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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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Cited by 11 (8 self)
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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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Cited by 10 (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.
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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Cited by 9 (1 self)
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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.
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 7 (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.
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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Cited by 7 (4 self)
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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.
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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Cited by 6 (5 self)
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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.
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 6 (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.
Link Identifiability in Communication Networks with Two Monitors
"... We investigate the problem of identifying individual link performance metrics in a communication network by measuring endtoend metrics of selected paths between monitors, under the assumption that link metrics are additive and constant during the measurement, and measurement paths cannot contain ..."
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Cited by 3 (1 self)
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We investigate the problem of identifying individual link performance metrics in a communication network by measuring endtoend metrics of selected paths between monitors, under the assumption that link metrics are additive and constant during the measurement, and measurement paths cannot contain cycles. In a previous work, we developed an algorithm that places the minimum number of monitors to identify all link metrics. However, even the minimum number can be large in some practical networks (e.g., 60 % of all the nodes), suggesting high monitor deployment cost. In this paper, we study the dual problem where given a fixed number of monitors, we want to place them to maximize the number of identifiable link metrics, with concrete results for the case of two monitors. The significance of the twomonitor case is that all the tomographic computation can be performed at the destination monitor without shipping measurements to a central node, thus enabling endhostbased network monitoring. We develop an efficient algorithm to determine all identifiable links in an arbitrary network with a given placement of two monitors, based on which we propose an optimal twomonitor placement algorithm to maximize the number of identifiable links. Our evaluation on real ISP topologies shows that although a large number of monitors is needed to identify all link metrics, we can usually identify a substantial portion (up to 97%) of the links using a single pair of optimally placed monitors.
Monitor Placement for Maximal Identifiability in Network Tomography
"... We investigate the problem of placing a given number of monitors in a communication network to identify the maximum number of link metrics from endtoend measurements between monitors, assuming that link metrics are additive, and measurement paths cannot contain cycles. Motivated by our previous r ..."
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Cited by 2 (2 self)
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We investigate the problem of placing a given number of monitors in a communication network to identify the maximum number of link metrics from endtoend measurements between monitors, assuming that link metrics are additive, and measurement paths cannot contain cycles. Motivated by our previous result that complete identification of all link metrics can require a large number of monitors, we focus on partial identification using a limited number of monitors. The basis to our solution is an efficient algorithm for determining all identifiable links for a given monitor placement. Based on this algorithm, we develop a polynomialtime greedy algorithm to incrementally place monitors such that each newly placed monitor maximizes the number of additional identifiable links. We prove that the proposed algorithm is optimal for 2vertexconnected networks, and demonstrate that it is nearoptimal for several real ISP topologies that are not 2vertexconnected. Our solution provides a quantifiable tradeoff between level of identifiability and available monitor resources.
Structural Models for Dual Modality Data With Application to Network Tomography
"... Abstract—We propose models for the joint distribution of two modalities for network flow volumes. While these models are motivated by computer network applications, the underlying structural assumptions are more generally applicable. In the case of computer network flow volumes, this corresponds to ..."
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Abstract—We propose models for the joint distribution of two modalities for network flow volumes. While these models are motivated by computer network applications, the underlying structural assumptions are more generally applicable. In the case of computer network flow volumes, this corresponds to joint modeling for packet and byte volumes and enables computer network tomography, whose goal is to estimate characteristics of sourcedestination flows based on aggregate link measurements. Network tomography is a prototypical example of a linear inverse problem on graphs. We introduce two generative models for the relation between packet and byte volumes, establish identifiability of their parameters, and discuss different estimating procedures. The proposed estimators of the flow characteristics are evaluated using both simulated and emulated data. Finally, the proposed models allow us to estimate parameters of the packet size distribution, thus providing additional insights into the composition of network traffic. Index Terms—Compound model, computer networks, identifiability, inverse problem, packet size distribution, tomography,