### Abstract

Dependability (reliability and availability) modeling of k-Ary n-cube architectures is addressed in this paper. The dependability model considered here is known as task-based dependability because the system working condition is specified by the task requirement. For the k-Ary n-cube, we therefore compute the probability of finding a working k-Ary m-cube. Due to the complexity of the problem, a structural decomposition technique is used to develop the analytical model. Two probability terms care required for computing either reliability or availability. The first term finds the probability that there are x working nodes in the system. Computation of this term for the availability analysis needs the solution of a simple Markov chain. The second term finds the probability that the x working nodes form the required subcube, called the task connection probability. A recursive expression, is developed for this. Analytical results are provided for various system configurations and task requirements. It is shown through simulation that the analytical model is quite accurate.

Original language | English (US) |
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Title of host publication | Architecture |

Editors | A. Reeves |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 9-16 |

Number of pages | 8 |

ISBN (Electronic) | 081867623X |

DOIs | |

State | Published - Jan 1 1996 |

Event | 25th International Conference on Parallel Processing, ICPP 1996 - Ithaca, United States Duration: Aug 12 1996 → Aug 16 1996 |

### Publication series

Name | Proceedings of the International Conference on Parallel Processing |
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Volume | 1 |

ISSN (Print) | 0190-3918 |

### Other

Other | 25th International Conference on Parallel Processing, ICPP 1996 |
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Country | United States |

City | Ithaca |

Period | 8/12/96 → 8/16/96 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)
- Hardware and Architecture

### Cite this

*Architecture*(pp. 9-16). [537137] (Proceedings of the International Conference on Parallel Processing; Vol. 1). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICPP.1996.537137

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*Architecture.*, 537137, Proceedings of the International Conference on Parallel Processing, vol. 1, Institute of Electrical and Electronics Engineers Inc., pp. 9-16, 25th International Conference on Parallel Processing, ICPP 1996, Ithaca, United States, 8/12/96. https://doi.org/10.1109/ICPP.1996.537137

**A task-based dependability model for k-Ary n-cubes.** / Vaidya, A. S.; Yoo, B. S.; Das, Chitaranjan; Kim, J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - A task-based dependability model for k-Ary n-cubes

AU - Vaidya, A. S.

AU - Yoo, B. S.

AU - Das, Chitaranjan

AU - Kim, J.

PY - 1996/1/1

Y1 - 1996/1/1

N2 - Dependability (reliability and availability) modeling of k-Ary n-cube architectures is addressed in this paper. The dependability model considered here is known as task-based dependability because the system working condition is specified by the task requirement. For the k-Ary n-cube, we therefore compute the probability of finding a working k-Ary m-cube. Due to the complexity of the problem, a structural decomposition technique is used to develop the analytical model. Two probability terms care required for computing either reliability or availability. The first term finds the probability that there are x working nodes in the system. Computation of this term for the availability analysis needs the solution of a simple Markov chain. The second term finds the probability that the x working nodes form the required subcube, called the task connection probability. A recursive expression, is developed for this. Analytical results are provided for various system configurations and task requirements. It is shown through simulation that the analytical model is quite accurate.

AB - Dependability (reliability and availability) modeling of k-Ary n-cube architectures is addressed in this paper. The dependability model considered here is known as task-based dependability because the system working condition is specified by the task requirement. For the k-Ary n-cube, we therefore compute the probability of finding a working k-Ary m-cube. Due to the complexity of the problem, a structural decomposition technique is used to develop the analytical model. Two probability terms care required for computing either reliability or availability. The first term finds the probability that there are x working nodes in the system. Computation of this term for the availability analysis needs the solution of a simple Markov chain. The second term finds the probability that the x working nodes form the required subcube, called the task connection probability. A recursive expression, is developed for this. Analytical results are provided for various system configurations and task requirements. It is shown through simulation that the analytical model is quite accurate.

UR - http://www.scopus.com/inward/record.url?scp=0002287992&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002287992&partnerID=8YFLogxK

U2 - 10.1109/ICPP.1996.537137

DO - 10.1109/ICPP.1996.537137

M3 - Conference contribution

AN - SCOPUS:0002287992

T3 - Proceedings of the International Conference on Parallel Processing

SP - 9

EP - 16

BT - Architecture

A2 - Reeves, A.

PB - Institute of Electrical and Electronics Engineers Inc.

ER -