Push sum with transmission failures

TL;DR

This paper studies the push-sum algorithm's robustness to message losses in unreliable networks, demonstrating exponential convergence and analyzing error behavior, with theoretical and numerical insights and comparisons to standard consensus methods.

Contribution

It provides the first analysis of push-sum under transmission failures, revealing convergence properties and error bounds in unreliable communication environments.

Findings

Exponential convergence persists despite message losses.

The final value distribution can be characterized implicitly.

Performance comparison shows advantages over standard consensus algorithms.

Abstract

The push-sum algorithm allows distributed computing of the average on a directed graph, and is particularly relevant when one is restricted to one-way and/or asynchronous communications. We investigate its behavior in the presence of unreliable communication channels where messages can be lost. We show that exponential convergence still holds and deduce fundamental properties that implicitly describe the distribution of the final value obtained. We analyze the error of the final common value we get for the essential case of two nodes, both theoretically and numerically. We provide performance comparison with a standard consensus algorithm.