### 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) |
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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) |
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ISSN (Print) | 0731-3071 |

### Other

Other | Nineteenth International Symposium on Fault-Tolerant Computing |
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City | Chicago, IL, USA |

Period | 6/21/89 → 6/23/89 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Hardware and Architecture

### Cite this

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

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*Digest of Papers - FTCS (Fault-Tolerant Computing Symposium).*Digest of Papers - FTCS (Fault-Tolerant Computing Symposium), Publ by IEEE, pp. 530-537, Nineteenth International Symposium on Fault-Tolerant Computing, Chicago, IL, USA, 6/21/89.

**Analytical model for computing hypercube availability.** / Das, Chita R.; Kim, Jong.

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

TY - GEN

T1 - Analytical model for computing hypercube availability

AU - Das, Chita R.

AU - Kim, Jong

PY - 1989/12/1

Y1 - 1989/12/1

N2 - 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 2n 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.

AB - 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 2n 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.

UR - http://www.scopus.com/inward/record.url?scp=0024873644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024873644&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0024873644

SN - 0818619597

T3 - Digest of Papers - FTCS (Fault-Tolerant Computing Symposium)

SP - 530

EP - 537

BT - Digest of Papers - FTCS (Fault-Tolerant Computing Symposium)

A2 - Anon, null

PB - Publ by IEEE

ER -