Financial networks, and neural architectures—generate nonstationary, heavy-tailed, and highly irregular time series that are poorly captured by classical statistical summaries. Conventional performance metrics like mean latency and throughput often fail to reveal early-warning signatures of systemic stress or impending failure. There is a growing need for scale-aware analytical tools that can capture hidden structure in consensus dynamics and network perturbations. We develop an end-to-end statistical framework that treats consensus protocols as high-dimensional discrete-time dynamical systems subject to stochastic latency and failure processes. Using a Python-based discrete-event simulator implementing the Raft consensus algorithm, we generate time series of consensus latency, message complexity, and network latency under multiple operational regimes (normal load, high load, denial-of-service–type attacks, and partial node failures). We then apply Multifractal Detrended Fluctuation Analysis (MF-DFA) to these time series to obtain the resulting generalized Hurst exponents and singularity spectra f (a) and spectrum width Δ α as multifractal quantities. Synthetic results are accompanied by an analysis using block chain-like data (based on block inter-arrival and propagation times). Across all simulated regimes, consensus latency shows nontrivial multifractal structure provided a finite spectrum width Δ α . Stress scenarios caused by heavy-tailed latency and node failures give much broader and left-skewed spectra than baseline conditions, suggesting richer intermittency, as well as clustered extremity. We find strong positive relationship between Δ α and mean consensus latency, and moderate relationship between Δ α and failure incidence. Comparative analysis of Raft-like traces and proof of work-like traces reveals multifractal spectra that preserve algorithm specific signatures while sharing common stress induced broadening. The findings provide support for the view that multifractal descriptors are a sensitive scale-aware complement to traditional performance metrics for distributed consensus systems. Spectrum width Δ α can be used as a quantitative measure of systemic complexity, and can serve as an early warning measure of performance degradation and partial instability. The framework proposed in this article bridges the gap between chaos theory, multifractal analysis, and consensus protocols and provides some practical ways to incorporate multifractals in monitoring the design, diagnosis, and control of big-data, block chain, and cyber-physical infrastructures.
Mohammed et al. (Sat,) studied this question.