基于DAG的区块链系统网络增长过程的Markov过程理论
A Markov Process Theory for Network Growth Processes of DAG-based Blockchain Systems
摘要：
需要注意的是，区块链的串行结构具有许多本质缺陷，因此引入数据网结构及其基于DAG的区块链来解决区块链缺陷。从这样的网络角度来看，基于DAG的区块链系统的分析变得有趣和具有挑战性。因此，仿真模型被广泛采用。在本文中，我们首先通过两层提示和内部提示的不耐烦连接行为描述了一个简单的基于DAG的IOTA Tangle区块链的马尔可夫模型。然后，我们建立了一个连续时间马尔可夫过程来分析基于DAG的区块链系统，并表明该马尔可夫过程是一个水平依赖的准生灭（QBD）过程。在此基础上，我们证明了QBD过程必不可约且是正常返的。此外，一旦给出QBD过程的平稳概率向量，我们就提供了基于DAG的区块链系统的性能分析。其次，我们提出了一个新的有效的方法来计算的平均确认时间的任何到达内部尖端在这个系统的第一次通过时间和PH分布。最后，我们使用数值例子来检查我们的理论结果的有效性，并指出一些关键的系统参数如何影响该系统的性能指标。因此，我们希望本文中开发的方法和结果可以适用于处理更一般的基于DAG的区块链系统，从而可以潜在地开发一系列有前途的研究。
英文摘要：
Note that the serial structure of blockchain has many essential pitfalls, thus a data network structure and its DAG-based blockchain are introduced to resolve the blockchain pitfalls. From such a network perspective, analysis of the DAG-based blockchain systems becomes interesting and challenging. So, the simulation models are adopted widely. In this paper, we first describe a simple Markov model for the DAG-based blockchain with IOTA Tangle by means of two layers of tips and internal tips' impatient connection behavior. Then we set up a continuous-time Markov process to analyze the DAG-based blockchain system and show that this Markov process is a level-dependent quasi-birth-and-death (QBD) process. Based on this, we prove that the QBD process must be irreducible and positive recurrent. Furthermore, once the stationary probability vector of the QBD process is given, we provide performance analysis of the DAG-based blockchain system. Next, we propose a new effective method for computing the average confirmation time of any arriving internal tip at this system by means of the first passage times and the PH distributions. Finally, we use numerical examples to check the validity of our theoretical results and indicate how some key system parameters influence the performance measures of this system. Therefore, we hope that the methodology and results developed in this paper can be applicable to deal with more general DAG-based blockchain systems such that a series of promising research can be developed potentially.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
