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On Identifying Additive Link Metrics Using Linearly Independent Cycles and Paths
 ACCEPTED FOR PUBLICATION IN IEEE/ACM TRANSACTIONS ON NETOWRKING
, 2011
"... In this paper, we study the problem of identifying constant additive link metrics using linearly independent monitoring cycles and paths. A monitoring cycle starts and ends at the same monitoring station while a monitoring path starts and ends at distinct monitoring stations. We show that three edge ..."
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In this paper, we study the problem of identifying constant additive link metrics using linearly independent monitoring cycles and paths. A monitoring cycle starts and ends at the same monitoring station while a monitoring path starts and ends at distinct monitoring stations. We show that three edge connectivity is a necessary and sufficient condition to identify link metrics using one monitoring station and employing monitoring cycles. We develop a polynomial time algorithm to compute the set of linearly independent cycles. For networks that are less than threeedge connected, we show how the minimum number of monitors required and their placement may be computed. For networks with symmetric directed links, we show the relationship between the number of monitors employed, the number of directed links for which metric is known a priori, and the identifiability for the remaining links. To the best of our knowledge, this is the first work that derives the necessary and sufficient conditions on the network topology for identifying additive link metrics and develops a polynomial time algorithm to compute linearly independent cycles and paths.
Statistical Aspects of the Analysis of Data Networks
"... Assessing and monitoring the performance of computer and communications networks is an important problem for network engineers. There has been a considerable amount of work on tools and techniques for data collection, modeling, and analysis within the network research community. The goal of this pap ..."
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Assessing and monitoring the performance of computer and communications networks is an important problem for network engineers. There has been a considerable amount of work on tools and techniques for data collection, modeling, and analysis within the network research community. The goal of this paper is to present an overview of the engineering problems and statistical issues, describe recent research developments, and summarize ongoing work and areas for further research. While there are many interesting issues related to network analysis, our focus here is on estimating and monitoring network QualityofService parameters. We discuss methods for estimating edgelevel parameters from endtoend pathlevel measurements, an important engineering problem that raises interesting statistical modeling issues. Other topics include network monitoring, network visualization, and discovering network topology. Data from a corporate network are used to illustrate the problems and techniques. As in any overview paper, the discussion is likely to be slanted towards our own research interests.
A Network Coding Approach to Loss Tomography
, 2013
"... 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 endtoend probes are typically used. Independen ..."
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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 endtoend 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 tradeoff 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.
GENERALIZED NETWORK TOMOGRAPHY ∗
"... Abstract. Generalized network tomography (GNT) deals with estimation of link performance parameters for networks with arbitrary topologies using only endtoend path measurements of pure unicast probe packets. In this paper, by taking advantage of the properties of generalized hyperexponential dist ..."
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Abstract. Generalized network tomography (GNT) deals with estimation of link performance parameters for networks with arbitrary topologies using only endtoend path measurements of pure unicast probe packets. In this paper, by taking advantage of the properties of generalized hyperexponential distributions and polynomial systems, a novel algorithm to infer the complete link metric distributions under the framework of GNT is developed. The significant advantages of this algorithm are that it does not require: i) the path measurements to be synchronous and ii) any prior knowledge of the link metric distributions. Moreover, if the pathlink matrix of the network has the property that every pair of its columns are linearly independent, then it is shown that the algorithm can uniquely identify the link metric distributions up to any desired accuracy. Matlab based simulations have been included to illustrate the potential of the proposed scheme.
TRANSACTIONS ON SIGNAL PROCESSING 1 Fast, MomentBased Estimation Methods for Delay Network Tomography
, 2008
"... Consider the delay network tomography problem where the goal is to estimate distributions of delays at the linklevel using data on endtoend delays. These measurements are obtained using probes that are injected at nodes located on the periphery of the network and sent to other nodes also located ..."
