Latency performance modeling and analysis for PBFT consensus in blockchain system: A synchronization perspective from Kuramoto model

In the rapidly evolving landscape of blockchain technology, achieving efficient and reliable consensus mechanisms is becoming more and more paramount. The Practical Byzantine Fault Tolerance (PBFT) algorithm has emerged as a prominent consensus protocol and is widely adopted in permissioned blockchain deployments. However, the latency performance of PBFT remains a critical concern, as it directly impacts the scalability and responsiveness of blockchain applications. Existing latency analyses typically rely on queueing theory, stochastic processes, or simulation-based approaches. While effective for empirical estimation, these methods offer limited insight into the underlying dynamical synchronization processes that govern consensus progression. As a result, a holistic theoretical framework capable of capturing the collective timing behavior of PBFT replicas is still lacking. Inspired by synchronization phenomena in networked oscillator systems, this paper introduces a novel framework for modeling and analyzing PBFT latency through the lens of synchronization theory, specifically using a Kuramoto-type model. By establishing a principled correspondence between PBFT message phases and oscillator phase evolution, we provide a unified dynamical perspective on consensus execution. Our analysis combines theoretical derivations with empirical evaluations to reveal how system parameters and fault conditions influence latency formation and evolution. The results contribute to a deeper understanding of consensus dynamics in permissioned blockchain systems and offer guidance for latency-aware PBFT optimization in practice.