Statistical Properties of Loss Rate Estimators in Tree Topology

TL;DR

This paper introduces three maximum likelihood-based estimators for link loss rates in tree-structured networks, providing their statistical properties, efficiencies, and variances, enabling better evaluation and selection of estimators for network analysis.

Contribution

It proposes new explicit loss rate estimators for tree networks, derives their statistical properties, and provides formulas to evaluate and compare their efficiencies and variances.

Findings

Estimators are asymptotically unbiased or unbiased.

Variance of the maximum likelihood estimator is related to the pass rates.

Formulas enable evaluation and selection of estimators for data sets.

Abstract

Three types of explicit estimators are proposed here to estimate the loss rates of the links in a network of the tree topology. All of them are derived by the maximum likelihood principle and proved to be either asymptotic unbiased or unbiased. In addition, a set of formulae are derived to compute the efficiencies and variances of the estimators that also cover some of the estimators proposed previously. The formulae unveil that the variance of the estimates obtained by a maximum likelihood estimator for the pass rate of the root link of a multicast tree is equal to the variance of the pass rate of the multicast tree divided by the pass rate of the tree connected to the root link. Using the formulae, we are able to evaluate the estimators proposed so far and select an estimator for a data set.