Моделирование однородной системы передачи данных облегчённого резервирования

Аннотация

В данной работе мы рассматриваем математическую модель восстанавливаемой резервированной системы передачи данных как модель замкнутой однородной системы облегчённого резервирования с одним ремонтным устройством, с экспоненциальной функцией распределения времени безотказной работы и произвольной функцией распределения времени ремонта её элементов. Используя метод дополнительных переменных и метод вариации постоянной с помощью Марковского процесса, были получены ясные аналитические выражения для стационарных вероятностей состояний системы и стационарной вероятности безотказной работы системы. Полученные формулы показали наличие явной зависимости этих характеристик от типов функций распределения времени восстановления элементов системы. Однако численные исследования и анализ построенных графиков показали, что эта зависимость становится исчезающе малой при «быстром» восстановлении элементов системы.

Сведения об авторе

Hector Gibson Kinmanhon Houankpo, Российский университет дружбы народов

аспирант кафедры прикладной информатики и теории вероятностей, факультет физико-математических и естественных наук

Литература

1. Ahmed W., Hasan O., Pervez U., Qadir J. Reliability modeling and analysis of communication networks. Journal of Network and Computer Applications. 2017; 78(C):191-215. (In Eng.) DOI: https://doi.org/10.1016/j.jnca.2016.11.008
2. Ometov A., Kozyrev D.V., Rykov V.V., Andreev S., Gaidamaka Y.V., Koucheryavy Y. Reliability-Centric Analysis of Offloaded Computation in Cooperative Wearable Applications. Wireless Communications and Mobile Computing. 2017; 2017:9625687. 15 p. (In Eng.) DOI: https://doi.org/10.1155/2017/9625687
3. Rykov V.V., Kozyrev D.V., Zaripova E. Modeling and Simulation of Reliability Function of a Homogeneous Hot Double Redundant Repairable System. In: Ed. by Z. Z. Paprika, P. Hora´k, K. Va´radi, P. T. Zwierczyk, ´A. Vidovics-Dancs, J. P. R´adics. Proceedings of the 31st European Conference on Modelling and Simulation ECMS2017 (May 23-26, 2017, Budapest, Hungary). Germany, Digitaldruck Pirrot GmbH.; 2017. p. 701-705. (In Eng.) DOI: https://doi.org/10.7148/2017-0701
4. Houankpo H.G.K., Kozyrev D.V. Sensitivity Analysis of Steady State Reliability Characteristics of a Repairable Cold Standby Data Transmission System to the Shapes of Lifetime and Repair Time Distributions of its Elements. CEUR Workshop Proceedings. 2017; 1995:107-113. Available at: http://ceur-ws.org/Vol-1995/paper-15-970.pdf (accessed 10.08.2021). (In Eng.)
5. Efrosinin D., Rykov V.V. Sensitivity Analysis of Reliability Characteristics to the Shape of the Life and Repair Time Distributions. In: Ed. by A. Dudin, A. Nazarov, R. Yakupov, A. Gortsev. Information Technologies and Mathematical Modelling. ITMM 2014. Communications in Computer and Information Science. 2014; 487:101-112. Springer, Cham. (In Eng.) DOI: https://doi.org/10.1007/978-3-319-13671-4_13
6. Rykov V., Efrosinin D., Vishnevsiy V. On Sensitivity of Reliability Models to the Shape of Life and Repair Time Distributions. 2014 Ninth International Conference on Availability, Reliability and Security. IEEE Press, Fribourg, Switzerland; 2014. p. 430-437. (In Eng.) DOI: https://doi.org/10.1109/ARES.2014.65
7. Rykov V.V., Kozyrev D.V. Analysis of Renewable Reliability Systems by Markovization Method. In: Ed. by V. Rykov, N. Singpurwalla, A. Zubkov. Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science. 2017; 10684:210-220. Springer, Cham. (In Eng.) DOI: https://doi.org/10.1007/978-3-319-71504-9_19
8. Rykov V., Kozyrev D. On Sensitivity of Steady-State Probabilities of a Cold Redundant System to the Shapes of Life and Repair Time Distributions of Its Elements. In: Ed. by J. Pilz, D. Rasch, V. Melas, K. Moder. Statistics and Simulation. IWS 2015. Springer Proceedings in Mathematics & Statistics. 2018; 231:391-402. Springer, Cham. (In Eng.) DOI: https://doi.org/10.1007/978-3-319-76035-3_28
9. Parshutina S.A., Bogatyrev V.A. Models to support design of highly reliable distributed computer systems with redundant processes of data transmission and handling. 2017 International Conference "Quality Management, Transport and Information Security, Information Technologies" (IT&QM&IS). IEEE Press, St. Petersburg, Russia; 2017. p. 96-99. (In Eng.) DOI: https://doi.org/10.1109/ITMQIS.2017.8085772
10. Teh J., Lai C.-M., Cheng Y.-H. Impact of the Real-Time Thermal Loading on the Bulk Electric System Reliability. IEEE Transactions on Reliability. 2017; 66(4):1110-1119. (In Eng.) DOI: https://doi.org/10.1109/TR.2017.2740158
11. Lisnianski A., Laredo D., BenHaim H. Multi-state Markov Model for Reliability Analysis of a Combined Cycle Gas Turbine Power Plant. 2016 Second International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management (SMRLO). IEEE Press, Beer Sheva, Israel; 2016. p. 131-135. (In Eng.) DOI: https://doi.org/10.1109/SMRLO.2016.31
