Performance evaluation of PBFT-based blockchain via a stage-Informed queueing model

Evaluating the performance of permissioned blockchain systems based on the Practical Byzantine Fault Tolerance (PBFT) consensus protocol is essential yet challenging due to complex information exchange patterns. We develop a stage-informed stochastic queueing model that captures transaction arrivals, block generation, and the multi-stage PBFT process. Based on this model, we derive the system’s stationary condition and establish key performance metrics: queue length, waiting time, duration of stay (sojourn time), and maximum throughput. These metrics reveal how performance depends on network bandwidth, processing capability, block capacity, node count, and transaction characteristics. Numerical and simulation experiments validate our theoretical findings. The results demonstrate that optimizing block capacity, the most readily adjustable parameter, can reduce the proportion of waiting time in total sojourn time from a dominant share to approximately half, significantly improving efficiency. This methodology enables adaptive parameter optimization for PBFT blockchains and is transferable to other BFT variants that share the leader-based, multi-round voting structure, providing a foundation for analyzing diverse blockchain architectures. The findings offer practical guidance for designing and optimizing efficient, scalable permissioned blockchains.