Statistical Properties of Loss Rate Estimators in Tree Topology

Abstract

Four types of explicit estimators are proposed here to estimate the loss rates of the links in a network with the tree topology and all of them are derived by the maximum likelihood principle. One of the four is developed from an estimator that was used but neglected because it was suspected to have a higher variance. All of the estimators are proved to be either unbiased or asymptotic unbiased. In addition, a set of formulae are derived to compute the efficiencies and variances of the estimates obtained by the estimators. One of the formulae shows that if a path is divided into two segments, the variance of the estimates obtained for the pass rate of a segment is equal to the variance of the pass rate of the path divided by the square of the pass rate of the other segment. A number of theorems and corollaries are derived from the formulae that can be used to evaluate the performance of an estimator. Using the theorems and corollaries, we find the estimators from the neglected one are the best estimator for the networks with the tree topology in terms of efficiency and computation complexity.