Analysis of blockchain system based on $$\hbox {M}/(\hbox {M}_1,\hbox {M}_2)/1$$ M / ( M 1 , M 2 ) / 1 vacation qu
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Analysis of blockchain system based on M∕(M1 , M2 )∕1 vacation queueing model Jiaqi Fan1 · Zhanyou Ma1 · Yang Zhang1 · Changzhen Zhang1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract With the rapid development of technology, the issues about blockchain are getting more and more attention from scholars. In order to study the operation of the blockchain system, this paper simulated the transaction confirmation process of a blockchain system with two miners. Combining with practice, factors such as adverse transactions, impatience phenomena of transactions, fault repairable conditions of the mining process and a spare miner are considered. An M/(M1,M2)/1 vacation queueing model with negative customers, impatient customers, optional services, repairable faults and a spare server is established. The stationary distribution of the system is obtained by using the matrix-geometric solution method, and expressions of the average confirmation time of transactions and other performance indexes are given. The influence of each parameter on the performance indexes of blockchain system is analyzed by using MATLAB software. Revenue function and equilibrium sleep rate of miners are discussed for optimizing the blockchain system. Keywords Blockchain · Optional service · Repairable fault · Spare miner · Matrixgeometric solution method
* Zhanyou Ma [email protected] Jiaqi Fan [email protected] Yang Zhang [email protected] Changzhen Zhang [email protected] 1
School of Science, Yanshan University, Qinhuangdao 066004, China
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J. Fan et al.
1 Introduction Blockchain is a decentralized, public, safe, point-to-point transporting and distributed ledger [1, 2]. Nakamoto [3] proposed decentralized and distributed accounting firstly, and he introduced the fundamental operation mechanism of blockchain, which laid a theoretical foundation for the study of blockchain. Since the concept of blockchain was proposed, blockchain technology had developed rapidly and played a greater application value in finance, Internet of Things, public services, legal affairs, medical hygiene and other areas [4–8]. Om et al. [9] analyzed infrastructure condition of the public key in blockchain system and discussed the key management method of blockchain wallet, which improved the confidentiality of blockchain network accounting. Chen et al. [10] proposed a distributed blockchain model to protect the sensitive information of users, and a protocol for maintaining the blockchain ledger was proposed to maintain the good operation of the client system. Zhao et al. [11] proposed new privacy protection software which updated protocol based on blockchain, and the delivery certificate of Internet of Things was analyzed. Alberto et al. [12] provided a control method of anonymous access for wireless network by applying blockchain technology, and wireless network congestion was avoided by using work-proof mechanism. The blockchain system mainly includes six parts: data, contract, in
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