间正则化，以从不完整的观察中恢复数据。此外，我们遵循交替最小化的精神，提出了两种易于实现的算法。值得注意的是，我们的算法具有封闭形式的解决方案，并且可以以并行方式实现一种算法来解决大规模问题。对真实世界数据集的一些数值实验表明，我们的方法在实现更高的准确性和对某些数据集花费更少的计算时间方面比一些现有的最先进的基于矩阵和张量的完成方法表现更好。