Simulation model of Blockchain System in the Higher Education Shmatko Olexandr 1, Serhii Yevseiev 2 Vladyslav Khvostenko3 1 National Technical University "Kharkiv Polytechnic Institute" st. Kirpichova, 2, Kharkiv, 61000, Ukraine 2,3 Simon Kuznets Kharkiv National University of Economics, ave. Nauki, 9-A, Kharkiv, 61166 Ukraine Abstract This article presents a mathematical model of a distributed ledger for higher education. The main components of this network are considered, as well as their formal presentation. The model of peer-to-peer network is visualized, the research of the parameters of the centralized and decentralized data processing network is carried out. Based on the data obtained, simulation models were built and investigated. The results of the simulation simulations were analyzed and the most optimal parameters were selected. Keywords 1 distributed ledger, blockchain, mathematical modeling, simulation, probability theory, theory of random processes. 1. Introduction – distributed registry systems (blockchain); – quantum technologies; – new production technologies; At present in the world there is a revolutionary – industrial internet; transition from informatization of the main – components of robotics and sensors; spheres of human activity to their digitalization. – wireless communication technologies; If informatization involves, in essence, the – virtual and augmented reality technologies. modernization of certain human activities through Continuing the cycle of work on the digital the use of information and communication transformation of education [3,4], the paper technologies, the digital transformation (or conducts research on the use of blockchain digitization) in its turn involves their qualitative technology (blockchain) for the tokenization of transformation, departure from the usual types educational assets and promising areas of its and forms of activity to the new ones, based on implementation in education. digital models and technologies [1,2]. The development of the digital environment requires the support and development of both 2. Literature review existing conditions for the emergence of promising end-to-end digital platforms and In [5,6] possible scenarios for using technologies, as well as the creation of conditions blockchain technology in the field of education for the emergence of new platforms and are considered. Methods and technologies of technologies. tokenization of assets, related to the educational The main end-to-end digital technologies are: process, are investigated. It is concluded, that the – big data; blockchain technology is decentralized and – neurotechnology and artificial intelligence; transparent with a high degree of reliability, which III International Scientific And Practical Conference “Information Security And Information Technologies”, September 13–19, 2021, Odesa, Ukraine EMAIL: oleksandr.shmatko@khpi.edu.ua (A. 1); serhii.yevseiev@hneu.net (A. 2); vladyslav.khvostenko@gmail.com (A. 3) ORCID: 0000-0002-2426-900X (A. 1); 0000-0003-1647-6444 (A. 2); 0000-0000-0000-1234 (A. 3) ©️ 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) ensures the equality of all users of the chain's In favor of using the methods of simulation in services. The transparency of the technology this situation is the impossibility of experimenting guarantees the participants in the process against on a real object, because then we would have to abuse and forgery of documents. The study of the develop two full-fledged systems. Also models features of smart contracts made it possible to will allow to demonstrate work of two form the advantages of smart contracts in the field architectures in time and to calculate indicators of education for decision-making in favor of one of them. In [7], provides a critical analysis of The main parameter of the study will be the application of the blockchain technology average transaction processing time of the system. considering with its applicability opportunities To simulate the model you need to know the and restrictions in education; it also aims to following parameters: identify the consequences of its influence upon 1 Average processing time of one application; the development of education. 2 Number of customers sending applications; The article [8] provides an overview of the use 3 Number of servers processing these requests. of blockchain for academic transcripts. The aim is Many transactions related to smart contracts to find, among the proposed models, overlapping circulate on the Ethereum platform. To calculate aspects that solve common problems and can lead the average processing time of one application, to a universally accepted de facto standard. In you need to include several assumptions and addition, since academic institutions will serve as simplifications: oracles for specific blockchain applications, a 1) The generation time of a new block is robustness study is underway to see if the subject to the exponential law (the covariance proposed applications effectively solve the oracle