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Vol:.(1234567890)
The Journal of Supercomputing (2024) 80:20518–20545
https://doi.org/10.1007/s11227-024-06236-0
1 3
Performance analysis ofmining pool withpower‑saving,
fault andmining competition
KaimingYang1,2· JianCao1,3
Accepted: 14 April 2024 / Published online: 3 June 2024
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature
2024
Abstract
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 min-
ing pool with these characteristics in PoW-based blockchain systems. In this paper,
we consider a queueing system with sleep–wakeup, working breakdown and impa-
tient strategies that are suitable to express well power-saving, fault and mining com-
petition in the mining process. By using a z-transform approach, the closed-form
expressions about various performance measures such as the mean number of blocks
and the mean confirmation time of block are obtained. Furthermore, we analyze the
power consumption by constructing the linear function based on the performance
measures and analyze the improvement of power-saving by comparing the power
consumption of a queueing model without various strategies. In order to mitigate
the negative effect stemming from the mining competition, we formulate the Nash
bargaining game to induce the cooperation and obtain the Nash solution and the cor-
responding mining pool’s optimal computation power.
Keywords Blockchain· Performance· Queueing· Power-saving· Mining
competition· Fault
* Jian Cao
jiancao@bupt.edu.cn
1 School ofScience, Beijing Univeristy ofPosts andTelecommunications, Beijing100876, China
2 Key Laboratory ofMathematics andInformation Networks, Beijing University ofPosts
andTelecommunications, Ministry ofEducation, Beijing, China
3 School ofApplied Mathematics, Nanjing University ofFinance andEconomics, Nanjing, China
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