Performance Analysis of DAG-Based Blockchain Systems Based on Markovian Arrival Process

Abstract

The Direct Acyclic Graph (DAG)-based blockchain offers impressive scalability and finds applications across various sectors, notably the Internet of Things (IoT) industry. Within this domain, IOTA has been purpose-built for IoT. This article analyzes the performance of IOTA’s data structure Tangle based on the Markovian arrival process (MAP). Meanwhile, we have considered this situation in a newly issued transaction and selected multiple tips for validation. Firstly, we show that this Markov process is a level-dependent quasi-birth-death (QBD) process. Then, we prove that the QBD process is irreducible, positive, and recurrent. Furthermore, smooth probability vectors for the QBD process are given, and the performance of the DAG-based blockchain system is analyzed. Moreover, we verify the validity of our theoretical results with numerical examples, pointing out how some key system parameters affect the performance metrics of this system. Therefore, we hope that the methodology and results presented in this paper will shed some light on DAG-based blockchain systems so that a series of promising research projects can be developed.

Keywords

• Internet of Things (IoT)
• direct acyclic graph (DAG)
• IOTA
• QBD process
• Markovian arrival process (MAP)