coefficient for this law is a constant equal to one) problem. [7]. The paper [9] is a Systematic Bibliometric 2) The Ethereum blockchain platform does not Review of the Literature on Blockchain have the maximum possible block size and limit Applications Research in Higher Education. The on the number and size of transactions, but there review includes 37 articles that provide up-to-date is a limit on the maximum amount of gas (gas, knowledge on the current implications of using transaction fees) used in the block. This value can blockchain technology to improve higher be reduced or increased in the next block by 20 education processes. The LRSB findings show percent [6]. that blockchain is being used to create new When developing a mathematical model, it is interventions to improve the prevailing ways of assumed that the maximum number of sharing, delivering and protecting student transactions in the block will be 77. This number knowledge data and personal records. is taken from the average number of transactions The relevance of this work is due to the in the block of the real network Ethereum [5], increasing popularity of distributed registry obtained as of November 2017 systems, in connection with which it is necessary 3) The emergence of new transactions (in other to assess the quantitative parameters of this words, applications) is subject to the simplest law network and determine the most optimal of distribution, namely Poisson's. In the parameters. developed mathematical model it is considered The general network model is a peer-to-peer that the flow of incoming applications is the network in which each participant has m client simplest, because it corresponds to the properties applications, an application server S, an N node (a of stationary, ordinary and no aftereffects in the server for communicating with other network considered conditions. nodes) Each transaction is processed sequentially and has a strict order of writing to the decentralized 3. Simulation model blockchain; this ensures the ordinary flow of applications. A centralized system can also be considered in Simulation is a method of research in which the context of queuing theory, because the server the studied system is replaced by a model, with is a single-phase queuing system. sufficient accuracy describes the real system from AnyLogic software environment is used to which experiments are conducted in order to build a simulation model and conduct obtain information about this system. experiments. Simulation models of two systems were built using AnyLogic tools. Input parameters of the model: 1. Requests with a given intensity come from 1 Number of customers sending requests customers 2 Number of miners in the blockchain network 2. Requests are queued on the application 3 Number of requests per 10 minutes from one server, where they are processed and sent to the client database server 4 Number of requests from one client 3. After processing on the database server, the Figures 1 and 2 show simulation models of transactions again fall on the application server, decentralized and centralized networks. where the result is sent back to the client 4. The client receives a response from the application server regarding the processing of its payment transaction In the decentralized model, transaction processing has a different form: 1. Customers send transactions with a given intensity 2. Transactions fall into the buffer, where they are collected in blocks 3. When the block is filled with transactions, the miner begins the Mining block process 4. When the first of the miners completes the process, the block is closed and placed in the chain chain, and the transactions in this block are considered processed, so the responses are sent back to customers. 4. Results of modeling Figure 1: Simulation model of centralized Consider the Hinchin-Polachek formula for network. calculating the average waiting time of the application: 𝜆 × 𝑏 2 × (1 + 𝑣 2 ) 𝜔= 2 × (1 − 𝜆 × 𝑏) where  - the intensity of the flow of applications, b is the average processing time of one application, v is the coefficient of variation of the law of distribution of the average processing time of one application. If the denominator of the formula is greater than or equal to one, the average waiting time for the execution of one application goes to infinity. Indeed, if the intensity is too high, the application will never be processed at an infinite interval. The calculated values corresponding to the blockchain system considered in the work. The average processing time of one application. Figure 2: Simulation model of decentralized network. 