Abstract
Blockchain is well known as a database technology supporting digital currencies, such as Bitcoin, Ether, and Ripple. 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 regeneration 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 regeneration points. Then, we derive the average number of transactions and the average confirmation time of transactions in the blockchain system. Finally, we provide numerical results with analysis and simulation to demonstrate how the average number of transactions and the average confirmation time of transactions in the blockchain system change with the mining parameter.
This work was supported in part by National Science Foundations (Nos. 61872311, 61472342) and Natural Science Foundation of Hebei Province (F2017203141), China, and was supported in part by MEXT and JSPS KAKENHI Grant (No. JP17H01825), Japan.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Wang, L., Shen, X., Li, J., Shao, J., Yang, Y.: Cryptographic primitives in blockchains. J. Netw. Comput. Appl. 127, 43–58 (2019)
Qian, W., Shao, Q., Zhu, Y., Jin, C., Zhou, A.: Research problems and methods in blockchain and trusted data management. J. Softw. 29(1), 150–159 (2018). (in Chinese)
Nakamoto, S.: Institute. https://nakamotoinstitute.org/bitcoin/. Accessed 21 Feb 2019
Christidis, K., Devetsikiotis, M.: Blockchains and smart contracts for the internet of things. IEEE Access 4, 2292–2303 (2016)
Huang, X., Xu, C., Wang, P., Liu, H.: LNSC: a security model for electric vehicle and charging pile management based on blockchain ecosystem. IEEE Access 6, 13565–13574 (2018)
Turkanović, M., Holbl, M., Kosic, K., Hericko, M., Kamisalic, A.: EduCTX: a blockchain-based higher education credit platform. IEEE Access 6, 5112–5127 (2018)
Kasahara, S., Kawahara, J.: Priority mechanism of bitcoin and its effect on transaction-confirmation process. J. Ind. Manag. Optim. 15(1), 365–386 (2019)
Kawase, Y., Kasahara, S.: Transaction-confirmation time for bitcoin: a queueing analytical approach to blockchain mechanism. In: Yue, W., Li, Q.-L., Jin, S., Ma, Z. (eds.) QTNA 2017. LNCS, vol. 10591, pp. 75–88. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68520-5_5
Li, Q., Ma, J., Chang, Y.: Cornell University. arXiv:abs/1808.01795. Accessed 21 Feb 2019
Rupp, R.: The symmetric versions of Rouché’s theorem via-calculus. J. Complex Anal. 2014, 9 (2014). https://doi.org/10.1155/2014/260953. Article ID 260953
Aguiar, M., Lauve, A.: Lagrange’s theorem for Hopf monoids in species. Can. J. Math. 65(2), 241–265 (2013)
Karr, A.: Stochastic processes (Sheldon M. Ross). SIAM Rev. 26(3), 448–449 (1984)
Wolff, R., Yao, Y.: Little’s law when the average waiting time is infinite. Queueing Syst. 76(3), 267–281 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Zhao, W., Jin, S., Yue, W. (2019). Analysis of the Average Confirmation Time of Transactions in a Blockchain System. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds) Queueing Theory and Network Applications. QTNA 2019. Lecture Notes in Computer Science(), vol 11688. Springer, Cham. https://doi.org/10.1007/978-3-030-27181-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-030-27181-7_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-27180-0
Online ISBN: 978-3-030-27181-7
eBook Packages: Computer ScienceComputer Science (R0)