12. Perkin S., et al. Framework for Threat Based Failure Rates in Transmission System Operation. 2016 Second International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management (SMRLO). IEEE Press, Beer Sheva, Israel; 2016. p. 150-158. (In Eng.) DOI: https://doi.org/10.1109/SMRLO.2016.34
13. Singh C. Assigning transition rates to unit models with incomplete data for power system reliability analysis. 2015 Annual IEEE India Conference (INDICON). New Delhi, India; 2015. p. 1-5. (In Eng.) DOI: https://doi.org/10.1109/INDICON.2015.7443163
14. Tourgoutian B., Yanushkevich A., Marshall R. Reliability and availability model of offshore and onshore VSC-HVDC transmission systems. 11th IET International Conference on AC and DC Power Transmission. IEEE Press, Birmingham; 2015. p. 1-8. (In Eng.) DOI: https://doi.org/10.1049/cp.2015.0101
15. Li X., Ao N., Wu L. The refining reliability modeling method for the satellite system. 2014 10th International Conference on Reliability, Maintainability and Safety (ICRMS). IEEE Press, Guangzhou, China; 2014. p. 484-488. (In Eng.) DOI: https://doi.org/10.1109/ICRMS.2014.7107244
16. Xu M., Zeng S., Guo J. Reliability modeling of a jet pipe electrohydraulic servo valve. 2014 Reliability and Maintainability Symposium. IEEE Press, Colorado Springs, CO, USA; 2014. p. 1-6. (In Eng.) DOI: https://doi.org/10.1109/RAMS.2014.6798480
17. Cao J., Wang Q., Shen Y. Research on modeling method of complex system mission reliability simulation. 2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering. Chengdu, China; 2012. p. 307-311. (In Eng.) DOI: https://doi.org/10.1109/ICQR2MSE.2012.6246242
18. Gu Z., Zhu C., Shang L., Dick R.P. Application-Specific MPSoC Reliability Optimization. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 2008; 16(5):603-608. (In Eng.) DOI: https://doi.org/10.1109/TVLSI.2008.917574
19. Huang W., Loman J., Song T. Reliability modeling of A warm standby redundancy configuration with active → standby → active units. 2014 Reliability and Maintainability Symposium. IEEE Press, Colorado Springs, CO, USA; 2014. p. 1-5. (In Eng.) DOI: https://doi.org/10.1109/RAMS.2014.6798473
20. Kendall D.G. Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain. The Annals of Mathematical Statistics. 1953; 24(3):338-354. (In Eng.) DOI: https://doi.org/10.1214/aoms/1177728975
21. Sevast’yanov B.A. An Ergodic Theorem for Markov Processes and Its Application to Telephone Systems with Refusals. Teoriya Veroyatnostei i ee Primeneniya = Theory of Probability & Its Applications. 1957; 2(1):104-112. (In Eng.) DOI: https://doi.org/10.1137/1102005
22. Houankpo H.G.K., Kozyrev D.V., Nibasumba E., Mouale M.N.B., Sergeeva I.A. A Simulation Approach to Reliability Assessment of a Redundant System with Arbitrary Input Distributions. In: Ed. by V. M. Vishnevskiy, K. E. Samouylov, D. V. Kozyrev. Distributed Computer and Communication Networks. DCCN 2020. Lecture Notes in Computer Science. 2020; 12563:380-392. Springer, Cham. (In Eng.) DOI: https://doi.org/10.1007/978-3-030-66471-8_29
23. Houankpo H.G.K., Kozyrev D.V., Nibasumba E., Mouale M.N.B. Reliability Analysis of a Homogeneous Hot Standby Data Transmission System. In: Ed. by P. Baraldi, F. Di Maio, E. Zio. Proceedings of the 30th European Safety and Reliability Conference and 15th Probabilistic Safety Assessment and Management Conference (ESREL2020 PSAM15). Research Publishing, Singapore; 2020. p. 1-8. (In Eng.) DOI: https://doi.org/10.3850/978-981-14-8593-0 5755-cd
24. Houankpo H.G.K., Kozyrev D.V., Nibasumba E., Mouale M.N.B. Mathematical Model for Reliability Analysis of a Heterogeneous Redundant Data Transmission System. 2020 12th International Congress on Ultra-Modern Telecommunications and Control Systems and Workshops (ICUMT). Brno, Czech Republic; 2020. p. 189-194. (In Eng.) DOI: https://doi.org/10.1109/ICUMT51630.2020.9222431
25. Houankpo H.G.K., Kozyrev D. Reliability Model of a Homogeneous Warm-Standby Data Transmission System with General Repair Time Distribution. In: Ed. by V. Vishnevskiy, K. Samouylov, D. Kozyrev. Distributed Computer and Communication Networks. DCCN 2019. Lecture Notes in Computer Science. 2019; 11965:443-454. Springer, Cham. (In Eng.) DOI: https://doi.org/10.1007/978-3-030-36614-8_34
Опубликована
2021-09-30
Как цитировать
HOUANKPO, Hector Gibson Kinmanhon. Моделирование однородной системы передачи данных облегчённого резервирования. Современные информационные технологии и ИТ-образование, [S.l.], v. 17, n. 3, p. 531-540, sep. 2021. ISSN 2411-1473. Доступно на: <http://sitito.cs.msu.ru/index.php/SITITO/article/view/771>. Дата доступа: 09 dec. 2022 doi: https://doi.org/10.25559/SITITO.17.202103.531-540.
Раздел
Теоретические вопросы информатики, прикладной математики, компьютерных наук