The modeling and analysis of computer communications networks give rise to a variety of interesting statistical problems. This paper focuses on network tomography, a term used to characterize two classes of large-scale inverse problems. The first deals with passive tomography where aggregate data are collected at the individual router/node level and the goal is to recover path-level information. The main problem of interest here is the estimation of the origin-destination traffic matrix. The second, referred to as active tomography, deals with reconstructing link-level information from end-to-end path-level measurements obtained by actively probing the network. The primary application in this case is estimation of quality-of-service parameters such as loss rates and delay distributions. The paper provides a review of the statistical issues and developments in network tomography with an emphasis on active tomography. An application to Internet telephony is used to illustrate the results.

Abstract — Information about the topology and link-level characteristics of a network is critical for many applications including network diagnostics and management. However, this information is not always directly accessible; subnetworks may not cooperate in releasing information and widespread local measurement can be prohibitively expensive. Network tomographic techniques obviate the need for network cooperation, but the majority assume probing from a single source, which imposes scalability limitations because sampling traffic is concentrated on network links close to the source. We describe a multiple source, end-toend sampling architecture that uses coordinated transmission of carefully engineered multi-packet probes to jointly infer logical topology and estimate link-level performance characteristics. We commence by demonstrating that the general multiple source, multiple destination tomography problem can be formally reduced to the two source, two destination case, allowing the immediate generalization of any sampling techniques developed for the simpler, smaller scenario. We then describe a method for testing whether links are shared in the topologies perceived by individual sources, and describe how to fuse the measurements in the shared case to generate more accurate estimates of the link-level performance statistics. Index Terms — Internet tomography, end-to-end measurements, active probing, topology discovery, loss rate estimation.

In this paper we address the problem of topology discovery in unicast logical tree networks using endto-end measurements. Without any cooperation from the internal routers, topology estimation can be formulated as hierarchical clustering of the leaf nodes based on pair-wise correlations as similarity metrics. We investigate three types of similarity metrics: queueing delay measured by sandwich probes, delay variance measured by packet pairs, and loss rate measured also by packet pairs. Unlike previous work which first assumes the network topology is a binary tree and then tries to generalize to a non-binary tree, we provide a framework which directly deals with general logical tree topologies. Based on our proposed finite mixture model for the set of similarity measurements we develop a penalized hierarchical topology likelihood that leads to a natural clustering of the leaf nodes level by level. A hierarchical algorithm to estimate the topology is developed in a similar manner by finding the best partitions of the leaf nodes. Our simulations show that the algorithm is more robust than binary-tree based methods. The three types of similarity metrics are also evaluated under various network load conditions using ns-2. 1

Abstract—In this paper, we address the problem of topology discovery in unicast logical tree networks using end-to-end measurements. Without any cooperation from the internal routers, topology estimation can be formulated as hierarchical clustering of the leaf nodes based on pairwise correlations as similarity metrics. Unlike previous work that first assumes the network topology is a binary tree and then tries to generalize to a nonbinary tree, we provide a framework that directly deals with general logical tree topologies. A hierarchical algorithm to estimate the topology is developed in a recursive manner by finding the best partitions of the leaf nodes level by level. Our simulations show that the algorithm is more robust than binary-tree based methods. Index Terms—Graph-based clustering, mixture models, network tomography, topology estimation. I.

Abstract — Information about the topology and link-level characteristics of a network is critical for many applications including network diagnostics and management. However, this information is not always directly accessible; subnetworks may not cooperate in releasing information and widespread local measurement can be prohibitively expensive. Network tomographic techniques obviate the need for network cooperation, but the majority assume probing from a single source, which imposes scalability limitations because sampling traffic is concentrated on network links close to the source. We describe a multiple source, end-toend sampling architecture that uses coordinated transmission of carefully engineered multi-packet probes to jointly infer logical topology and estimate link-level performance characteristics. We commence by demonstrating that the general multiple source, multiple destination tomography problem can be formally reduced to the two source, two destination case, allowing the immediate generalization of any sampling techniques developed for the simpler, smaller scenario. We then describe a method for testing whether links are shared in the topologies perceived by individual sources, and describe how to fuse the measurements in the shared case to generate more accurate estimates of the link-level performance statistics. Index Terms — Internet tomography, end-to-end measurements, active probing, topology discovery, loss rate estimation.