Network Tomography: Identifiability and Fourier Domain Estimation

TL;DR

This paper investigates the identifiability and estimation of link delay distributions in network tomography, proposing a Fourier domain method that outperforms previous discretization-based approaches in simulations.

Contribution

It establishes the identifiability of the link delay distribution up to a shift and introduces a Fourier-based estimation algorithm for network tomography.

Findings

The distribution is identifiable up to a shift under mild conditions.

The proposed Fourier domain method is faster and more accurate than previous discretization methods.

Simulation results show improved inference of link delays in heterogeneous networks.

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.