Performance Analysis of Mining Pool with Power-saving, Fault and Mining Competition

Blockchain has emerged as a disruptive technology with potential applications in various industries. Although the proof-of-work (PoW) blockchain systems have worked so successfully, the mining pools in PoW-based blockchain systems have certain drawbacks: high power expenditure, mining competition and fault. It is essential to implement the power saving and evaluate the performance of the mining pool with these characteristics in PoW-based blockchain systems. In this paper, we consider a queueing system with sleep-wakeup, working breakdown and impatient strategies, that are suitable to {express well} power saving, fault and mining competition in the mining process. For our proposed system, by using a z-Transform approach, the closed-form expressions about various performance measures like the mean number of blocks and the mean confirmation time of block are obtained. Furthermore, we construct the power consumption function and the power-saving rate function to analyze the improvement of power-saving. In order to mitigate the negative effect which stems from the mining competition, we formulate the Nash bargaining game and obtain the Nash solution, which implies the optimal control of the computation power.