Performance Analysis for DAG-based Blockchain Systems Based on the Markov Process  

作　　者：Xingshuo Song Shiyong Li Yanxia Chang Chi Zhang Quanlin Li 

机构地区：[1]School of Economics and Management,Yanshan University,Qinhuangdao,066004,China [2]School of Economics and Management,Bering University of Technology,Beijing,100124,China

出　　处：《Journal of Systems Science and Systems Engineering》2025年第1期29-54,共26页系统科学与系统工程学报(英文版)

基　　金：supported in part by the National Natural Science Foundation of China(NSFC),under Grant Nos.71932002,71971188;Humanity and Social Science Foundation of Ministry of Education of China,under Grant No.22YJCZH086.

摘　　要：As an innovative approach, Direct Acyclic Graph (DAG)-based blockchain is designed to overcome the scalability and performance limitations of traditional blockchain systems, which rely on sequential structures. The graph-based architecture of DAG allows for faster transactions and parallel processing, making it a compelling option across various industries. To enhance the analytical understanding of DAG-based blockchains, this paper begins by introducing a Markov model tailored for a DAG-based blockchain system, specifically focusing on the Tangle structure and the interaction between tips and newly arrived transactions. We then establish a continuous-time Markov process to analyze the DAG-based blockchain, demonstrating that this process is a level-dependent quasi-birth-and-death (QBD) process. We further prove that the QBD process is both irreducible and positively recurrent. Building on this foundation, we conduct a performance analysis of the DAG-based blockchain system by deriving the stationary probability vector of the QBD process. Notably, we introduce a novel method to calculate the average sojourn time of any arriving internal tip within the system using first passage times and Phase-type (PH) distributions. Finally, numerical examples are provided to validate our theoretical findings and to illustrate the influence of system parameters on the performance metrics.

关 键 词：Blockchain direct acyclic graph(DAG) QBD process performance analysis sojourn time 

分 类 号：O15[理学—数学]