A Stochastic Kaczmarz Algorithm for Network Tomography

TL;DR

This paper introduces a stochastic Kaczmarz algorithm tailored for network tomography, capable of real-time noisy data processing, and proven to converge similarly to the classical method, with demonstrated effectiveness through simulations.

Contribution

It presents a novel stochastic approximation of the Kaczmarz algorithm that is incremental and suitable for real-time noisy data in network tomography.

Findings

Algorithm converges to the same point as the deterministic Kaczmarz method.

Proven convergence with probability one.

Numerical simulations confirm effectiveness.

Abstract

We develop a stochastic approximation version of the classical Kaczmarz algorithm that is incremental in nature and takes as input noisy real time data. Our analysis shows that with probability one it mimics the behavior of the original scheme: starting from the same initial point, our algorithm and the corresponding deterministic Kaczmarz algorithm converge to precisely the same point. The motivation for this work comes from network tomography where network parameters are to be estimated based upon end-to-end measurements. Numerical examples via Matlab based simulations demonstrate the efficacy of the algorithm.