An efficient loss rate estimator in multicast tomography and its validity

Abstract

Network tomography receives a considerable attention in recent years that provides a viable methodology to discover network charateristics, such as the loss rate of a link, the delay distribution of a link, from end-to-end observations. In the loss rate estimation, the previous studies show that to find the maximum likelihood estimate (MLE) of a link/path, we need to solve a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since there is no analytical solution to a polynomial of 5 degree or higher, the main concern is focused on the methods to obtain MLE without using iterative approximation. An explicit estimator based on the Law of Large Numbers has been proposed. However, the estimate obtained from the estimator is not a MLE. If n < ∞, the estimator may fail or produce an estimate that is significantly different from the MLE. In this paper, we propose an algorithm that can obtain the estimate analytically. In addition, we will point out the restriction of the previous estimators.

Statistical Properties of Loss Rate Estimators in Tree Topology

“…Although simulations show the estimator preforms better than that proposed in [9], there is little statistical analysis to explain why it is better and the authors even suspect the estimator may yield high variance. Although the estimator is proved to be a MLE in [21], there is no proof whether it is the same as that proposed in [2] since the lack of finite sample properties for both of them.…”

Network tomography application in mobile ad-hoc network using stitching algorithm

“…Presti et al [13] studied internal delays using a multicastbased inference NT algorithm. Zhu [16] designed an explicit estimator based on the Law of Large Numbers to evaluate the loss rate. The estimator in this work found the maximum likelihood estimate (MLE) of a link or path without using iterative approximation.…”

“…In addition to topology, the NT approach as described in [12]- [15] and in [16]- [21] has been extensively used to evaluate aspects of network performance such as the loss rate of links and the delay distribution of a link. NT makes it possible to evaluate packet loss ratios and link delays only from end-to-end observations, without knowing the internal network structure.…”

Network tomography application in mobile ad-hoc networks.

“…In ad-hoc networks, due to the diversity of node's motion, the randomness of wireless transceiver turno, the variety of transmission power, the disturbance between wireless channels and the inuence of from land and weather, etc., network topology architecture based on shared wireless channels among dierent mobile nodes and link number distribution will change with time going by [24,57]. Specially, ad-hoc network topology management, system architecture and protocol design is dierent from that in Cellular wireless network and IP network because of small transmission power of mobile nodes, low bandwidth of wireless channel, and energy limited or constraint.…”

“…Presti et al [21] studied the internal delay by a multicast-based inference network tomography algorithm. Zhu [24] designed an explicit estimator based on the Law of Large Numbers to evaluate the loss rate. The estimator in this work nd the maximum likelihood estimate (MLE) of a link/path without using iterative approximation.…”