Search for optimality in traffic matrix estimation: a rational approach by Cramer-Rao lower bounds

In this paper we study the problem of traffic matrix estimation. The problem is ill-posed and thus some additional information has to be brought in to obtain an estimate. One common approach is to use the second moment statistics through a functional mean-variance relationship. We derive analytically the Fisher information matrix under this framework and obtain the Cramer-Rao lower bound (CRLB) for the variance of an estimator of the traffic matrix. Applications for the use of the CRLB are then demonstrated. From the bounds we can directly obtain confidence intervals for maximum likelihood estimates. Another use for the CRLB is the possibility to evaluate the efficiency of an estimator against the lower bound. A third possible application is to utilize the bounds in an approach to find the best placement for direct measurements of OD flows, so that it is optimal with regard to the traffic matrix estimation problem