### Abstract

An analytical model is presented for computing the availability of an n-dimensional hypercube. The model computes the probability of j connected working nodes in a hypercube by multiplying two probabilistic terms. The firsts term is the probability of x connected nodes (x ≥ j) working out of 2^{n} fully connected nodes. This is obtained from the numerical solution of the well-known machine repairman model, modified to capture imperfect coverage and imprecise repair. The second term, which is the probability of having j connected nodes in a hypercube, is computed from an approximate model of the hypercube. The approximate model, in turn, is based on a decomposition principle, where an n-cube connectivity is computed from a two-cube base model using a recursive equation. The availability model studied here is known as a task-based availability, where a system remains operational as long as a task can be executed on the system. Analytical results for n-dimensional cubes are given for various task requirements. The model is validated by comparing the analytical results with those from simulation.

Original language | English (US) |
---|---|

Title of host publication | Digest of Papers - FTCS (Fault-Tolerant Computing Symposium) |

Editors | Anon |

Publisher | Publ by IEEE |

Pages | 530-537 |

Number of pages | 8 |

ISBN (Print) | 0818619597 |

State | Published - Dec 1 1989 |

Event | Nineteenth International Symposium on Fault-Tolerant Computing - Chicago, IL, USA Duration: Jun 21 1989 → Jun 23 1989 |

### Publication series

Name | Digest of Papers - FTCS (Fault-Tolerant Computing Symposium) |
---|---|

ISSN (Print) | 0731-3071 |

### Other

Other | Nineteenth International Symposium on Fault-Tolerant Computing |
---|---|

City | Chicago, IL, USA |

Period | 6/21/89 → 6/23/89 |

### All Science Journal Classification (ASJC) codes

- Hardware and Architecture

## Fingerprint Dive into the research topics of 'Analytical model for computing hypercube availability'. Together they form a unique fingerprint.

## Cite this

*Digest of Papers - FTCS (Fault-Tolerant Computing Symposium)*(pp. 530-537). (Digest of Papers - FTCS (Fault-Tolerant Computing Symposium)). Publ by IEEE.