## 6 Conclusions and Future Works  
In a blockchain network, consensus algorithms are crucial as they ensure all participants reach an agreement on consensus messages, including transactions, thus maintaining the integrity and security of the distributed ledger. PBFT, a consensus algorithm often used in private blockchains, provides reliability but encounters scalability challenges, as its performance can significantly decline with an increasing number of participating nodes.  
This paper proposed an enhanced PBFT method through dynamic hierarchy management and location-based clustering to address the scalability issue. This method extends the typical PBFT and DLM-PBFT by organizing nodes into clusters based on geographical information, which accelerates the consensus process within clusters. Its primary advantage is the reduction in consensus processing time and communication overhead across the blockchain network. By optimizing communication paths and minimizing the travel distance of messages, the method significantly enhances scalability and efficiency, especially in networks with a large number of nodes.  
Additionally, we have proposed a model for calculating the time required for each phase of the proposed PBFT protocol. Based on this model, we present a method to dynamically adjust the blockchain network's hierarchical structure to minimize the estimated time for consensus. This takes into account variables such as the number of nodes in each group and the total number of nodes within each cluster. This dynamic management of the network's hierarchy has been applied to the PBFT method we propose.  
Simulations were conducted to compare the performance of the proposed PBFT method against that of the typical PBFT and DLM-PBFT. The proposed PBFT method demonstrated significant performance improvements based on the experimental results. It showed a processing performance enhancement of approximately 107% to 128% over the typical PBFT, and 11% to 99% over DLM-PBFT. The proposed PBFT method is expected to substantially reduce latency and enhance throughput in blockchain operations, offering a scalable solution for networks with a high volume of transactions. By optimizing node communication, it can maintain robust security while increasing overall network efficiency.  
The performance and effectiveness of the proposed PBFT scheme have been verified through simulation. In future work, we plan to apply this scheme to an actual blockchain environment to further verify its performance and effectiveness. Additionally, we intend to research methods for minimizing the overhead associated with dynamic hierarchy management and location-based clustering.  
Conceptualization, G.K., J.C. and B.K.; methodology, G.K., J.C. and B.K.; software, G.K. and J.C.; validation, G.K., B.K. and M.C.; formal analysis, G.K. and B.K.; investigation, G.K. and J.C.; resources, B.K. and M.C.; data curation, G.K., J.C. and B.K.; writing--original draft preparation, G.K., J.C. and B.K.; writing--review and editing, B.K., G.K., J.C. and M.C.; visualization, G.K.; supervision, B.K. and M.C.; project administration, B.K. and M.C.; funding acquisition, M.C. and B.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIT) (No. NRF-2017R1E1A1A01075128).  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflict of interest.