Markov Processes In Blockchain System

As the most successful distributed digital currency,Bitcoin has attracted great attention since it appeared in the white paper in 2008.In the past 12 years,such a system without a central management server,any responsible entities,and external credit endorsement,has been running stably,which undoubtedly shows the completeness and reliability of blockchain technology.As a key underlying technology generated with Bitcoin system,blockchain technology has been explored and developed by more and more people and shows a great vitality in many real applications due to its great impact on financial,supply chain,energy,internet of things,healthcare,sharing economy and so on.Throughout the research history of blockchain,development of the basic theory has become an increasingly important research direction,such as mathematical models of mining management and consensus mechanism(Markov processes,queuing theory and game models,etc.),performance analysis and optimization of blockchain system,etc.This dissertation uses queuing theory to design a Markov batch service queuing system with two different service stages for the blockchain system,so as to describe the mining process of miners and the building process of a new blockchain.This dissertation assumes that the arrival processes of the transaction are Poisson arrival and Markovian arrival process,respectively,the service times are exponential distribution and PH distribution,respectively,and provides the stability condition of the blockchain system,the expressions of the average transaction number in the queue,the average transaction number in the block and the average transaction confirmation time.What’s more,numerical examples are employed to verify the correctness of the theoretical results,and illustrate how the important performance measures are influenced by parameters of the blockchain system.It is hoped that the methods and results presented in this dissertation will open up a new way for the queuing analysis of more general blockchain system in practice,and stimulate a series of meaningful researches on the development prospects of blockchain technology.