Network Tomography: Identifiability and Fourier Domain Estimation

The statistical problem for network tomography is to infer the distribution of $\mathbf{X}$, with mutually independent components, from a measurement model $\mathbf{Y}=A\mathbf{X}$, where $A$ is a given binary matrix representing the routing topology of a network under consideration. The challenge is that the dimension of $\mathbf{X}$ is much larger than that of $\mathbf{Y}$ and thus the problem is often called ill-posed. This paper studies some statistical aspects of network tomography. We first address the identifiability issue and prove that the $\mathbf{X}$ distribution is identifiable up to a shift parameter under mild conditions. We then use a mixture model of characteristic functions to derive a fast algorithm for estimating the distribution of $\mathbf{X}$ based on the General method of Moments. Through extensive model simulation and real Internet trace driven simulation, the proposed approach is shown to be favorable comparing to previous methods using simple discretization for inferring link delays in a heterogeneous network.Comment: 21 page

A Network Coding Approach to Loss Tomography

Network tomography aims at inferring internal network characteristics based on measurements at the edge of the network. In loss tomography, in particular, the characteristic of interest is the loss rate of individual links and multicast and/or unicast end-to-end probes are typically used. Independently, recent advances in network coding have shown that there are advantages from allowing intermediate nodes to process and combine, in addition to just forward, packets. In this paper, we study the problem of loss tomography in networks with network coding capabilities. We design a framework for estimating link loss rates, which leverages network coding capabilities, and we show that it improves several aspects of tomography including the identifiability of links, the trade-off between estimation accuracy and bandwidth efficiency, and the complexity of probe path selection. We discuss the cases of inferring link loss rates in a tree topology and in a general topology. In the latter case, the benefits of our approach are even more pronounced compared to standard techniques, but we also face novel challenges, such as dealing with cycles and multiple paths between sources and receivers. Overall, this work makes the connection between active network tomography and network coding

Multicast-based inference of network-internal loss performance

©2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.The use of multicast traffic as measurement probes is efficient and effective to infer network-internal characteristics. We propose a new statistical approach to infer network internal link loss performance from end-to-end measurements. Incorporating with the procedure of topology inference, we present an inference algorithm that can infer loss rates of individual links in the network when it infers the network topology. It is proved that the loss rate inferred by our approach is consistent with the real loss rate as the number of probe packets tends to infinity. The approach is also extended to general trees case for loss performance inference. Loss rate-based scheme on topology inference is built in view of correct convergence to the true topology for general trees.Hui Tian, Hong She

Discover multicast network internal characteristics based on Hamming distance

Copyright © 2005 IEEEOne of the important techniques to monitor and control large-scale networks today is to implement only at the end. However end-based control needs to have the knowledge of network internal characteristics. The paper proposes a novel approach to discover network internal characteristics from end-to-end multicast traffic measurements, which requires no support from internal routers. Our approach is based on Hamming distance of sequences on receipt/loss of probe packets maintained at each pair of nodes. As we discuss in this paper, our approach mainly focuses on identification of network internal characteristics of routing topology and loss performance. The simulation shows that the Hamming distance-based approach can discover the routing topology which is more accurate and efficient with a finite number of probe packets than before. The Hamming distance matrix proposed in this paper can also effectively discover the loss performance of the network.Hui Tian, Hong She

Measuring the dynamical state of the Internet: Large-scale network tomography via the ETOMIC infrastructure

In this paper we show how to go beyond the study of the topological properties of the Internet, by measuring its dynamical state using special active probing techniques and the methods of network tomography. We demonstrate this approach by measuring the key state parameters of Internet paths, the characteristics of queuing delay, in a part of the European Internet. In the paper we describe in detail the ETOMIC measurement platform that was used to conduct the experiments, and the applied method of queuing delay tomography. The main results of the paper are maps showing various spatial structure in the characteristics of queuing delay corresponding to the resolved part of the European Internet. These maps reveal that the average queuing delay of network segments spans more than two orders of magnitude, and that the distribution of this quantity is very well fitted by the log-normal distribution. Copyright © 2006 S. Karger AG

Network delay tomography using flexicast experiments

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73739/1/j.1467-9868.2006.00567.x.pd