Abstract: The Blockchain has been applied to a variety of sectors with great prospects. The main technological challenge the Blockchain facing is its performance bottleneck. The paper constructs a model to fit the Blockchain performance, analyzes the quantitative relationship between block creation rate, block size, network propagation speed and Blockchain performance, the security of the system. Increasing the block’s size or the block creation rate are equivalent in increasing the Blockchain’s performance through the quantitative analysis, but the increment shows marginal decline. And the network propagation speed restricts the improvement effect the block size or block creation rate has on the Blockchain performance and the security of the system. When their increments match the network propagation speed, the best improvement effect occurs. The mathematical model not only provides the theoretic support for the customization of the Blockchain system but also helps us understand the performance bottleneck of Blockchain which can offer the theoretic guidance to the development of efficient Blockchain technology.

Key words: Blockchain, performance, security, Transactions Per Second（TPS）

摘要： 区块链技术在很多领域有着广泛的应用前景，如何提高区块链性能是目前区块链应用面临的一个主要挑战。通过建立区块链性能的数学模型，研究区块大小、区块生成速率以及网络传输速度等因素与区块链性能和安全性之间的定量关系。通过量化分析可知，增加区块大小或区块生成速率可以等效地提升区块链性能和安全性，但是提升效果是边际递减的。而且增加区块大小或区块生成速率对区块链性能和安全性的提升作用受到网络传输速度的限制，区块大小和区块生成速率需要与网络传输速度相匹配，才能达到最佳的提升效果。该数学模型不仅可以为定制区块链系统提供理论支持，而且可以帮助人们理解区块链性能瓶颈，为进一步发展高效区块链技术的研究提供参考依据。

关键词: 区块链, 性能, 安全性, 每秒交易处理量