𝑡ℎ𝑒 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑚𝑖𝑛𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑙𝑜𝑐𝑘 𝑏= 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑙𝑜𝑐𝑘 The algorithm of centralized work is as follows: The average mining time of the block and the average number of transactions in the block were obtained from the average indicators of the Conduct experiment 2 with another data set: actually working Ethereum network in November Number of clients: 20 2017 [9, 10]. Miner's number: 15 15 Number of transactions from the client per 𝑏= ≈ 0.195 𝑠𝑒𝑐 minute: 1 77 Number of requests: 20 The coefficient of variation for the exponential Let's calculate the values for modeling: law, which determines the processing time of one  = 0.2 / 600 = 0.016 sec. application, is equal to one. Thus, we obtain the  = (  0.091) / (1-  0.303) = 0.0014 sec. formula of the average waiting time for And for centralized respectively: processing one application, which depends on the  = (  0.038) / (1-  0.195) = 0.00060 sec. intensity of the input stream: The experiment will run for 10 minutes. In the decentralized system, this experiment ends at 𝜆 × 0.038 79.833 seconds of simulation, and the centralized 𝜔= 1 − 𝜆 × 0.195 system completed its work in 6673.53 seconds, processing only 124 applications. For the centralized model: Based on this, we can conclude that the processing of transactions in the decentralized b = average time of application processing on network model is almost 47 times faster than in the application server + average time of the centralized. At the same time, the centralized application processing by the database server = system has less fault tolerance than the 200ms + 103ms. = 0.303 sec. decentralized one, as experiment 2 showed. In addition, the centralized system is vulnerable to Then the formula for the average waiting time DDoS attacks, while in the decentralized model, for processing one application, which depends on one of the nodes would have to take at least 51% the intensity of the input stream for the centralized of the load, which is completely unrealistic. That network model: is why the confidentiality of data in a decentralized system is an order of magnitude 𝜆 × 0.091 higher than in a centralized one. 𝜔= 1 − 𝜆 × 0.303 In order to clearly demonstrate the importance of the data, it was decided to conduct 23 It is proposed to conduct several experiments, experiments on different data sets and to track with different indicators of the intensity of the how each of the systems will behave as the flow of requests and the number of customers. number of queries increases. A constant number Parameters of first experiment. of clients was selected for the experiments - 5 Number of clients: 5 pieces and the range of requests from 5 to 205. Miner's number: 10 This means that each client will send 1,3,5,7 ... 41 Number of transactions from the client per requests. The results of these experiments are minute: 0.2 presented in Figure 3. Number of requests: 10 First of all, you should calculate the intensity of the flow of applications per second:  = 0.2 / 60 = 0.003 sec The next step is to calculate the average waiting time for processing one application for a centralized system:  = (  0.091) / (1-  0.303) = 0.00027 sec. And for centralized respectively:  = ( 0.038) / (1- 0.195) = 0.00011 sec. The experiment will run for 10 minutes. The Figure 3: Graph of fault tolerance of systems centralized system processed requests in 3190,767 seconds, and the decentralized system in 66,880 seconds. A total of 50 requests were As can be seen from the figure, after 25 processed, as evidenced by the green colors of requests, the centralized system does not process both rectangles. the total number of requests coming into the system. This means that the load of 5 requests [1] Nakamoto, S., Bitcoin, A. 2008. Bitcoin: A from each of the 5 customers per minute for her peer-to-peer electronic cash system. was the maximum. The decentralized system Available at: https://bitcoin.org/bitcoin.pdf processed all incoming requests. [2] Tulchinsky, G. 2017. Digital Transformation The graph clearly shows that the curve of the of Education: Challenges for Higher School. centralized system breaks at the coordinate Russian Journal of Philosophical Sciences, 6, (183,132; 25). And the curve of the decentralized рр.121–136. system is growing [3] Antonova, D. A., Ospennikova, E. V., Spirin, E. V. 2019. TSifrovaya 5. Conclusions transformatsiya sistemy obrazovaniya. Proektirovanie resursov dlya sovremennoy tsifrovoy uchebnoy sredy kak odno iz ee The experiment showed that the performance osnovnykh napravleniy. Vestnik Permskogo of the network depends on the intensity of the gosudarstvennogo gumanitarno- appearance of applications, while for the correct pedagogicheskogo universiteta. Seriya: operation of the blockchain technology of the Informatsionnye kompyuternye tekhnologii presented type, it is possible to vary the values of v obrazovanii, 14. Available at: the intensity of nodes and the values https://cyberleninka.ru/article/n/tsifrovaya- buffer size. transformatsiya-sistemy-obrazovaniya- The authors did not consider internal proektirovanie-resursov-dlya-sovremennoy- connections between network elements when tsifrovoyuchebnoy-sredy-kak-odno-iz-ee building the models, which could affect the [4] Oleg Barabash, Andrii Musienko, Spartak results. 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