Reliability Model of a Homogeneous Hot-Standby k-Out-of-n: G System

Hector G.K. Houankpo, Dmitry Kozyrev

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We consider the mathematical model of a closed homogenous redundant hot-standby system. This system consists of an arbitrary number of data links with an exponential distribution function (DF) of uptime and a general independent (GI) distribution function of the repair time of its elements with a single repair unit. We also consider the simulation model for the cases where it’s not always possible to carry out the mathematical model (to obtain explicit analytic expressions). The system with n components works until k components fail. With introduction of additional variable, explicit analytic expressions are obtained for the steady-state probabilities (SSP) of the system and the steady-state probability of failure-free system operation (PFFSO) using the constant variation method to solving the Kolmogorov differential equations systems. The SSP of the system are obtained with general independent distribution function of uptime using a simulation approach. We built dependence plots of the probability of system uptime against the fast relative speed of recovery; also plots of the reliability function relative to the reliability assessment. Five different distributions were selected for numerical and graphical analysis as Exponential (M), Weibull-Gnedenko (WG), Pareto (PAR), Gamma (G) and Lognormal (LN) distributions. The simulation algorithms were performed in the R programming language.

Original languageEnglish
Title of host publicationDistributed Computer and Communication Networks
Subtitle of host publicationControl, Computation, Communications - 24th International Conference, DCCN 2021, Revised Selected Papers
EditorsVladimir M. Vishnevskiy, Dmitry V. Kozyrev, Konstantin E. Samouylov, Dmitry V. Kozyrev
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages11
ISBN (Print)9783030925062
Publication statusPublished - 2021
Event24th International Conference on Distributed and Computer and Communication Networks, DCCN 2021 - Moscow, Russian Federation
Duration: 20 Sep 202124 Sep 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13144 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th International Conference on Distributed and Computer and Communication Networks, DCCN 2021
CountryRussian Federation


  • Hybrid data transmission systems
  • Mathematical model
  • Sensitivity
  • Simulation
  • Steady-state probabilities
  • System reliability

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