DATA PROCESSING AND ANALYSIS
CONTROL AND DECISION-MAKING
MATHEMATICAL MODELING
V. A. Evsin, S. N. Shirobokova, S. P. Vorobyev A Model of a Distributed Registry System with the Approximation of Applications by the Erlang Flow
INTELLIGENCE SYSTEMS AND TECHNOLOGIES
V. A. Evsin, S. N. Shirobokova, S. P. Vorobyev A Model of a Distributed Registry System with the Approximation of Applications by the Erlang Flow
Abstract. 

In this paper, we propose a method for mathematically describing a distributed registry as a queuing system. A conceptual model is presented that defines the main structural elements of the topological structure of a distributed registry, such as network nodes, registry nodes, and distributed registry services for conducting transaction verification operations. The distribution functions of a random variable characteristic of these processes are determined and presented. The application distribution is approximated by Erlang flows to obtain the most accurate value. The conditions for constructing an infinitesimal matrix are determined, taking into account the features of information processes in a distributed registry. Formed the conditions for the normalization. The main integral characteristic indicators required for the analysis of the distributed registry as a queuing system are presented. In order to determine the main integral characteristic indicators of the distributed registry system, a simulation model was developed on the AnyLogic platform.

Keywords: 

mathematical modeling, queuing systems, distributed registry, approximation, Erlang phase method, simulation model.

PP. 58-69.

DOI 10.14357/20718632210107
 
References

1. D. Tapscott. 2017. Blockchain Technology: what drives the financial revolution today, Moscow: Eksmo, 448p.
2. Deep Shift – Technology Tipping Points and Societal Impact. 2015. World Economic Forum Survey Report. Available at: http://www3.weforum.org/docs/ WEF_GAC15_Technological_Tipping_Points_report_2015.pdf#page=2 (accessed January 25, 2021). 
3. Swan M. 2015. Blockchain. Blueprint for a New Economy. - Gravenstein Highway North, Sebastopol: O’Reilly, 149 p.
4. Evsin V.A., Shirobokova S.N., Prodan E.A. 2018. Ispol'zovanie tekhnologii raspredelennyh reestrov pri proektirovanii informacionnoj sistemy "Arenda nedvizhimosti" s primeneniem iskusstvennyh nejronnyh setej [Use of distributed registry technology in the design of the information system "real estate rental" using artificial neural networks] Inzhenernyj vestnik Dona [Engineering Bulletin of the Don], 1 Available at: http://ivdon.ru/ru/magazine/archive/n1y2018/4655 (accesed January 25, 2021).
5. Naraevskij O.A., Evsin V.A. 2018. Model' avtomatizacii biznes-processov dokumentooborota s ispol'zovaniem tekhnologii raspredelyonnyh reestrov. Modelirovanie. Fundamental'nye issledovaniya, teoriya, metody i sredstva: materialy 18-oj Nacional'noj molodezhnoj nauch.-prakt. konf. [Model of automation of business processes of workflow using technology of distributed registries,” Modeling. Fundamental research, theory, methods and tools: the 18th international conference. youth scientific-practical Conf.] Novocherkassk. 165-170.
6. Savel'ev A.I. 2016. Dogovornoe pravo 2.0: "Umnye" kontrakty kak nachalo konca klassicheskogo dogovornogo prava [Contract Law 2.0: «Smart» contracts as the beginning of the end of classical contract law]. "Vestnik grazhdanskogo prava" [Bulletin of Civil Law]. 3:32-60.
7. D. Drescher. 2017. The basics of the blockchain. Moscow: DMK Press, 312 p.
8. Andryushchin S.A. 2018. Tekhnologiya raspredelennyh reestrov v finansovoj sfere Rossii [Technology of distributed registers in the financial sphere of Russia]. Bankovskoe delo [Banking]. 2:4-15.
9. Naraevskij O.A., Evsin V.A. 2018. Formalizovannyj analiz funkcional'noj polnoty platform raspredelyonnyh reestrov. Fundamental'nye osnovy, teoriya, metody i sredstva izmerenij, kontrolya i diagnostiki: materialy 19-oj Nacional'noj molodezhnoj nauch.-prakt. konf. [Formalized analysis of the functional completeness of the platforms of distributed ledger. Fundamentals, theory, methods and tools of measurement, control and diagnostics: the 19th international conference. youth scientific and practical Conf.] Novocherkassk. 396-404.
10. Evsin V.A., Prodan E.A., Evsina V.A. 2018. Aspekty proektirovaniya informacionnoj sistemy po arende nedvizhimosti s ispol'zovaniem tekhnologii raspredelennyh reestrov. Fundamental'nye osnovy, teoriya, metody i sredstva izmerenij, kontrolya i diagnostiki: materialy 19-oj Nacional'noj molodezhnoj nauch.-prakt. konf. [Aspects of design of information systems real estate rental using the technology of distributed registries. Fundamentals, theory, methods and means of measurement, control and diagnostics: the 19th international conference. youth scientific-practical Conf.], Novocherkassk. 318-323.
11. Kosorukov O.A. 2003. Issledovanie operacij. [Operation research] – Moskow: Ekzamen. 448p.
12. Halin V.G. 2017. Teoriya prinyatiya reshenij [Theory of decision-making]. - Moskow: Yurajt. 432 s.
13. Chernomorov G.A. 2005. Teoriya prinyatiya reshenij: Uchebnoe posobie / YUzh.-Ros. gos. tekhn. un-t. - 3-e izd. pererab. i dop. [Theory of decision-making, South-Russian state technical University, 3 rd ed]. Novocherkassk: «Izv.Vuzov. Elektromekhanika». 448p.
14. R. Chakka and G. P. Garrison. 2001. “Markovsky modulated multi-server queue with negative applications-IgE mm NCL/gr/gr/LG-queue,” Informatika ASTA. 785-799.
15. Abramov P.B., Len'shin A.V. 2012. Ocenka parametrov sistem massovogo obsluzhivaniya pri approksimacii discipliny obsluzhivaniya potokami Erlanga [Estimation of mass service systems parameters at approximation of service discipline by Erlang streams]. Vestnik Voronezhskogo instituta MVD Rossii. [Bulletin of the Voronezh Institute of the ministry of internal affairs of Russia].2:13-18.
16. Gross D., Harris C. M. 2008. Fundamentals of Queueing Theory. – Fourth edition N.-Y.: Wiley. 528p.
17. Panomarev D. Yu. The theory of teletraf. Krasnoyarsk: SibSU named after M. F. Reshetnikov, 2017. – 160 p.
18. Evsin V.A., Litvyak R.K. 2016. Matematicheskaya model' informacionnoj sistemy vysokoj gotovnosti na baze klasternoj arhitektury. Modelirovanie. Teoriya, metody i sredstva: materialy 16-oj Mezhdunar. nauch.-prakt. konf. [“Mathematical model of information high availability system based on cluster architecture,” Modeling. Theory, methods and tools: the 16th international conference. scientific-practical Conf.], Novocherkassk. 176-179.
19. A. Hemdi Taha. 2005. Introduction to operations research, 7 rd ed. Moscow: Williams. 912p.
 

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