Nash Equilibrium and Social Optimization of Transactions in Blockchain System Based on Discrete-Time Queue

Blockchain technology has been used in many fields such as data management, cloud computing and Internet of Things with the features of decentralization, transparency and immutability. In order to study the performance of a blockchain system with a light-load traffic, we establish a discrete-time non-exhaustive vacation queue with batch service and gated service. In this model, we regard transaction initiation, mining processing and block verification as arrival, vacation and service period, respectively. By using an embedded Markov chain method and a regeneration cycle approach, we derive the average response time of transactions. Experiment results with analysis and simulation show that the average response time of transactions is impacted by the arrival rate of transactions. Finally, we study the Nash equilibrium behavior and the socially optimal behavior of transactions, and present a pricing policy for transactions to maximize the social profit.