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34
Network Loss Inference with Second Order Statistics of EndtoEnd Flows
, 2007
"... We address the problem of calculating link loss rates from endtoend measurements. Contrary to existing works that use only the average endtoend loss rates or strict temporal correlations between probes, we exploit secondorder moments of endtoend flows. We first prove that the variances of lin ..."
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Cited by 21 (3 self)
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We address the problem of calculating link loss rates from endtoend measurements. Contrary to existing works that use only the average endtoend loss rates or strict temporal correlations between probes, we exploit secondorder moments of endtoend flows. We first prove that the variances of link loss rates can be uniquely calculated from the covariances of the measured endtoend loss rates in any realistic topology. After calculating the link variances, we remove the uncongested links with small variances from the firstorder moment equations to obtain a full rank linear system of equations, from which we can calculate precisely the loss rates of the remaining congested links. This operation is possible because losses due to congestion occur in bursts and hence the loss rates of congested links have high variances. On the contrary, most links on the Internet are uncongested, and hence the averages and variances of their loss rates are virtually zero. Our proposed solution uses only regular unicast probes and thus is applicable in today’s Internet. It is accurate and scalable, as shown in our simulations and experiments on PlanetLab.
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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Cited by 11 (1 self)
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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.
Identifiability of Link Metrics Based on Endtoend Path Measurements
, 2013
"... We investigate the problem of identifying individual link metrics in a communication network from endtoend path measurements, under the assumption that link metrics are additive and constant. To uniquely identify the link metrics, the number of linearly independent measurement paths must equal the ..."
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Cited by 8 (4 self)
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We investigate the problem of identifying individual link metrics in a communication network from endtoend path measurements, under the assumption that link metrics are additive and constant. To uniquely identify the link metrics, the number of linearly independent measurement paths must equal the number of links. Our contribution is to characterize this condition in terms of the network topology and the number/placement of monitors, under the constraint that measurement paths must be cyclefree. Our main results are: (i) it is generally impossible to identify all the link metrics by using two monitors; (ii) nevertheless, metrics of all the interior links not incident to any monitor are identifiable by two monitors if the topology satisfies a set of necessary and sufficient connectivity conditions; (iii) these conditions naturally extend to a necessary and sufficient condition for identifying all the link metrics using three or more monitors. We show that these conditions not only allow efficient identifiability tests, but also enable an efficient algorithm to place the minimum number of monitors in order to identify all link metrics. Our evaluations on both random and real topologies show that the proposed algorithm achieves identifiability using a much smaller number of monitors than a baseline solution.
Efficient Identification of Additive Link Metrics via Network Tomography
"... Abstract—We investigate the problem of identifying individual link metrics in a communication network from accumulated endtoend metrics over selected measurement paths, under the assumption that link metrics are additive and constant during the measurement, and measurement paths cannot contain cyc ..."
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Cited by 7 (4 self)
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Abstract—We investigate the problem of identifying individual link metrics in a communication network from accumulated endtoend metrics over selected measurement paths, under the assumption that link metrics are additive and constant during the measurement, and measurement paths cannot contain cycles. We know from linear algebra that all link metrics can be uniquely identified when the number of linearly independent measurement paths equals n, the number of links. It is, however, inefficient to collect measurements from all possible paths, whose number can grow exponentially in n, as the number of useful measurements (from linearly independent paths) is at most n. The aim of this paper is to develop efficient algorithms for constructing linearly independent measurement paths and calculating link metrics. We show that whenever there exists a set of n linearly independent measurement paths, there must exist a set of three pairwise independent spanning trees. We exploit this property to develop an algorithm that can construct n linearly independent, cyclefree paths between monitors without examining all candidate paths, whose complexity is quadratic in n. A further benefit of the proposed algorithm is that the generated paths satisfy a nested structure that allows lineartime computation of link metrics without explicitly inverting the measurement matrix. Our evaluations on both synthetic and real network topologies verify the superior efficiency of the proposed algorithms, which are orders of magnitude faster than benchmark solutions for large networks. I.
Spectral probing, crosstalk and frequency multiplexing in internet paths
 in Proc. of ACM SIGCOMM IMC
, 2008
"... We present an endtoend active probing methodology that creates frequencydomain signals in IP network paths. The signals are generated by periodic packet trains that cause shortlived queueing delay spikes. Different probers can be multiplexed in the frequencydomain on the same path. Further, a s ..."
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Cited by 7 (1 self)
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We present an endtoend active probing methodology that creates frequencydomain signals in IP network paths. The signals are generated by periodic packet trains that cause shortlived queueing delay spikes. Different probers can be multiplexed in the frequencydomain on the same path. Further, a signal that is introduced by a “prober ” in one path can cause a crosstalk effect, inducing a signal of the same frequency into another path (the “sampler”) as long as the two paths share one or more bottleneck queues. Applications of the proposed methodology include the detection of shared storeandforward devices among two or more paths, the creation of covert channels, and the modulation of voice or video periodic packet streams in less noisy frequencies. In this paper we focus on the first application. Our goal is to detect shared bottleneck(s) between a “sampler ” and one or more “prober ” paths. We present a spectral probing methodology as well as the corresponding signal processing/detection process. The accuracy of the method has been evaluated with controlled and repeatable simulation experiments, and it has also been tested on some Internet paths.
