Asynchronous Distributed Averaging: A Switched System Framework for Average Error Analysis

TL;DR

This paper analyzes the expected average error in asynchronous distributed averaging systems using a switched system framework, accounting for communication uncertainties like delays and packet drops, and provides bounds on the average error.

Contribution

It introduces a switched system framework to analyze and bound the average error in asynchronous distributed averaging without modifying existing algorithms.

Findings

Provides an upper bound on asynchronous average error.

Validates theoretical results with numerical examples.

Addresses communication uncertainties in asynchronous averaging.

Abstract

This paper investigates an expected average error for distributed averaging problems under asynchronous updates. The asynchronism in this context implies no existence of a global clock as well as random characteristics in communication uncertainty such as communication delays and packet drops. Although some previous works contributed to the design of average consensus protocols to guarantee the convergence to an exact average, these methods may increase computational burdens due to extra works. Sometimes it is thus beneficial to make each agent exchange information asynchronously without modifying the algorithm, which causes randomness in the average value as a trade-off. In this study, an expected average error is analyzed based on the switched system framework, to estimate an upper bound of the asynchronous average compared to the exact one in the expectation sense. Numerical examples are provided to validate the proposed results.