Analysis of blockchain system based on BMAP/PH[b]/1 queueing model

Abstract

In this modern era, the security and safety of financial and personal digital data are crucial considerations. Blockchain technology offers a secure framework for the transmission of data between devices, without the interference of malicious actors. With the growing demand for this technology, it has become essential to evaluate the impact of its processes on system characteristics to forecast transactions behavior and ensure necessary quality indicators, as well as the stability of system components while the blockchain technology is in operation. Queueing models are a highly effective mathematical tool for analyzing and optimizing the performance of blockchain systems. In this study, a more generic queueing model is utilized to evaluate a blockchain application. The transactions arrive in batches according to a Markovian arrival process, and the service times for the block-generation (the first stage) and blockchain-building (the second stage) follow phase-type distributions. Using matrix-analytic method, we study the model in steady-state. The stationary distribution and the stability condition of the system have been derived. Further, by determining key system performance measures, illustrative numerical examples covering a wide range of batch size and service time distributions have been discussed. In conclusion, our hope is that the methodology and findings presented in this paper will pave the way for the queueing analysis of more extensive and diverse blockchain systems in practice. Furthermore, we believe that it will inspire a series of promising future quantitative and qualitative studies aimed at the development of blockchain technologies.