Range Tomography: Combining the Practicality of Boolean Tomography with the Resolution of Analog Tomography
"... The objective of early network tomography approaches was to produce a point estimate for the performance of each network link (Analog tomography). When it became clear that the previous approach is errorprone in practice, research shifted to Boolean tomography where each link is estimated as either ..."
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Cited by 6 (0 self)
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The objective of early network tomography approaches was to produce a point estimate for the performance of each network link (Analog tomography). When it became clear that the previous approach is errorprone in practice, research shifted to Boolean tomography where each link is estimated as either“good”or“bad”. The Boolean approach is more practical but its resolution is too coarse. We propose a new tomography framework that combines the best of both worlds: we still distinguish between good and bad links (for practicality reasons) but we also infer a range estimate for the performance of each bad link. We apply the Range tomography framework in two path performance metric functions (Min and Sum) and propose an efficient algorithm for each problem. Together with simulations, we have also applied Range tomography in three operational networks allowing us to identify the location of bad links and to estimate their performance during congestion episodes. We also compare the proposed method with existing Analog and Boolean tomography algorithms.
Temporal Delay Tomography
 In Proceedings of the IEEE INFOCOM Conference
, 2008
"... Abstract—Multicastbased network tomography enables inference of average loss rates and delay distributions of internal network links from endtoend measurements of multicast probes. Recent work showed that this method, based on correlating observations of multicast receivers, also supports the inf ..."
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Abstract—Multicastbased network tomography enables inference of average loss rates and delay distributions of internal network links from endtoend measurements of multicast probes. Recent work showed that this method, based on correlating observations of multicast receivers, also supports the inference of temporal loss characteristics of network links. In this paper, we show that temporal characteristics can, in fact, be estimated even for link delay processes. Knowledge of temporal delay characteristics has applications for delay sensitive services such as VoIP as well as for characterizing the queueing behavior of bottleneck links. By assuming mutually independent, but arbitrary link delay processes, we develop estimators which can infer, in addition to delay distributions, the probabilities of arbitrary patterns of delay, means and full distributions of delayrun periods at chosen delay levels, for each link in the multicast tree. By applying the recently proposed principle of subtreepartitioning, the estimator is made scalable to multicast trees of large degree. Estimation error and convergence rates are evaluated using simulations. I.
Network Tomography on Correlated Links
"... Network tomography establishes linear relationships between the characteristics of individual links and those of endtoend paths. It has been proved that these relationships can be used to infer the characteristics of links from endtoend measurements, provided that links are not correlated, i.e., ..."
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Cited by 6 (3 self)
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Network tomography establishes linear relationships between the characteristics of individual links and those of endtoend paths. It has been proved that these relationships can be used to infer the characteristics of links from endtoend measurements, provided that links are not correlated, i.e., the status of one link is independent from the status of other links. In this paper, we consider the problem of identifying link characteristics from endtoend measurements when links are “correlated, ” i.e., the status of one link may depend on the status of other links. There are several practical scenarios in which this can happen; for instance, if we know the network topology at the IPlink or at the domainlink level, then links from the same localarea network or the same administrative domain are potentially correlated, since they may be sharing physical links, network equipment, even management processes. We formally prove that, under certain well defined conditions, network tomography works when links are correlated, in particular, it is possible to identify the probability that each link is congested from endtoend measurements. We also present a practical algorithm that computes these probabilities. We evaluate our algorithm through extensive simulations and show that it is accurate in a variety of realistic congestion scenarios. Categories andSubjectDescriptors
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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Cited by 4 (0 self)
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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.
Inference with Multivariate HeavyTails in Linear Models
"... Heavytailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closedform in graphical models which involve such heavytailed distributions. In this work, we propose a novel simple linear graphical model for independent lat ..."
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Heavytailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closedform in graphical models which involve such heavytailed distributions. In this work, we propose a novel simple linear graphical model for independent latent random variables, called linear characteristic model (LCM), defined in the characteristic function domain. Using stable distributions, a heavytailed family of distributions which is a generalization of Cauchy, Lévy and Gaussian distributions, we show for the first time, how to compute both exact and approximate inference in such a linear multivariate graphical model. LCMs are not limited to stable distributions, in fact LCMs are always defined for any random variables (discrete, continuous or a mixture of both). We provide a realistic problem from the field of computer networks to demonstrate the applicability of our construction. Other potential application is iterative decoding of linear channels with nonGaussian noise. 1