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Network tomography: recent developments
 Statistical Science
, 2004
"... Today's Int ernet is a massive, dist([/#][ net work which cont inuest o explode in size as ecommerce andrelatH actH]M/# grow. Thehet([H(/#]H( and largelyunregulatS stregula of t/ Int/HH3 renderstnde such as dynamicroutc/[ opt2]3fl/ service provision, service level verificatflH( and det(2][/ of ..."
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Cited by 132 (4 self)
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Today's Int ernet is a massive, dist([/#][ net work which cont inuest o explode in size as ecommerce andrelatH actH]M/# grow. Thehet([H(/#]H( and largelyunregulatS stregula of t/ Int/HH3 renderstnde such as dynamicroutc/[ opt2]3fl/ service provision, service level verificatflH( and det(2][/ of anomalous/malicious behaviorext/[(22 challenging. The problem is compounded bytS fact tct onecannot rely ont[ cooperatH2 of individual servers and routSS t aid intS collect[3 of net workt/[S measurement vits fort/]3 t/]3] In many ways, net workmonit]/#[ and inference problems bear a st[fl[ resemblancet otnc "inverse problems" in which key aspect of asystfl are not direct/ observable. Familiar signal processing orst[]23/#[S problems such ast omographic imagereconst[/#[S] and phylogenet# tog identn/HH2[M have int erest3/ connect[HU t tonn arising in net working. This artflMM int/ ducesnet workt/H3]S]/ y, a new field which we believe will benefit greatU from tm wealt of stH2](/#S( ttH2 andalgorit#S( It focuses especially on recent development s int2 field includingtl applicat[fl of pseudolikelihoodmetfl ds andt reeestfl3](/# formulat]M23 Keyw ords:Net workt/HflS33/ y, pseudolikelihood,t opology identn/]H22(/ tn est/]H tst 1 Introducti6 Nonet work is an island, ent/S ofitS[S] everynet work is a piece of an int/]SS work, a part of t/ main . Alt[]][ administHSHSS of smallscale net works can monit( localt ra#ccondit][/ and ident ify congest/# point s and performance botU((2/ ks, very few net works are complet/# # Rui Castroan Robert Nowak are with theDepartmen t of Electricalan ComputerEnterX Rice Unc ersity,Houston TX; Mark Coates is with the Departmen t of Electricalan ComputerEnterX McGill UnG ersity,Mon treal, Quebec,Can Gan Lian an Bin Yu are with theDepartmen t of Statistics,...
Network Tomography of Binary Network Performance Characteristics
 IEEE Transactions on Information Theory
, 2006
"... In network performance tomography, characteristics of the network interior, such as link loss and packet latency, are inferred from correlated endtoend measurements. Most work to date is based on exploiting packet level correlations, e.g., of multicast packets or unicast emulations of them. Howeve ..."
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Cited by 61 (3 self)
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In network performance tomography, characteristics of the network interior, such as link loss and packet latency, are inferred from correlated endtoend measurements. Most work to date is based on exploiting packet level correlations, e.g., of multicast packets or unicast emulations of them. However, these methods are often limited in scope—multicast is not widely deployed—or require deployment of additional hardware or software infrastructure. Some recent work has been successful in reaching a less detailed goal: identifying the lossiest network links using only uncorrelated endtoend measurements. In this paper we abstract the properties of network performance that allow this to be done and exploit them with a quick and simple inference algorithm that, with high likelihood, identifies the worst performing links. We give several examples of real network performance measures that exhibit the required properties. Moreover, the algorithm is sufficiently simple that we can analyze its performance explicitly.
Learning Latent Tree Graphical Models
 J. of Machine Learning Research
, 2011
"... We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing me ..."
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Cited by 44 (12 self)
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We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our algorithms can be applied to both discrete and Gaussian random variables and our learned models are such that all the observed and latent variables have the same domain (state space). Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using socalled information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a preprocessing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures such as neighborjoining) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare
Network tomography: identifiability and fourier domain estimation
 Proc. IEEE INFOCOM’07
, 2007
"... ar ..."
Network tomography: A review and recent developments
 In Fan and Koul, editors, Frontiers in Statistics
, 2006
"... 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 largescale inverse problems. The first deals with passive tomography where aggregate data ar ..."
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Cited by 27 (7 self)
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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 largescale 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 pathlevel information. The main problem of interest here is the estimation of the origindestination traffic matrix. The second, referred to as active tomography, deals with reconstructing linklevel information from endtoend pathlevel measurements obtained by actively probing the network. The primary application in this case is estimation of qualityofservice 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.
Unicastbased inference of network link delay distributions with finite mixture models
 IEEE Transactions on Signal Processing
, 2003
"... Abstract—Providers of high qualityofservice over telecommunication networks require accurate methods for remote measurement of linklevel performance. Recent research in network tomography has demonstrated that it is possible to estimate internal link characteristics, e.g., link delays and packet ..."
