Analysis of blockchain system based on $$\hbox {M}/(\hbox {M}_1,\hbox {M}_2)/1$$ vacation queueing model

Abstract

With the rapid development of technology, the issues about blockchain are getting more and more attention from scholars. In order to study the operation of the blockchain system, this paper simulated the transaction confirmation process of a blockchain system with two miners. Combining with practice, factors such as adverse transactions, impatience phenomena of transactions, fault repairable conditions of the mining process and a spare miner are considered. An M/(M $$_1$$ ,M $$_2$$ )/1 vacation queueing model with negative customers, impatient customers, optional services, repairable faults and a spare server is established. The stationary distribution of the system is obtained by using the matrix-geometric solution method, and expressions of the average confirmation time of transactions and other performance indexes are given. The influence of each parameter on the performance indexes of blockchain system is analyzed by using MATLAB software. Revenue function and equilibrium sleep rate of miners are discussed for optimizing the blockchain system.