Mathematical Model of the Reliability Analysis of a Heterogeneous Duplicate Data Transmission System
In this work, we consider the mathematical model of the repaired data transmission system as a model of a closed heterogeneous cold standby system with one repair device with an arbitrary number of data sources with an exponential distribution function of uptime and an arbitrary distribution functio...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | Russian |
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The Fund for Promotion of Internet media, IT education, human development «League Internet Media»
2020-09-01
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| Series: | Современные информационные технологии и IT-образование |
| Subjects: | |
| Online Access: | http://sitito.cs.msu.ru/index.php/SITITO/article/view/644 |
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| author | Hector Gibson Kinmanhon Houankpo Dmitry Kozyrev Emmanuel Nibasumba Moutouama N’dah Bienvenu Mouale |
| author_facet | Hector Gibson Kinmanhon Houankpo Dmitry Kozyrev Emmanuel Nibasumba Moutouama N’dah Bienvenu Mouale |
| author_sort | Hector Gibson Kinmanhon Houankpo |
| collection | DOAJ |
| description | In this work, we consider the mathematical model of the repaired data transmission system as a model of a closed heterogeneous cold standby system with one repair device with an arbitrary number of data sources with an exponential distribution function of uptime and an arbitrary distribution function of the repair time of its elements. We study the reliability of the system, defined as the steady-state probability of failure-free system operation. The proposed analytical methodology made it possible to evaluate the reliability of the entire system in case of failure of its elements. Explicit analytic and asymptotic expressions are obtained for the steady-state probabilities of system and the steady-state probability of failure-free system operation. The problem of analyzing the sensitivity of the reliability characteristics of the system under consideration to the types of repair time distributions was also studied. The obtained formulas showed the presence of a clear dependence of these characteristics on the types of distribution functions of the recovery time of system elements. However, numerical studies and analysis of the constructed graphs showed that this dependence becomes vanishingly small with a “quick” restoration of system elements. |
| first_indexed | 2024-12-17T13:05:22Z |
| format | Article |
| id | doaj.art-d0fe5743ee6e4d00b90714dc840ce519 |
| institution | Directory Open Access Journal |
| issn | 2411-1473 |
| language | Russian |
| last_indexed | 2024-12-17T13:05:22Z |
| publishDate | 2020-09-01 |
| publisher | The Fund for Promotion of Internet media, IT education, human development «League Internet Media» |
| record_format | Article |
| series | Современные информационные технологии и IT-образование |
| spelling | doaj.art-d0fe5743ee6e4d00b90714dc840ce5192022-12-21T21:47:16ZrusThe Fund for Promotion of Internet media, IT education, human development «League Internet Media»Современные информационные технологии и IT-образование2411-14732020-09-0116228529410.25559/SITITO.16.202002.285-294Mathematical Model of the Reliability Analysis of a Heterogeneous Duplicate Data Transmission SystemHector Gibson Kinmanhon Houankpo0https://orcid.org/0000-0003-1399-3817Dmitry Kozyrev1https://orcid.org/0000-0003-0538-8430Emmanuel Nibasumba2https://orcid.org/0000-0001-5334-6388Moutouama N’dah Bienvenu Mouale3https://orcid.org/0000-0002-7230-5714Peoples' Friendship University of RussiaPeoples' Friendship University of Russia, V. A. Trapeznikov Institute of Control Sciences of Russian Academy of SciencesPeoples' Friendship University of RussiaPeoples' Friendship University of RussiaIn this work, we consider the mathematical model of the repaired data transmission system as a model of a closed heterogeneous cold standby system with one repair device with an arbitrary number of data sources with an exponential distribution function of uptime and an arbitrary distribution function of the repair time of its elements. We study the reliability of the system, defined as the steady-state probability of failure-free system operation. The proposed analytical methodology made it possible to evaluate the reliability of the entire system in case of failure of its elements. Explicit analytic and asymptotic expressions are obtained for the steady-state probabilities of system and the steady-state probability of failure-free system operation. The problem of analyzing the sensitivity of the reliability characteristics of the system under consideration to the types of repair time distributions was also studied. The obtained formulas showed the presence of a clear dependence of these characteristics on the types of distribution functions of the recovery time of system elements. However, numerical studies and analysis of the constructed graphs showed that this dependence becomes vanishingly small with a “quick” restoration of system elements.http://sitito.cs.msu.ru/index.php/SITITO/article/view/644reliability of redundant systemssteady-state probabilitiesstochastic modelingsensitivityasymptotic analysis |
| spellingShingle | Hector Gibson Kinmanhon Houankpo Dmitry Kozyrev Emmanuel Nibasumba Moutouama N’dah Bienvenu Mouale Mathematical Model of the Reliability Analysis of a Heterogeneous Duplicate Data Transmission System Современные информационные технологии и IT-образование reliability of redundant systems steady-state probabilities stochastic modeling sensitivity asymptotic analysis |
| title | Mathematical Model of the Reliability Analysis of a Heterogeneous Duplicate Data Transmission System |
| title_full | Mathematical Model of the Reliability Analysis of a Heterogeneous Duplicate Data Transmission System |
| title_fullStr | Mathematical Model of the Reliability Analysis of a Heterogeneous Duplicate Data Transmission System |
| title_full_unstemmed | Mathematical Model of the Reliability Analysis of a Heterogeneous Duplicate Data Transmission System |
| title_short | Mathematical Model of the Reliability Analysis of a Heterogeneous Duplicate Data Transmission System |
| title_sort | mathematical model of the reliability analysis of a heterogeneous duplicate data transmission system |
| topic | reliability of redundant systems steady-state probabilities stochastic modeling sensitivity asymptotic analysis |
| url | http://sitito.cs.msu.ru/index.php/SITITO/article/view/644 |
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