A STOCHASTIC MODEL AND SOCIAL OPTIMIZATION OF A BLOCKCHAIN SYSTEM BASED ON A GENERAL LIMITED BATCH SERVICE QUEUE

【Author】 Zhao, Wenjuan; Jin, Shunfu; Yue, Wuyi

【Source】JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION

【影响因子】1.411

【Abstract】Blockchain is well known as a database technology supporting digital currencies such as Bitcoin, Ether and Ripple. For the purpose of maximizing the overall revenue of the blockchain system, we propose a pricing policy to impose on transactions. Regarding the mining process as a vacation, and the block-verification process as a service, we establish a type of non-exhaustive queueing model with a limited batch service and a possible zero-transaction service. By selecting the beginning instant of a block-verification process as a Markov point and using the method of a generating function, we obtain the stationary probability distribution for the number of transactions in the system at the Markov points and analyze the elapsed time for the mining cycle. Based on the model analysis results, we derive the average latency of transactions and demonstrate how the average latency of transactions changes in relation to the arrival rate of transactions. With a reward-cost structure, we construct an individual benefit function and a social benefit function. By improving the Grasshopper Optimization Algorithm (GOA), we search for the Nash equilibrium and the socially optimal arrival rates of transactions. Numerical results show that the Nash equilibrium arrival rate of transactions is always higher than the socially optimal arrival rate of transactions for a given mining parameter and a specific block capacity. For this, we propose a pricing policy that forces the transactions to accept the socially optimal arrival rate and maximize the overall revenue of the blockchain system, including all transactions and miners.

【Keywords】Blockchain; limited batch service; Markov chain; Nash equilibrium; social optimization; intelligent optimization algorithm; pricing policy

【发表时间】2021 JUL

【收录时间】2022-01-02

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