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16
Optimal Sampling in State Space Models with Applications to Network Monitoring
"... Advances in networking technology have enabled network engineers to use sampled data from routers to estimate network flow volumes and track them over time. However, low sampling rates result in large noise in traffic volume estimates. We propose to combine data on individual flows obtained from sam ..."
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Advances in networking technology have enabled network engineers to use sampled data from routers to estimate network flow volumes and track them over time. However, low sampling rates result in large noise in traffic volume estimates. We propose to combine data on individual flows obtained from sampling with highly aggregate data obtained from SNMP measurements (similar to those used in network tomography) for the tracking problem at hand. Specifically, we introduce a linearized state space model for the estimation of network traffic flow volumes from combined SNMP and sampled data. Further, we formulate the problem of obtaining optimal sampling rates under router resource constraints as an experiment design problem. Theoretically it corresponds to the problem of optimal design for estimation of conditional means for state space models and we present the associated convex programs for a simple approach to it. The usefulness of the approach in the context of network monitoring is illustrated through an extensive numerical study.
Identifiability of Flow Distributions from Link Measurements with Applications to Computer Networks
, 2007
"... We study the problem of identifiability of distributions of flows on a graph from aggregate measurements collected on its edges. This is a canonical example of a statistical inverse problem motivated by recent developments in computer networks. In this paper (i) we introduce a number of models for m ..."
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We study the problem of identifiability of distributions of flows on a graph from aggregate measurements collected on its edges. This is a canonical example of a statistical inverse problem motivated by recent developments in computer networks. In this paper (i) we introduce a number of models for multimodal data that capture their spatiotemporal correlation, (ii) provide sufficient conditions for the identifiability of nth order cumulants and also for a special class of heavy tailed distributions. Further, we investigate conditions on network routing for the flows that prove sufficient for identifiability of their distributions. Finally, we extend our results to directed acyclic graphs and discuss some open problems. 1
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.
Link failure monitoring via network coding
 in Proc. IEEE 35th Conference on Local Computer Networks
"... Abstract—In network tomography, we seek to infer link status parameters (delay, congestion, loss rates etc.) inside a network through endtoend measurements at (external) boundary nodes. As can be expected, such approaches generically suffer from identifiability problems; i.e., status of links in a ..."
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Abstract—In network tomography, we seek to infer link status parameters (delay, congestion, loss rates etc.) inside a network through endtoend measurements at (external) boundary nodes. As can be expected, such approaches generically suffer from identifiability problems; i.e., status of links in a large number of network topologies is not identifiable. We introduce an innovative approach based on linear network coding that overcomes this problem. We provide sufficient conditions on network coding coefficients and training sequence under which any logical network is guaranteed to be identifiable. In addition, we show that it is possible to locate any congested link inside a network during an arbitrary amount of time by increasing size of transmitted packets, leading to raise in complexity of the method. Further, a probability of success is provided for a random network. OPNET is used to implement the concept and confirm the validity of the claims simulation results confirm that LNC correctly detects the congested link in situations where standard probing based algorithm fails.
Network tomography via compressed sensing
 IN PROC. OF IEEE GLOBECOM
, 2010
"... In network tomography, we seek to infer link parameters inside a network (such as link delays) by sending endtoend probes between (external) boundary nodes. The main challenge here is to estimate linklevel attributes from endtoend measurements. In this paper, based on the idea of combinatorial ..."
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In network tomography, we seek to infer link parameters inside a network (such as link delays) by sending endtoend probes between (external) boundary nodes. The main challenge here is to estimate linklevel attributes from endtoend measurements. In this paper, based on the idea of combinatorial compressed sensing, we specify conditions on network routing matrix under which it is possible to estimate link delays from measurements of endtoend delay. Moreover, we provide an upperbound on the estimation error.
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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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.
Link Delay Estimation via Expander Graphs
, 2012
"... In network tomography, we seek to infer the status of parameters (such as delay) for links inside a network through endtoend probing between (external) boundary nodes along predetermined routes. In this work, we apply concepts from compressed sensing for network topologies that are expanders, to t ..."
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In network tomography, we seek to infer the status of parameters (such as delay) for links inside a network through endtoend probing between (external) boundary nodes along predetermined routes. In this work, we apply concepts from compressed sensing for network topologies that are expanders, to the delay estimation problem. We first show that a relative majority of network topologies are not expanders for the existing error bounds. Motivated by this, we relax this bound leading to evidence that for 30 % more networks, the link delays can be estimated. We provide simulation performance analysis of delay estimation based on l1 minimization, showing that accurate estimation is feasible for an increasing proportion of networks.
Identifiability of Link Metrics Based on Endtoend Path Measurements ∗
"... 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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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. ∗Research was partially sponsored by the U.S. Army Research Laboratory and the U.K. Ministry of Defence and was accomplished under Agreement Number W911NF063
Topological Constraints on Identifying Additive Link Metrics via Endtoend Paths Measurements
"... Abstract—We investigate the problem of identifying individual link metrics in a communication network through measuring accumulated endtoend metrics over selected paths, under the assumption that link metrics are additive (e.g., delay) and constant in the measurement duration. Based on linear alge ..."
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Abstract—We investigate the problem of identifying individual link metrics in a communication network through measuring accumulated endtoend metrics over selected paths, under the assumption that link metrics are additive (e.g., delay) and constant in the measurement duration. Based on linear algebra, we know that all the link metrics can be uniquely identified when the number of linearly independent paths is equal to the number of links in the network. There lacks, however, a fundamental theory to relate the number of linearly independent paths (and thus link identifiability) to externally observable parameters such as network topology, number of monitoring nodes, and routing restrictions. The aim of this paper, therefore, is to study constraints on the network topology for identifying additive link metrics, conditioned on the number of monitoring nodes being fixed, and cycles being prohibited in constructing measurement paths. Our first main result is that it is impossible to identify all the link metrics in any network with a nontrivial topology (having more than one link) using only two monitoring nodes; nevertheless, the interior links not incident with any monitoring node might be identifiable. Our second main result is a set of necessary and sufficient conditions for identifying all the interior links using two monitoring nodes. Furthermore, we show that these conditions have a natural extension to identifying the entire network using three or more monitoring nodes. To the best of our knowledge, this is the first work providing fundamental constraints on network topology for identifying additive link metrics using endtoend measurements on cyclefree paths. I.
Submitted to the Annals of Applied Statistics arXiv: math.PR/0000000 NETWORK–WIDE STATISTICAL MODELING AND PREDICTION OF COMPUTER TRAFFIC
"... Computer network use is becoming increasingly widespread, both in terms of number of users and variety of applications. In order to provide consistently high quality service, network engineers and other professionals must monitor several aspects of the network, including the traffic intensity on the ..."
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Computer network use is becoming increasingly widespread, both in terms of number of users and variety of applications. In order to provide consistently high quality service, network engineers and other professionals must monitor several aspects of the network, including the traffic intensity on the links that comprise the network. As networks grow, this type of monitoring has potential to become burdensome in terms of resources required. Motivated by the prospect of monitoring only a small subset of links, this paper explores the problem of using observed traffic measurements on selected links to predict the traffic on other, unobserved links. The characteristics of such unobserved links are learned through auxiliary data. Although more expensive to obtain, this extra data set provides the necessary information to represent important structure in the network, and can significantly improve the results of prediction as compared with more naive approaches. In addition, we introduce an adjusted control chart methodology that shows possible applications of our prediction results in situations where all links may be observed. 1. Introduction. Modern