Inferring traffic matrix (TM) from link measurements and routing information has important applications including capacity planning, traffic engineering and network reliability analysis. The challenge comes from that there are more unknowns than data. To face this challenge, this paper describes the inference problem as an optimization problem, where the objective is to minimize the Mahalanobis distance between the solution and a certain prior distribution, subject to the routing and link measurement constraints. This optimization problem is then solved by the Moore-Penrose inverse of the routing matrix. To reduce the computing complexity, a principal component analysis (PCA) approach is further applied in solving the optimization problem. We obtain the explicit formulas by using the Moore-Penrose inverse and the PCA theory. On the basis of the generalized inverse of routing matrix and the PCA theory, we propose an interesting generalized Tomogravity approach, which is subsequently termed as PCAOM. We present the complete mathematical solution and the algorithm of the described TM estimation problem. By introducing a weight parameter, a generalized algorithm is presented, which can be applied flexibly by adjusting the importance of the prior according to the accuracy of the prior or even no prior is required when the prior is unavailable. Numerical results are provided to demonstrate the accuracy of our method with the dataset of Abilene network through the comparison with the famous Tomogravity method. Given that we have proposed two algorithms for the optimization problem of TM estimation, we also provide a guideline on how to choose the proper algorithm according to the availability of the prior information.
Zhao, E., & Tan, L. (2015). A PCA based optimization approach for IP traffic matrix estimation. Journal of Network and Computer Applications, 57, 12–20. https://doi.org/10.1016/j.jnca.2015.07.006