Generalized Network Tomography

TL;DR

This paper introduces a novel algorithm for generalized network tomography that estimates link performance in arbitrary network topologies using only unicast end-to-end measurements, without prior distribution knowledge.

Contribution

It presents a new method to estimate link distributions in any network topology using polynomial systems and moment generating functions, removing the need for multicast data or tree structures.

Findings

Successfully estimates link distributions without prior knowledge.

Applicable to networks with arbitrary topologies.

Validated through Matlab simulations.

Abstract

For successful estimation, the usual network tomography algorithms crucially require i) end-to-end data generated using multicast probe packets, real or emulated, and ii) the network to be a tree rooted at a single sender with destinations at leaves. These requirements, consequently, limit their scope of application. In this paper, we address successfully a general problem, henceforth called generalized network tomography, wherein the objective is to estimate the link performance parameters for networks with arbitrary topologies using only end-to-end measurements of pure unicast probe packets. Mathematically, given a binary matrix $A,$ we propose a novel algorithm to uniquely estimate the distribution of $X,$ a vector of independent non-negative random variables, given only IID samples of the components of the random vector $Y = AX.$ This algorithm, in fact, does not even require any prior knowledge of the unknown distributions. The idea is to approximate the distribution of each component of $X$ using linear combinations of known exponential bases and estimate the unknown weights. These weights are obtained by solving a set of polynomial systems based on the moment generating function of the components of $Y.$ For unique identifiability, it is only required that every pair of columns of the matrix $A$ be linearly independent, a property that holds true for the routing matrices of all multicast tree networks. Matlab based simulations have been included to illustrate the potential of the proposed scheme.