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A Closed Form Maximum Likelihood Estimator to End-to-End Loss Rate Estimation

Loss tomography has been studied for more than 10 years and a number of estimators have been proposed. The estimators can be divided into two classes: maximum likelihood and non-maximum likelihood. The maximum likelihood estimators rely on the maximum likelihood principle to ensure the accuracy of the estimates obtained by the estimators. Unfortunately, all of the maximum likelihood estimators need to use an iterative procedure to search the solution space for the maximum or to solve a high degree polynomial. An iterative procedure can be computationally expensive and may even converge to a local maximum. On the other hand, the non-maximum likelihood estimators pursue closed form solutions by scarifying the accuracy of estimates. To overcome the pitfalls, we, in this paper, propose a closed form and maximum likelihood estimator to estimate the loss rate of a link in a network. The closed form solution is built on the discovery of a connection between the number of probes passing a link and the number of probes passing its parent. The proposed estimator is applicable to both the tree topology and the general one.