### Abstract

In this paper, numerical methods for the solution of a reliability modeling problem are presented by finding the steady state solution of a Markov chain. The reliability modeling problem analyzed is that of a large system made up of two smaller systems each with a varying number of subsystems. The focus of this study is on the optimal choice and formulation of algorithms for the steady-state solution of the generator matrix for the Markov chain associated with the given reliability modeling problem. In this context, iterative linear equation solution algorithms were compared. The Conjugate-Gradient method was determined to have the quickest convergence with the Gauss-Seidel method following close behind for the relevant model structures. Current work associated with this project analyzes the convergence of the Successive Over-Relaxation method. This work is part of a larger program for simulating, processing, and analyzing stochastic processes associated with simulation of naval systems.

Original language | English (US) |
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Pages (from-to) | 1-2 |

Number of pages | 2 |

Journal | Simulation Series |

Volume | 47 |

Issue number | 6 |

State | Published - Jan 1 2015 |

Event | Poster Session and Student Colloquium Symposium 2015, Part of the 2015 Spring Simulation Multi-Conference, SpringSim 2015 - Alexandria, United States Duration: Apr 12 2015 → Apr 15 2015 |

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### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications

### Cite this

*Simulation Series*,

*47*(6), 1-2.

}

*Simulation Series*, vol. 47, no. 6, pp. 1-2.

**Convergence of linear algebraic reliability simulation.** / Henry, Seth M.; Griffin, Christopher H.; Bruhn, Paul L.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Convergence of linear algebraic reliability simulation

AU - Henry, Seth M.

AU - Griffin, Christopher H.

AU - Bruhn, Paul L.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - In this paper, numerical methods for the solution of a reliability modeling problem are presented by finding the steady state solution of a Markov chain. The reliability modeling problem analyzed is that of a large system made up of two smaller systems each with a varying number of subsystems. The focus of this study is on the optimal choice and formulation of algorithms for the steady-state solution of the generator matrix for the Markov chain associated with the given reliability modeling problem. In this context, iterative linear equation solution algorithms were compared. The Conjugate-Gradient method was determined to have the quickest convergence with the Gauss-Seidel method following close behind for the relevant model structures. Current work associated with this project analyzes the convergence of the Successive Over-Relaxation method. This work is part of a larger program for simulating, processing, and analyzing stochastic processes associated with simulation of naval systems.

AB - In this paper, numerical methods for the solution of a reliability modeling problem are presented by finding the steady state solution of a Markov chain. The reliability modeling problem analyzed is that of a large system made up of two smaller systems each with a varying number of subsystems. The focus of this study is on the optimal choice and formulation of algorithms for the steady-state solution of the generator matrix for the Markov chain associated with the given reliability modeling problem. In this context, iterative linear equation solution algorithms were compared. The Conjugate-Gradient method was determined to have the quickest convergence with the Gauss-Seidel method following close behind for the relevant model structures. Current work associated with this project analyzes the convergence of the Successive Over-Relaxation method. This work is part of a larger program for simulating, processing, and analyzing stochastic processes associated with simulation of naval systems.

UR - http://www.scopus.com/inward/record.url?scp=84937793016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937793016&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84937793016

VL - 47

SP - 1

EP - 2

JO - Simulation Series

JF - Simulation Series

SN - 0735-9276

IS - 6

ER -