1,626 research outputs found
Identifiability of link metrics based on end-to-end path measurements
We investigate the problem of identifying individual link metrics in a communication network from end-to-end 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 cycle-free. Our main results are: (i) it is generally impossible to identify all the link met-rics 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 moni-tors. 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 iden-tifiability using a much smaller number of monitors than a baseline solution
A Network Coding Approach to Loss Tomography
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 end-to-end 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 trade-off 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
Topology Discovery of Sparse Random Graphs With Few Participants
We consider the task of topology discovery of sparse random graphs using
end-to-end random measurements (e.g., delay) between a subset of nodes,
referred to as the participants. The rest of the nodes are hidden, and do not
provide any information for topology discovery. We consider topology discovery
under two routing models: (a) the participants exchange messages along the
shortest paths and obtain end-to-end measurements, and (b) additionally, the
participants exchange messages along the second shortest path. For scenario
(a), our proposed algorithm results in a sub-linear edit-distance guarantee
using a sub-linear number of uniformly selected participants. For scenario (b),
we obtain a much stronger result, and show that we can achieve consistent
reconstruction when a sub-linear number of uniformly selected nodes
participate. This implies that accurate discovery of sparse random graphs is
tractable using an extremely small number of participants. We finally obtain a
lower bound on the number of participants required by any algorithm to
reconstruct the original random graph up to a given edit distance. We also
demonstrate that while consistent discovery is tractable for sparse random
graphs using a small number of participants, in general, there are graphs which
cannot be discovered by any algorithm even with a significant number of
participants, and with the availability of end-to-end information along all the
paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is
scheduled to appear in J. on Random Structures and Algorithm
Estimating Dynamic Traffic Matrices by using Viable Routing Changes
Abstract: In this paper we propose a new approach for dealing with the ill-posed nature of traffic matrix estimation. We present three solution enhancers: an algorithm for deliberately changing link weights to obtain additional information that can make the underlying linear system full rank; a cyclo-stationary model to capture both long-term and short-term traffic variability, and a method for estimating the variance of origin-destination (OD) flows. We show how these three elements can be combined into a comprehensive traffic matrix estimation procedure that dramatically reduces the errors compared to existing methods. We demonstrate that our variance estimates can be used to identify the elephant OD flows, and we thus propose a variant of our algorithm that addresses the problem of estimating only the heavy flows in a traffic matrix. One of our key findings is that by focusing only on heavy flows, we can simplify the measurement and estimation procedure so as to render it more practical. Although there is a tradeoff between practicality and accuracy, we find that increasing the rank is so helpful that we can nevertheless keep the average errors consistently below the 10% carrier target error rate. We validate the effectiveness of our methodology and the intuition behind it using commercial traffic matrix data from Sprint's Tier-1 backbon
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