Characterizing Information Accuracy in Timeliness-Based Gossip Networks

TL;DR

This paper analyzes how information accuracy propagates in timeliness-based gossip networks with Markovian source states, introducing metrics and a stochastic hybrid systems framework to quantify accuracy and freshness in such networks.

Contribution

It develops a stochastic hybrid systems approach to characterize information accuracy metrics in gossip networks with Markovian sources, including multi-state sources and the impact of source pushes versus gossip exchanges.

Findings

Derived steady-state balance equations for accuracy metrics.

Extended analysis to multi-state source models.

Quantified the impact of source pushes versus gossip exchanges.

Abstract

We investigate information accuracy in timeliness-based gossip networks where the source evolves according to a continuous-time Markov chain (CTMC) with $M$ states and disseminates status updates to a network of $n$ nodes. In addition to direct source updates, nodes exchange their locally stored packets via gossip and accept incoming packets solely based on whether the incoming packet is fresher than their local copy. As a result, a node can possess the freshest packet in the network while still not having the current source state. To quantify the amount of accurate information flowing in the network under such a gossiping scheme, we introduce two accuracy metrics, average accuracy, defined as the expected fraction of nodes carrying accurate information in any given subset, and freshness-based accuracy, defined as the accuracy of the freshest node in any given subset. Using a stochastic hybrid systems (SHS) framework, we first derive steady-state balance equations and obtain matrix-valued recursions that characterize these metrics in fully connected gossip networks under binary CTMCs. We then extend our analysis to the general multi-state information source using a joint CTMC approach. Finally, we quantify the fraction of nodes whose information is accurate due to direct source pushes versus gossip exchanges. We verify our findings with numerical analyses and provide asymptotic insights.