Network Tomography: Identifiability and Fourier Domain Estimation

Abstract

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

A Linear Algebraic Approach for Loss Tomography in Mesh Topologies Using Network Coding

“…We 2 . Let node 4 use coding coefficients [2,1], so that r would receive (010) 2 for P (s, 1, 2, 3, 4, r).…”

“…Let node 4 use coding coefficients [2,1], so that r would receive (010) 2 for P (s, 1, 2, 3, 4, r). Suppose only P (s, 1, 3, 4, r) has successfully transmitted a probe.…”

“…Then, r would also receive (010) 2 . Let node 3 use coding coefficients [2,1], so that r would receive (100) 2 for P (s, 1, 3, 4, r). A received probe packet with multiple 1's represents that a batch of probes has been successfully transmitted on multiple paths.…”

Topology Property Based on Network Tomography for Wireless Mobile Multihop Communication Network

“…The network tomography is usually adopted on the premise of the fixed or already-known network topology [11,12]. However, the nodes random movement raises new limitations for the network tomography in wireless mobile multihop communication network [13], since the false route information A will produce errors for X.…”

“…The mobility model of wireless mobile multihop communication network should satisfy the following assumptions: (1) the network area is much larger than the node coverage; (2) the node moving direction obeys the uniform distribution on [0, 2 ); that is to say, the mobility model has no direction specificity with the pause time as 0. The probability distribution of the link duration equals the product of the probability distribution of the link duration 12 and the velocity probability of the mobility model in the condition of any two nodes ( 1 , 2 ) with the velocity known and the angle between the relative velocity directions obeying the uniform distribution on [0, 2 ), as shown in the following equation:…”