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Cited by 26 (4 self)
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Abstract—Providers of high qualityofservice over telecommunication networks require accurate methods for remote measurement of linklevel performance. Recent research in network tomography has demonstrated that it is possible to estimate internal link characteristics, e.g., link delays and packet losses, using unicast probing schemes in which probes are exchanged between several pairs of sites in the network. In this paper, we present a new method for estimation of internal link delay distributions using the endtoend packet pair delay statistics gathered by backtoback packetpair unicast probes. Our method is based on a variant of the penalized maximum likelihood expectationmaximization (PMLEM) algorithm applied to an additive finite mixture model for the link delay probability density functions. The mixture model incorporates a combination of discrete and continuous components, and we use a minimum message length (MML) penalty for selection of model order. We present results of matlab and ns 2 simulations to illustrate the promise of our network tomography algorithm for light crosstraffic scenarios. Index Terms—EM algorithm, mixture models, MML penalties, network tomography, signal processing in networking. I.
Network radar: Tomography from round trip time measurements
 In IMC’04
, 2004
"... Knowledge of link specific traffic characteristics is important in the operation and design of wide area networks. Network tomography is a powerful method for measuring characteristics such as delay and loss on networkinternal links using end–to–end active probes. Prior work has established the bas ..."
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Cited by 25 (3 self)
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Knowledge of link specific traffic characteristics is important in the operation and design of wide area networks. Network tomography is a powerful method for measuring characteristics such as delay and loss on networkinternal links using end–to–end active probes. Prior work has established the basic mechanisms for the use of tomographic inference techniques in the networking context. However, the measurement methods described in prior network tomography studies require cooperation between sending and receiving endhosts, which limits the scope of the paths over which the measurements can be made. In this paper, we describe a new network tomographic technique based on round trip time (RTT) measurements which eliminates the need for specialpurpose cooperation from receivers. Our technique uses RTT measurements from TCP SYN and SYNACK segments to estimate the delay variance of the shared network segment in the standard one sender two receivers configuration. We call this approach Network Radar since it is analogous to standard radar. We present an analytic evaluation of Network Radar that specifies the variance bounds within which the technique is effective. We also evaluate Network Radar in a series of tests conducted in a controlled laboratory environment using live end hosts and IP routers. These tests demonstrate the boundaries of effectiveness of the RTTbased approach.
Estimating network loss rates using active tomography
"... Active network tomography refers to an interesting class of largescale inverse problems that arise in estimating the quality of service parameters of computer and communications networks. This article focuses on estimation of loss rates of the internal links of a network using endtoend measurem ..."
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Cited by 15 (5 self)
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Active network tomography refers to an interesting class of largescale inverse problems that arise in estimating the quality of service parameters of computer and communications networks. This article focuses on estimation of loss rates of the internal links of a network using endtoend measurements of nodes located on the periphery. A class of flexible experiments for actively probing the network is introduced, and conditions under which all of the linklevel information is estimable are obtained. Maximum likelihood estimation using the EM algorithm, the structure of the algorithm, and the properties of the maximum likelihood estimators are investigated. This includes simulation studies using the ns (network simulator) to obtain realistic network traffic. The optimal design of probing experiments is also studied. Finally, application of the results to network monitoring is briefly illustrated.
Efficient and Dynamic Routing Topology Inference From EndtoEnd Measurements
"... Inferring the routing topology and link performance from a node to a set of other nodes is an important component in network monitoring and application design. In this paper we propose a general framework for designing topology inference algorithms based on additive metrics. The framework can flexi ..."
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Cited by 15 (0 self)
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Inferring the routing topology and link performance from a node to a set of other nodes is an important component in network monitoring and application design. In this paper we propose a general framework for designing topology inference algorithms based on additive metrics. The framework can flexibly fuse information from multiple measurements to achieve better estimation accuracy. We develop computationally efficient (polynomialtime) topology inference algorithms based on the framework. We prove that the probability of correct topology inference of our algorithms converges to one exponentially fast in the number of probing packets. In particular, for applications where nodes may join or leave frequently such as overlay network construction, applicationlayer multicast, peertopeer file sharing/streaming, we propose a novel sequential topology inference algorithm which significantly reduces the probing overhead and can efficiently handle node dynamics. We demonstrate the effectiveness of the proposed inference algorithms via Internet experiments.
Statistical Inverse Problems in Active Network Tomography
"... Abstract: Active network tomography includes several interesting statistical inverse problems that arise in the context of computer and communication networks. The primary goal in these problems is to recover linklevel information about qualityofservice parameters from aggregate endtoend data m ..."
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Cited by 11 (2 self)
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Abstract: Active network tomography includes several interesting statistical inverse problems that arise in the context of computer and communication networks. The primary goal in these problems is to recover linklevel information about qualityofservice parameters from aggregate endtoend data measured on paths across the network. The estimation and monitoring of these parameters are of considerable interest to network engineers and Internet service providers. This paper provides a review of the inverse problems and recent research on inference for loss rates and delay distributions. Some new results on parametric inference for delay distributions are developed. The results are illustrated using a network application related to Internet telephony. 1. The Inverse Problems Consider a tree T = {V, E} with a set of nodes V and a set of links or edges E. Figure 1 shows two examples: a simple twolayer symmetric binary tree on the left and a more general fourlayer tree on the right. Each member of E is a directed link numbered after the node at its terminus. V includes a root node 0, a set of receiver or destination nodes R and a set of internal nodes I. All transmissions on the tree are initiated at the root node. The internal nodes have a single incoming link and at least two outgoing links (children). The receiver nodes have a single incoming link but no