# Hybrid Consensus Algorithm Based on Modified Proof-of-Probability and DPoS
## 5 Evaluation and Results
### Scalability  
The algorithm proposed in this paper implements a multi-node consensus process. In theory, the algorithm will have good scalability. In order to verify the scalability of the algorithm, we designed an experiment to explore the relationship between the number of nodes and transaction throughput. The experiment compares the transaction throughput of the blockchain system based on this algorithm and the PoW algorithm under the conditions of 18 nodes, 36 nodes, 72 nodes, and 144 nodes. In each case, we did 20 sets of experiments and took the average of the throughput. The experimental results are shown in Figure 9.  
It can be seen from the above figure that the PoW algorithm's throughput will decrease with the increase in nodes, which is usually caused by the increase in the difficulty of hash calculation and the increase in consensus time. In contrast, the algorithm proposed in this paper has relatively low throughput only in the case of an increase in the number of elections caused by a small number of  
Figure 8: Transaction throughput. Figure 9: Scalability. supernodes. As the number of nodes increases, its throughput will gradually increase and stabilize, that is, the throughput of the algorithm is not easily affected by the increase in the number of nodes. In general, under the same number of nodes, the throughput of this algorithm is basically higher than that of the PoW algorithm. After algorithm analysis and performance evaluation, we explain how our proposed consensus algorithm meets all the requirements mentioned in Section 2.5. Bookkeeping rights: In the consensus algorithm proposed in this paper, due to the introduction of the waiting time mechanism and the expected value mechanism, even if the node with high computing power first calculates the nonce value, it has very small probability of matching the expected value, and then, it will enter the waiting time. This significantly weakens the advantages of high computing power nodes, so that other general nodes have a greater opportunity to obtain bookkeeping rights. This effectively avoids excessive computing power competition. At the same time, due to the special setting of the expected value mechanism, block generation efficiency can also be guaranteed, that is, a block can be generated in one minute at the fastest time and in ten minutes at the slowest time (the bitcoin system generates a block every ten minutes). Therefore, the proposed algorithm can provide fair and efficient bookkeeping rights competition. Resource saving: Due to the algorithm providing fair and reasonable bookkeeping rights competition, the opportunity for nodes to obtain bookkeeping rights is not linearly related to its computing power, so nodes will not excessively pursue high computing power, which obviously avoids excessive computing power competition and reduces the waste of computing power and electric power. Thus, the running cost of nodes is reduced. After further optimization, the algorithm can also be deployed on some lightweight devices. Therefore, the proposed algorithm has the characteristics of resource saving. High efficiency: By introducing the expected value mechanism, block generation speed is significantly improved compared with the bitcoin system. In the worst case, it has the same generation speed as the bitcoin system, and in the best case, it is ten times as fast as the bitcoin system. In fact, the bits dynamic adjustment algorithm can shorten the mining time and further improve block generation speed. Therefore, the efficiency of this algorithm is better than that of the bitcoin system. Decentralization: In PoW and other mining-based consensus algorithms, the competition for bookkeeping rights seems fair, but it will be monopolized by high computing power nodes. In a consensus algorithm such as DPoS, the supernodes obtained by election can be used for bookkeeping.