*Result*: Performance Analysis for DAG-based Blockchain Systems Based on the Markov Process.
*Further Information*
*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. [ABSTRACT FROM AUTHOR]
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