### Abstract

In this paper, we present an analytical model for computing the dependability of hypercube systems. The model, referred to as task-based dependability (TBD), is developed under the assumption that a task needs at least an m-cube (m < n) in an n-cube for its execution. Two probabilistic terms are required for computing this dependability. The first is the probability of any x nodes working out of 2
^{n}
nodes. The second term is a conditional probability that at least a connected m-cube exists among those x working nodes. This term is computed using a recursive expression. Two dependability measures, reliability and availability, are analyzed in this paper. A combinatorial enumeration is used in the reliability analysis, and a machine repairman model is used in the availability analysis to find the first probability. The machine repairman model is modified to capture imperfect coverage and imprecise repair. The TBD model is also extended to find multitask dependability. Numerical results are presented for n-cubes with different task requirements and are validated through extensive simulation. It is observed that an m-cube requirement is highly restrictive compared to the simple 2
^{m}
-connected node requirement.

Original language | English (US) |
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Title of host publication | Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991 |

Publisher | Association for Computing Machinery, Inc |

Pages | 111-119 |

Number of pages | 9 |

ISBN (Print) | 0897913922, 9780897913928 |

State | Published - Apr 2 1991 |

Event | 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991 - San Diego, United States Duration: May 21 1991 → May 24 1991 |

### Publication series

Name | Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991 |
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### Other

Other | 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991 |
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Country | United States |

City | San Diego |

Period | 5/21/91 → 5/24/91 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computational Theory and Mathematics
- Software

### Cite this

*Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991*(pp. 111-119). (Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991). Association for Computing Machinery, Inc.

}

*Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991.*Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991, Association for Computing Machinery, Inc, pp. 111-119, 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991, San Diego, United States, 5/21/91.

**On subcube dependability in a hypercube.** / Kim, Jong; Das, Chitaranjan.

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

TY - GEN

T1 - On subcube dependability in a hypercube

AU - Kim, Jong

AU - Das, Chitaranjan

PY - 1991/4/2

Y1 - 1991/4/2

N2 - In this paper, we present an analytical model for computing the dependability of hypercube systems. The model, referred to as task-based dependability (TBD), is developed under the assumption that a task needs at least an m-cube (m < n) in an n-cube for its execution. Two probabilistic terms are required for computing this dependability. The first is the probability of any x nodes working out of 2 n nodes. The second term is a conditional probability that at least a connected m-cube exists among those x working nodes. This term is computed using a recursive expression. Two dependability measures, reliability and availability, are analyzed in this paper. A combinatorial enumeration is used in the reliability analysis, and a machine repairman model is used in the availability analysis to find the first probability. The machine repairman model is modified to capture imperfect coverage and imprecise repair. The TBD model is also extended to find multitask dependability. Numerical results are presented for n-cubes with different task requirements and are validated through extensive simulation. It is observed that an m-cube requirement is highly restrictive compared to the simple 2 m -connected node requirement.

AB - In this paper, we present an analytical model for computing the dependability of hypercube systems. The model, referred to as task-based dependability (TBD), is developed under the assumption that a task needs at least an m-cube (m < n) in an n-cube for its execution. Two probabilistic terms are required for computing this dependability. The first is the probability of any x nodes working out of 2 n nodes. The second term is a conditional probability that at least a connected m-cube exists among those x working nodes. This term is computed using a recursive expression. Two dependability measures, reliability and availability, are analyzed in this paper. A combinatorial enumeration is used in the reliability analysis, and a machine repairman model is used in the availability analysis to find the first probability. The machine repairman model is modified to capture imperfect coverage and imprecise repair. The TBD model is also extended to find multitask dependability. Numerical results are presented for n-cubes with different task requirements and are validated through extensive simulation. It is observed that an m-cube requirement is highly restrictive compared to the simple 2 m -connected node requirement.

UR - http://www.scopus.com/inward/record.url?scp=84942840374&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84942840374&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0897913922

SN - 9780897913928

T3 - Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991

SP - 111

EP - 119

BT - Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991

PB - Association for Computing Machinery, Inc

ER -