Statistical Properties of Loss Rate Estimators in Tree Topology

A two-segment model is introduced here to model the probing process in a network with the tree topology that subsequently leads to four types of explicit estimators to estimate the loss rates of the links within the network. All of the estimators are derived by the maximum likelihood principle, where one of them is developed from an estimator that was used but neglected previously. The estimators are proved to be either unbiased or asymptotic unbiased, and 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 to evaluate the performance of an estimator. One of them shows that the estimators derived from the neglected ones are the best in terms of efficiency and computation complexity for the networks of the tree topology.