Practical Approach to Identifying Additive Link Metrics with Shortest Path Routing

© 2015 IEEE. We revisit the problem of identifying link metrics from end- to-end path measurements in practical IP networks where shortest path routing is the norm. Previous solutions rely on explicit routing techniques (e.g., source routing or MPLS) to construct independent measurement paths for efficient link metric identification. However, most IP networks still adopt shortest path routing paradigm, while the explicit routing is not supported by most of the routers. Thus, this paper studies the link metric identification problem under shortest path routing constraints. To uniquely identify the link metrics, we need to place sufficient number of monitors into the network such that there exist m (the number of links) linear independent shortest paths between the monitors. In this paper, we first formulate the problem as a mixed integer linear programming problem, and then to make the problem tractable in large networks, we propose a Monitor Placement and Measurement Path Selection (MP-MPS) algorithm that adheres to shortest path routing constraints. Extensive simulations on random and real networks show that the MP- MPS gets near-optimal solutions in small networks, and MP- MPS significantly outperforms a baseline solution in large networks

Analysis on binary loss tree classification with hop count for multicast topology discovery

Copyright © 2004 IEEEThe use of multicast inference on end-to-end measurement has recently been proposed as a means of obtaining the underlying multicast topology. We analyze the algorithm of binary loss tree classification with hop count (HBLT). We compare it with the binary loss tree classification algorithm (BLT) and show that the probability of misclassification of HBLT decreases more quickly than that of BLT as the number of probing packets increases. The inference accuracy of HBLT is always 1 (the inferred tree is identical to the physical tree) in the case of correct classification, whereas that of BLT is dependent on the shape of the physical tree and inversely proportional to the number of internal nodes with a single child. Our analytical result shows that HBLT is superior to BLT, not only on time complexity, but also on misclassification probability and inference accuracy.Hui Tian, Hong She

Network tomography based on 1-D projections

Network tomography has been regarded as one of the most promising methodologies for performance evaluation and diagnosis of the massive and decentralized Internet. This paper proposes a new estimation approach for solving a class of inverse problems in network tomography, based on marginal distributions of a sequence of one-dimensional linear projections of the observed data. We give a general identifiability result for the proposed method and study the design issue of these one dimensional projections in terms of statistical efficiency. We show that for a simple Gaussian tomography model, there is an optimal set of one-dimensional projections such that the estimator obtained from these projections is asymptotically as efficient as the maximum likelihood estimator based on the joint distribution of the observed data. For practical applications, we carry out simulation studies of the proposed method for two instances of network tomography. The first is for traffic demand tomography using a Gaussian Origin-Destination traffic model with a power relation between its mean and variance, and the second is for network delay tomography where the link delays are to be estimated from the end-to-end path delays. We compare estimators obtained from our method and that obtained from using the joint distribution and other lower dimensional projections, and show that in both cases, the proposed method yields satisfactory results.Comment: Published at http://dx.doi.org/10.1214/074921707000000238 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Network Tomography: Identifiability and Fourier Domain Estimation

The statistical problem for network tomography is to infer the distribution of $\mathbf{X}$, with mutually independent components, from a measurement model $\mathbf{Y}=A\mathbf{X}$, where $A$ is a given binary matrix representing the routing topology of a network under consideration. The challenge is that the dimension of $\mathbf{X}$ is much larger than that of $\mathbf{Y}$ and thus the problem is often called ill-posed. This paper studies some statistical aspects of network tomography. We first address the identifiability issue and prove that the $\mathbf{X}$ distribution is identifiable up to a shift parameter under mild conditions. We then use a mixture model of characteristic functions to derive a fast algorithm for estimating the distribution of $\mathbf{X}$ based on the General method of Moments. Through extensive model simulation and real Internet trace driven simulation, the proposed approach is shown to be favorable comparing to previous methods using simple discretization for inferring link delays in a heterogeneous network.Comment: 21 page

Stability analysis of discrete-time recurrent neural networks with stochastic delay

This paper is concerned with the stability analysis of discrete-time recurrent neural networks (RNNs) with time delays as random variables drawn from some probability distribution. By introducing the variation probability of the time delay, a common delayed discrete-time RNN system is transformed into one with stochastic parameters. Improved conditions for the mean square stability of these systems are obtained by employing new Lyapunov functions and novel techniques are used to achieve delay dependence. The merit of the proposed conditions lies in its reduced conservatism, which is made possible by considering not only the range of the time delays, but also the variation probability distribution. A numerical example is provided to show the advantages of the proposed conditions. © 2009 IEEE.published_or_final_versio