Distribution of Fee between Blockchain Nodes and the Rule of their Motivation

Abstract

The article сconsiders the proposed approach for assessing the possibility of equitable receipt of fees by blockchain nodes for closing blocks. The theory of random processes is applied to describe transaction flows and block closings. The distribution of fees received by the nodes for closing a block is analyzed. The fees are the values of a normally distributed random variable and they differ slightly in value. The concept of a master node and an empty block is specified. An estimate of the probability of fee receiving by blockchain nodes for closing a block which are close to the average value is proposed based on the law of large numbers. The variant of the operation of the blockchain network, in which some of the nodes are disconnected from the network, is considered. In this case, the distribution of fees between the nodes is changed, but the equality of the nodes can still be preserved if the proposed additional conditions are met. A rule is formulated for motivating nodes to maintain their constant connection to the network by transferring fees intended for nodes that did not respond to the request to become a master node and summing them with the fee for the first node that responded to the request. Special penalty functions regulating the amount of the fee are applied, which makes it possible to maintain the equality of nodes in this case as well. The more general case allowing temporary shutdown of a part of the nodes of the blockchain network is considered. The analysis of the situation when the nodes are forced to shut down for technical reasons is performed

Please cite this article in English as:

Bardin A.P., Novitskiy A.V., Shumilov Yu.Yu. Distribution of fee between blockchain nodes and the rule of their motivation. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2022, no. 2 (139), pp. 4--17 (in Russ.). DOI: https://doi.org/10.18698/0236-3933-2022-2-4-17

References

[1] Satoshi N. Bitcoin: a peer-to-peer electronic cash system. bitcoin.org: website. Available at: https://bitcoin.org/en/bitcoin-paper (accessed: 20.01.2018).

[2] Chepurnoy A., Larangeira М., Ojiganov A. Rollerchain, a blockchain with safely pruneable full blocks. arXiv preprint arXiv:1603.07926, 2016. DOI: https://doi.org/10.48550/arXiv.1603.07926

[3] Transactions speeds: how do cryptocurrencies stack up to Visa or PayPal? howmuch.net: website. Available at: https://howmuch.net/articles/crypto-transaction-speeds-compared (accessed: 12.08.2019).

[4] Proof of stake versus proof of work. bitfury.com: website. Available at: http://bitfury.com/content/5-white-apersresearch/pos-vs-pow-1.0.2.pdf (accessed: 02.10.2019).

[5] Budish E. The economic limits of bitcoin and the blockchain. NBER Working Paper Series, 2018, no. 24717. Available at: http://www.nber.org/papers/w24717 (accessed: 04.04.2022).

[6] Senatov V.V. Tsentral’naya predel’naya teorema. Tochnost’ approksimatsii i asimptoticheskie razlozheniya [Central-limit theorem. Approximation accuracy and asymptotic expansions]. Moscow, Librokom Publ., 2009.

[7] De Groot M. Optimal statistical decisions. John Wiley & Sons, 2004.

[8] Lehmann E.L., Romano J.P. Testing statistical hypotheses. Springer Science + + Business Media, 2005.

[9] Ethereum. bits.media: website. Available at: https://bits.media/ethereum (accessed: 26.05.2020).

[10] Kudryavtsev K.Ya. Proof of normality of distribution of a subset of random variables based on the transformation of block matrices. Vestnik NIYaU MIFI, 2021, vol. 10, no. 1, pp. 70--76 (in Russ.). DOI: https://doi.org/10.1134/S2304487X21010107

[11] Shumilov Yu.Yu., Shumilov B.F. Analiticheskoe opisanie mnogomernykh mnogoznachnykh funktsiy v sistemakh upravleniya [Analytic description of multidimensional multivalue functions in control systems]. V kn.: Metody proektirovaniya slozhnykh system [In: Design methods for complex systems]. Moscow, Energoatomizdat Publ., 1985, pp. 42--48 (in Russ.).

[12] Deon A.F., Menyaev Yu.A. Complete factorial simulation of integer random number uniform sequences. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2017, no. 5 (116), pp. 132--149 (in Russ.). DOI: https://doi.org/10.18698/0236-3933-2017-5-132-149

[13] Applebaum B. Pseudorandom generators with long stretch and low locality from random local one-way functions. Proc. 44th Ann. ACM STOC, 2012, pp. 805--816. DOI: https://doi.org/10.1145/2213977.2214050

[14] Lewis T.G., Payne W.H. Generalized feedback shift register pseudorandom number algorithm. J. ACM, 1973, vol. 20, no. 3, pp. 456--486. DOI: https://doi.org/10.1145/321765.321777

[15] Sunklodas J. On normal approximations to strongly mixing random fields. Theory Probab. Appl., 2010, vol. 52, no. 1, pp. 125--132. DOI: https://doi.org/10.1137/S0040585X97982815