Measuring Consensus Stability Through Validator Behavior Patterns in Byzantine Distributed Network

Abstract

This paper presents a framework for analyzing and modeling validator behavior in dynamic consensus protocols. A discrete state-based model is proposed in order to represent four key validator states: majority, non-faulty minority, faulty minority, and non-validator, enabling systematic behavioral analysis through three complementary metrics: Jensen-Shannon Divergence (JSD) for entropy-based behavioral differences, the Bhattacharyya Coefficient for distribution similarity, and Wasserstein distance for state transition costs. To identify coherent validator groups and detect outliers, an HDBSCAN (Hierarchical Density-Based Spatial Clustering of Applications with Noise) clustering is used since it is well-suited for detecting clusters in data with varying densities. Using JSD-based similarity measures in HDBSCAN, transient convergence patterns and stable behavioral clusters are uncovered, even in decentralized networks with diverse fault conditions. Simulation results on a 50-node network demonstrate the framework’s effectiveness, providing insights into system dynamics and offering tools for validator selection, fault detection, and stability monitoring in distributed ledger systems. This approach is particularly relevant, as consensus protocols evolve beyond traditional PBFT (Practical Byzantine Fault Tolerance) implementations, combining theoretical metrics with clustering techniques to enhance consensus robustness.