On IP Traffic Matrix Estimation

It is very useful to infer traffic matrix (TM) from link measurements and routing information, especially for the tasks of capacity planning, traffic engineering and network reliability analysis. This inference problem is ill-posed as it involves more unknowns than data and the challenge lies in this problem is its ill-posed nature. To overcome this challenge, this paper firstly describes the inference problem into an optimization problem, in which the objective is to minimize the Euclidean distance between a certain predetermined prior and the target TM subject to the routing constraints upon the link measurements and TM. We secondly solve this problem by transforming the available routing matrix and applying the Lagrange multipliers method. We therefore propose a novel proposal on inferring TM, termed matrix partitioning and Lagrange multipliers (MPLM). An expression is derived for calculating the TMs from the link measurements and the transformations of the routing matrix. We analyze the computational complexity of MPLM, which comes out to be much less than the state-of-the-art approaches. We also suggest a new method to generate the prior. Numerical results are provided to demonstrate the accuracy of MPLM in estimating TMs, and the on-line TM estimation is also discussed in detail to show the techniques in MPLM.