## 3 Improved RE-BPFT Blockchain Consensus Algorithm
### View Change Protocol
In conclusion, RE-PBFT efficiently achieves consensus even in complex environments with numerous nodes and large transaction data, proving its superior latency performance and scalability in large-scale blockchain systems. Figure 3 shows the box plot of consensus latency obtained from 20 independent experiments conducted by four consensus algorithms in a consortium blockchain scenario with a transaction size of 100 KB and node counts ranging from 10 to 60. As observed, the latency of the PBFT algorithm increases most significantly with the growth of node count, exhibiting a wide distribution range and certain volatility. RBFT shows improvement over PBFT in terms of overall latency and volatility but still demonstrates some instability. The PPoR algorithm maintains good stability and low latency under most node scales. The proposed RE-PBFT algorithm achieves the lowest mean latency and smallest fluctuation range across all node scales, demonstrating superior consensus efficiency and stability. Overall, RE-PBFT exhibits stronger performance robustness and scalability compared with other algorithms when handling large-scale transaction loads and node growth. Figure 2: Consensus latency of four consensus algorithms transmitting 1 KB, 10 KB, 50 KB, and 100 KB. ### Throughput Testing

A series of comparative experiments was conducted to evaluate the throughput performance of RE-PBFT against the traditional PBFT, RBFT, and PPoR algorithms, considering different node scales. Throughput, defined as the number of consensus requests a system can handle within a specific timeframe, indicates the processing capability of the consensus algorithm and overall system capacity. Higher throughput suggests greater efficiency in handling requests or transactions. In these tests, node counts in the consortium blockchain were incrementally raised from 10 to 60. For each scenario, the average throughput of all four algorithms was collected and analyzed. Figure 4 illustrates the throughput variations of PBFT, RBFT, PPoR, and the proposed RE-PBFT as the number of nodes in the network increases. The \(x\)-axis values in Figure 4 represent the number of network nodes, while the \(y\)-axis values denote the network throughput. The results indicate that under identical experimental conditions, RE-PBFT demonstrates overall superior throughput compared with the other three algorithms. With an initial node count of 10, RE-PBFT achieves a throughput of 850 TPS, slightly higher than PPoR (840 TPS) and significantly surpassing PBFT (820 TPS) and RBFT (830 TPS). As the number of nodes increases from 10 to 60, all algorithms exhibit a declining throughput trend, albeit with varying degrees of reduction. Among them, PBFT experiences the fastest throughput drop, decreasing from 820 to 300 TPS, making it the weakest performer. In contrast, RE-PBFT demonstrates strong stability throughout the node expansion process, with the smallest throughput decline, ultimately maintaining 380 TPS--slightly higher than PPoR (370 TPS) and notably superior to RBFT (320 TPS) and PBFT (300 TPS). Figure 3: Consensus Delay Box Diagram for Four Consensus Algorithms. The experimental results demonstrate that RE-PBFT not only achieves higher throughput when fewer nodes are involved but also exhibits outstanding scalability as the number of nodes increases. These findings imply that the RE-PBFT algorithm offers superior concurrent processing and consensus efficiency, making it highly suitable for large-scale blockchain environments that require high throughput. The notable throughput improvements of RE-PBFT can be attributed primarily to the optimized reputation evaluation strategy, which reduces unnecessary message exchanges and improves verification efficiency. Additionally, simplifications within the enhanced consensus mechanism contribute to quicker consensus decisions, further elevating throughput performance.