Application Of Queueing System In Research On Blockchain Network

With the rapid development of blockchain technology,the service pressure of blockchain network nodes has increased,which results that the queueing phenomenon stills exist in the blockchain network.Combining with the operating mechanism of blockchain system,the selectivity of miners and the actual conditions of the blockchain system such as repairable failures of miners are considered,and two queueing models are established in this paper.Parameters of the blockchain queueing system are determined based on statistical data,and the system is analyzed from the perspective of miners,which provides a new idea for the optimization research on the blockchain system.Firstly,the blockchain transaction data of Bitcoin is obtained through the browser of blockchain.According to the data,hypothesis test is used to judge that the generation of the transaction obeys the Poisson process,which provides a strong theoretical basis for the establishment of the blockchain queueing system.Secondly,two service processes about mining and transmission of transactions are sim-ulated.It is assumed that transactions need to be transmitted and stored after mining service,and an M/(M₁,M₂)+M/1 blockchain queueing model is established.Using the quasi-birth-and-death process and matrix-geometric solution,the stationary distribution of the system is proved and solved.Based on the steady state of the system,numerical experiments and equi-librium optimization analysis of the blockchain system are performed,and the equilibrium arrival rate and equilibrium reception rate are obtained.Finally,the situation that the system is equipped with a spare miner which provides mining services for transactions when the ordinary miners are not working normally is con-sidered,and an M/(M₁,M₂)/1 blockchain queueing model is established.Combining related theories of queueing system,the stationary distribution of the system is analyzed and solved.The influence of parameters change on performance indicators such as the average transac-tion confirmation time is analyzed by using MATLAB software.The revenue function of the system is constructed to the equilibrium optimization analysis of the blockchain system.