Performance and Reliability Analysis for PBFT-Based Blockchain Systems With Repairable Voting Nodes

In a practical blockchain system based on the Practical Byzantine Fault Tolerance (PBFT) protocol, the voting nodes can fail at any time due to non-Byzantine errors, such as autonomous shutdowns, device crashes, and communication link failures caused by mobility or obstacles. These errors may cause voting nodes to exit the PBFT-based blockchain system unpredictably, resulting in a variable number of voting nodes available at any given time. To maintain optimal performance and consistency while adapting a PBFT-based blockchain system to this dynamic change, this paper proposes an extension to the PBFT protocol by introducing a repair process for failed nodes. The new PBFT-based blockchain system with repairable voting nodes is then analyzed for performance and reliability analysis by using multi-dimensional Markov processes, queueing theory, and the first passage time method. Additionally, we validate the accuracy of our theoretical findings by conducting numerical examples and simulation experiments. These experiments demonstrate that the introduction of a repair process can improve the performance and reliability of the PBFT-based blockchain system. Furthermore, we illustrate how various system parameters impact the performance measures of the PBFT-based blockchain system with repairable voting nodes. We hope that the methodology and results presented in this paper will establish a common framework for deriving theoretical analysis of existing PBFT-based blockchain systems and inspire future research efforts in this field.