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The Traffic matrix Estimation of IP networks has become a research topic in this later 10 years, where several methods have been used to resolve this ill posed problem. This paper deals with the later and presents a comparison study on training algorithms in Artificial Neural Networks (ANN) method, namely the BFGS Quasi-Newton; the Levenberg-Marquardt and Bayesian Regularization algorithms, which yields us accurate results as outputs, the comparison between them is made on estimating the error robustness, execution time and regression. It appears that the Levenberg-Marquardt algorithm performs the best results. We have used a real data from the American well known IP Network, called the Abilene network, to validate and evaluate our comparison, our implementation shows that the chosen algorithm has earned the challenge and ensure the smallest error in the shortest time and the estimated matrix is …