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Consider the delay network tomography problem where the goal is to estimate distributions of delays at the linklevel using data on endtoend delays. These measurements are obtained using probes that are injected at nodes located on the periphery of the network and sent to other nodes also located on the periphery. Much of the previous literature deals with discrete delay distributions by discretizing the data into small bins. This paper considers more general models with a focus on computationally efficient estimation. The momentbased schemes presented here are designed to function well for larger networks and for applications like monitoring that require speedy solutions. EDICS: SSPDECO, SSPHIER, SSPNGAU, SSPPARE
DOI 10.1007/s1113401091959 Statistical estimation of delays in a multicast tree using
"... Abstract Tomography is one of the most promising techniques today to provide spatially localized information about internal network performance in a robust and scalable way. The key idea is to measure performance at the edge of the network, and to correlate these measurements to infer the internal ..."
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Abstract Tomography is one of the most promising techniques today to provide spatially localized information about internal network performance in a robust and scalable way. The key idea is to measure performance at the edge of the network, and to correlate these measurements to infer the internal network performance. This paper focuses on a specific delay tomographic problem on a multicast diffusion tree, where endtoend delays are observed at every leaf of the tree, and mean sojourn times are estimated for every node in the tree. The estimation is performed using the Maximum Likelihood Estimator (MLE) and the ExpectationMaximization (EM) algorithm. Using queuing theory results, we carefully justify the model we use in the case of rare probing. We then give an explicit EM implementation in the case of i.i.d. exponential delays for a general tree. As we work with nondiscretized delays and a full MLE, EM is known to be slow. We hence present a very simple but, in our case, very effective speedup technique using Principal Component Analysis (PCA). MLE estimations are provided for a few different trees to evaluate our technique.
A. Internet Tomography and Network Probing
"... Abstract—Numerous probing and tomography techniques have been developed for the Internet. They all either flood the network with probing TCP connections or require to send additional probing packets which delays must be precisely measured. In this paper, we propose a new approach, on the basis of ex ..."
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Abstract—Numerous probing and tomography techniques have been developed for the Internet. They all either flood the network with probing TCP connections or require to send additional probing packets which delays must be precisely measured. In this paper, we propose a new approach, on the basis of existing TCP connections and reaching therefore a zero probing overhead. The foundation of the proposed technique lies in the theory of inverse problems in bandwidth sharing networks, and the approximation of Internet and TCP behavior by that of a bandwidth sharing network. The field of this kind of inverse problems is explored, and we give a few application to toy networks, either with fixed population or with elastic traffic. I.
Generalized Network Tomography
"... Abstract — For successful estimation, the usual network tomography algorithms crucially require i) endtoend data generated using multicast probe packets, real or emulated, and ii) the network to be a tree rooted at a single sender with destinations at leaves. These requirements, consequently, lim ..."
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Abstract — For successful estimation, the usual network tomography algorithms crucially require i) endtoend data generated using multicast probe packets, real or emulated, and ii) the network to be a tree rooted at a single sender with destinations at leaves. These requirements, consequently, limit their scope of application. In this paper, we address successfully a general problem, henceforth called generalized network tomography, wherein the objective is to estimate the link performance parameters for networks with arbitrary topologies using only endtoend measurements of pure unicast probe packets. Mathematically, given a binary matrix A, we propose a novel algorithm to uniquely estimate the distribution of X, a vector of independent nonnegative random variables, using only IID samples of the components of the random vector Y = AX. This algorithm, in fact, does not even require any prior knowledge of the unknown distributions. The idea is to approximate the distribution of each component of X using linear combinations of known exponential bases and estimate the unknown weights. These weights are obtained by solving a set of polynomial systems based on the moment generating function of the components of Y. For unique identifiability, it is only required that every pair of columns of the matrix A be linearly independent, a property that holds true for the routing matrices of all multicast tree networks. Matlab based simulations have been included to illustrate the potential of the proposed scheme. I.
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"... We develop a stochastic approximation version of the classical Kaczmarz algorithm that is incremental in nature and takes as input noisy real time data. Our analysis shows that with probability one it mimics the behavior of the original scheme: starting from the same initial point, our algorithm and ..."
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We develop a stochastic approximation version of the classical Kaczmarz algorithm that is incremental in nature and takes as input noisy real time data. Our analysis shows that with probability one it mimics the behavior of the original scheme: starting from the same initial point, our algorithm and the corresponding deterministic Kaczmarz algorithm converge to precisely the same point. The motivation for this work comes from network tomography where network parameters are to be estimated based upon end–to–end measurements. Numerical examples via Matlab based simulations demonstrate the efficacy of the algorithm.